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CN1547806A - 使用结构化奇偶校验矩阵的低密度奇偶校验码的编码 - Google Patents

使用结构化奇偶校验矩阵的低密度奇偶校验码的编码 Download PDF

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CN1547806A
CN1547806A CNA038008491A CN03800849A CN1547806A CN 1547806 A CN1547806 A CN 1547806A CN A038008491 A CNA038008491 A CN A038008491A CN 03800849 A CN03800849 A CN 03800849A CN 1547806 A CN1547806 A CN 1547806A
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ldpc
code
parity check
bch
row
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CN100356697C (zh
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姆斯塔法·伊罗兹
孙丰文
李林楠
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Dtvg Licensing Co
DirecTV Group Inc
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Hughes Electronics Corp
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Abstract

为对结构化低密度奇偶校验(LDPC)码进行编码的方法提供了方案。在编码处理期间访问存储表示低密度奇偶校验(LDPC)码的结构化奇偶校验矩阵的信息的存储器(1605，1607)。信息被组织成表格形成，其中每个行表示数值1在奇偶校验矩阵的列组的第一列内的存在。各个行对应于奇偶校验矩阵的各个列组，其中根据预定操作导出每个分组内的后续列。根据所存储的表示奇偶校验矩阵的信息输出LDPC编码信号。

Description

使用结构化奇偶校验矩阵的低密度奇偶校验码的编码
相关专利申请
本专利申请与以下专利申请相关，并根据35 U.S.C.§119(e)要求其在先申请日的优先权：2002年7月3日提交(案号：PD-202095)的标题为″低密度奇偶校验码的编码设计和实现改进″的美国临时专利申请(序号60/393,457)，2002年7月26日提交(案号：PD-202101)的标题为″低密度奇偶校验码的编码设计和实现改进″的美国临时专利申请(序号60/398,760)，2002年8月15日提交(案号：PD-202105)的标题为″用于直接广播卫星与广播卫星通信的有效利用功率和带宽的调制和编码方案″的美国临时专利申请(序号60/403,812)，2002年10月25日提交(案号：PD-202101)的标题为″用于产生低密度奇偶校验码的方法和系统″的美国临时专利申请(序号60/421,505)，2002年10月29日提交(案号：PD-202105)的标题为″利用低密度奇偶校验码的卫星通信系统″的美国临时专利申请(序号60/421,999)，2002年11月4日提交(案号：PD-202101)的标题为″低密度奇偶校验码的编码设计和实现改进″的美国临时专利申请(序号60/423,710)，2003年1月15日提交(案号：PD-203009)的标题为″低密度奇偶校验码中路由问题的新颖解决方案″的美国临时专利申请(序号60/440,199)，2003年2月14日提交(案号：PD-203016)的标题为″低密度奇偶校验码编码器设计″的美国临时专利申请(序号60/447,641)，2003年3月20日提交(案号：PD-203021)的标题为″LDPC和BCH编码器说明″的美国临时专利申请(序号60/456,220)，2003年5月9日提交(案号：PD-203030)的标题为″LDPC和BCH编码器说明″的美国临时专利申请，2003年6月24日提交(案号：PD-203044)的标题为″LDPC和BCH编码器说明″的美国临时专利申请，和2003年6月24日提交(案号：PD-203059)的标题为″LDPC和BCH编码器说明″的美国临时专利申请；这里完整地参考引用了所述专利申请。
技术领域
本发明涉及通信系统，尤其涉及编码系统。
背景技术
通信系统使用编码来保证含噪声通信信道上的可靠通信。这些通信信道在一定的信噪比(SNR)条件下表现出可以表示为比特每符号的固定容量，该固定容量定义了理论上限(被称为香农极限)。结果，编码设计的目标是实现接近此香农极限的比率。一个这种类别的接近香农极限的编码是低密度奇偶校验(LDPC)码。
通常，由于存在若干缺点，LDPC码没有得到广泛采用。一个缺点是LDPC编码技术非常复杂。使用其生成矩阵对LDPC码进行编码，会需要存储非常大的非稀疏矩阵。另外，LDPC码只有在分组较大的情况下才能起作用；因此，即使LDPC码的奇偶校验矩阵是稀疏的，然而存储这些矩阵会有问题。
从实现的角度看，需要面临若干挑战。例如，存储便是一个导致LDPC码没有广泛地实际使用的重要原因。并且，LDPC码实现中的一个关键问题是如何在解码器的若干处理引擎(节点)之间实现连接网络。此外，解码处理，尤其是校验节点运算中的计算负载也会带来问题。
因此，需要一种使用简单的编码和解码处理的LDPC通信系统。还需要使用LDPC码高效地支持高数据速率，而无需引入更大的复杂度。还需要改进LDPC编码器和解码器的性能。还需要使实现LDPC编码的存储要求最小。还需要一种简化LDPC解码器的处理节点之间的通信的方案。
发明内容
本发明满足了这些和其它的需要，其中提供了用于对结构化低密度奇偶校验(LDPC)码进行编码的方案。通过将奇偶校验矩阵的部分限制为下三角，并且/或者满足其它要求以简化解码器的比特节点和校验节点之间的通信，提供LDPC码的结构。访问存储表示结构化奇偶校验矩阵的信息的存储器。信息被组织成表格形式，其中每个行表示数值1在奇偶校验矩阵的列组的第一列内的存在。各个行对应于奇偶校验矩阵的各个列组，其中根据预定操作(例如循环移位，相加等等)导出每个分组内的后续列。LDPC编码信号基于所存储的表示奇偶校验矩阵的信息。根据本发明的一个实施例，利用博斯-乔赫里-霍克文黑姆码(BCH)编码器，发送器使用BCH码对输入信号进行编码，其中对应于输入信号的输出LDPC编码信号表示具有外BCH码和内LDPC码的码。此外，提供循环冗余校验(CRC)编码器以便根据CRC码对输入信号进行编码。有利的是，此方案提供了方便的LDPC码的编码和解码。
根据本发明实施例的一个方面，公开了一种编码方法。此方法包含访问存储器，所述存储器存储有表示低密度奇偶校验(LDPC)码的结构化奇偶校验矩阵的信息。信息被组织成表格形式，其中每个行表示数值1在奇偶校验矩阵的列组的第一列内的存在。各个行对应于奇偶校验矩阵的各个列组，其中根据预定操作导出每个分组内的后续列。该方法还包含根据所存储的表示奇偶校验矩阵的信息输出LDPC编码信号。
根据本发明实施例的另一个方面，公开了一种用于产生低密度奇偶校验(LDPC)码的编码器。编码器包含存储器，所述存储器存储有表示LDPC码的结构化奇偶校验矩阵的信息。信息被组织成表格形式，其中每个行表示数值1在奇偶校验矩阵的列组的第一列内的存在。各个行对应于奇偶校验矩阵的各个列组，其中根据预定操作导出每个分组内的后续列。编码器还包含用于检索所存储的表示奇偶校验矩阵的信息，以输出LDPC编码信号的装置。
根据本发明实施例的另一个方面，公开了一种利用所公开的低密度奇偶校验(LDPC)编码的发送器。发送器包含存储器，所述存储器存储有表示LDPC码的结构化奇偶校验矩阵的信息，信息被组织成表格形式，其中每个行表示数值1在奇偶校验矩阵的列组的第一列内的存在。各个行对应于奇偶校验矩阵的各个列组，其中根据预定操作导出每个分组内的后续列。发送器还包含LDPC编码器，所述LDPC编码器被构造成访问存储器中存储的信息以输出LDPC编码信号。
单纯通过图解包含本发明的最优实施方式的若干具体实施例和实现，根据下面的详细描述可以容易地理解本发明的其它方面，特性和优点。本发明还能够具有其它和不同的实施例，并且在不偏离本发明的宗旨和范围的前提下，可以在各个明显的方面修改其若干细节。因此，附图和说明在性质上是示例性的，而不是限制性的。
附图说明
在附图中通过例子图解本发明，但这些例子不对本发明产生限制，图中用类似的附图标记表示类似的要件，其中：
图1的图例根据本发明的实施例示出了被构造成利用低密度奇偶校验(LDPC)码的通信系统；
图2A和2B是图1的发送器中采用的示例性LDPC编码器的图例；
图3是图1的系统中的示例性接收器的图例；
图4的图例根据本发明的实施例示出了稀疏奇偶校验矩阵的图例；
图5是图4中矩阵的LDPC码的双向图的图例；
图6的图例根据本发明的实施例示出了稀疏奇偶校验矩阵的子矩阵，其中子矩阵包含限制到下三角区的奇偶校验值；
图7的图表示出了利用非限制奇偶校验矩阵(H矩阵)的码和利用具有图6中子矩阵的限制H矩阵的码之间的性能对比；
图8A和8B的图例分别示出了均可以在图1的系统中使用的非Gray 8-PSK调制方案和Gray 8-PSK调制方案；
图9的图表示出了利用Gray标记和非Gray标记的码之间的性能对比；
图10的流程图根据本发明的实施例示出了使用非Gray映射的LDPC解码器的操作；
图11的流程图根据本发明的实施例示出了图3的使用Gray映射的LDPC解码器的操作；
图12A-12C的图例根据本发明的实施例示出了解码处理中校验节点和比特节点之间的交互；
图13A和13B的流程图根据本发明的各个实施例示出了分别使用正反向方案和并行方案计算校验节点和比特节点之间的传出消息的处理；
图14A-14C的图表示出了根据本发明的各个实施例产生的LDPC码的模拟结果；
图15A和15B的图例根据本发明的实施例分别示出了存储器的上边和下边，所述存储器被组织成支持结构化访问，以实现LDPC编码中的随机性；而
图16的图例根据本发明的实施例示出了可以执行LDPC码的编码和解码处理的计算机系统。
具体实施方式
现在描述用于对结构化低密度奇偶校验(LDPC)码进行高效解码的系统，方法和软件。在下面的说明中，出于说明的目的，提出许多特定的细节以便彻底地理解本发明。然而本领域技术人员明白，即使没有这些特定细节，或者通过等价的方案，仍然可以实施本发明。在其它实例中，以模块图形式示出了众所周知的结构和设备，以避免对本发明产生不必要的干扰。
图1的图例根据本发明的实施例示出了被构造成利用低密度奇偶校验(LDPC)码的通信系统。数字通信系统100包含发送器101，其在到达接收器105的通信信道103上产生信号波形。在这个离散通信系统100中，发送器101具有产生离散的可能信息集合的信息源；每个可能信息具有相应的信号波形。这些信号波形被通信信道103衰减或改变。为了对付有噪声的信道103，使用LDPC码。
发送器101产生的LDPC码允许得到高速实现，但不导致任何性能损失。这些从发送器101输出的结构化LDPC码避免为已经易受调制方案(例如8-PSK)所产生的信道差错的损害的比特节点分配少量校验节点。
这种LDPC码具有可并行解码算法(不同于turbo码)，其有利之处是涉及例如相加，比较和表查找的简单操作。此外，精心设计的LDPC码不会表现出差错平台的任何迹象。
根据本发明的一个实施例，发送器101使用相对简单的编码技术产生基于奇偶校验矩阵(利于在解码期间进行高效的存储器访问)的LDPC码，以便与接收器105通信。发送器101使用优于串联turbo+RS(里德-索罗蒙)码的LDPC码，假定分组长度足够地大。
图2A和2B是图1的发送器中采用的示例性LDPC编码器的图例。如图2A所示，发送器200配备有LDPC编码器203，LDPC编码器203接受来自信息源201的输入，并且输出具有更高冗余度、适于接收器105上的纠错处理的编码流。信息源201根据离散字符表X产生k个信号。
LDPC码被指定有奇偶校验矩阵。另一方面，对LDPC码进行编码通常需要指定生成矩阵。即使可以使用高斯消去法由奇偶校验矩阵获得生成矩阵，然而所得到的矩阵不再是稀疏的，并且存储较大的生成矩阵会更加复杂。
通过使奇偶校验矩阵结构化，编码器203使用仅利用奇偶校验矩阵的简单编码技术根据字符表Y产生提供给调制器205的信号。具体地，通过将某部分矩阵限制为三角矩阵，对奇偶校验矩阵产生限制。下面在图6中更加全面地描述这种奇偶校验矩阵的构造。这种限制导致微小的性能损失，因此构成有吸引力的折衷。
调制器205将来自编码器203的编码消息映射成发送给发送天线207的信号波形，发送天线207通过通信信道103发射这些波形。因此，编码消息被调制和发送到发送天线207。如下所述，从发送天线207发送的信号传播到接收器。
图2B根据本发明的一个实施例示出了用于博斯-乔赫里-霍克文黑姆码(BCH)编码器和循环冗余校验(CRC)编码器的LDPC编码器。在这种情况下，LDPC编码器203和CRC编码器209与BCH编码器211一起产生的代码具有串联的外BCH码和内低密度奇偶校验(LDPC)码。此外，使用循环冗余校验(CRC)码实现检错。在示例性实施例中，CRC编码器209使用具有生成多项式(x5+x4+x3+x2+1)(x2+x+1)(x+1)的8位CRC码进行编码。
LDPC编码器203系统地将具有长度kldpc的信息分组 i = ( i 0 , i 1 , . . . , i k ldpc - 1 ) 编码成具有长度nlpdc的码字 c = ( i 0 , i 1 , . . . , i k ldpc - 1 , p 0 , p 1 , . . . , p n ldpc - k ldpc - 1 ) . 码字的发送按照指定顺序从i0开始，并且以pnldpc-kldpc-1结束。
在下面的表1中提供了LDPC码参数(nldpc，kldpc)。
    LDPC码参数(nldpc，kldpc)
    编码率     LDPC未编码分组长度kldpc     LDPC编码分组长度nldpc
    1/2     32400     64800
    2/3     43200     64800
    3/4     48600     64800
    4/5     51840     64800
    5/6     54000     64800
    3/5     38880     64800
    8/9     57600     64800
    9/10     58320     64800
表1
LDPC编码器203的任务是确定具有kldpc个信息比特(i0，i1，...，ikldpc-1)的每个分组的nldpc-kldpc个奇偶校验比特(p0，p1，...，pnldpc-kldpc-1)。该过程如下所述。首先，初始化奇偶校验比特； p 0 = p 1 = p 2 = . . . = p n ldpc - k ldpc - 1 = 0 . 在表3至10的第一行中指定的奇偶校验比特地址上累加第一信息比特i0。例如，对于比率2/3(表3)，得到以下结果：
p0    ＝p0_i0
p10491＝p10491_i0
p16043＝p16043_i0
p506  ＝p506_i0
p12826＝p12826_i0
p8065 ＝p8065_i0
p8226 ＝p8226_i0
p2767 ＝p2767_i0
p240  ＝p240_i0
p18673＝p18673_i0
p9279 ＝p9279_i0
p10579＝p10579_i0
P20928＝p20928_i0
(所有相加均在GF(2)中)。
接着，对于下面的359个信息比特im，m＝1，2，...，359，在奇偶校验比特地址{x+m mod 360×q}mod(nldpc-kldpc)上累加这些比特，其中x表示对应于第一比特i0的奇偶校验比特累加器(parity bit accumulator)的地址，q是表2中指定的编码率相关常数。继续讨论此例子，对于比率2/3，q＝60。例如，对于信息比特i1，执行以下操作：
p60   ＝p60_i1
p10551＝p10551_i1
p16103＝p16103_i1
p566  ＝p566_i1
p12886＝p12886_i1
p8125 ＝p8125_i1
p8286 ＝p8286_i1
p2827 ＝p2827_i1
p300  ＝p300_i1
p18733＝p18733_i1
p9339 ＝p9339_i1
p10639＝p10639_i1
p20988＝p20988_i1
对于第361个信息比特i360，在表3至10的第二行中指定了奇偶校验比特累加器的地址。以类似的方式，使用公式{x+m mod360×q}mod(nldpc-kldpc)获得后面359个信息比特im，m＝361，362，...，719的奇偶校验比特累加器的地址，其中x表示对应于信息比特i360的奇偶校验比特累加器的地址，即表3-10中第二行的表项。以类似的方式，对于具有360个新信息比特的每个组，表3至10中的新行被用来寻找奇偶校验比特累加器的地址。
在处理完所有的信息比特之后，获得如下所示的最终奇偶校验比特。首先，从i＝1开始执行以下操作
pi＝pi_pi-1，i＝1，2，...，nldpc-kldpc-1。
pi，i＝0，1，...，nldpc-kldpc-1的最终内容等于奇偶校验比特pi。
    编码率     q
    2/3     60
    5/6     30
    1/2     90
    3/4     45
    4/5     36
    3/5     72
    8/9     20
    9/10     18
表2
                     奇偶校验比特累加器的地址(比率2/3)
 0 10491 16043 506 12826 8065 8226 2767 240 186 73 9279 10579 209281 17819 8313 6433 6224 5120 5824 12812 17187 9940 13447 13825 184832 17957 6024 8681 18628 12794 5915 14576 10970 12064 20437 4455 71513 19777 6183 9972 14536 8182 17749 11341 5556 4379 17434 15477 185324 4651 19689 1608 659 16707 14335 6143 3058 14618 17894 20684 53065 9778 2552 12096 12369 15198 16890 4851 3109 1700 18725 1997 158826 486 6111 13743 11537 5591 7433 15227 14145 1483 3887 17431 124307 20647 14311 11734 4180 8110 5525 12141 15761 18661 18441 10569 8192
 8 3791 14759 15264 19918 10132 9062 10010 12786 10675 9682 19246 54549 19525 9485 7777 19999 8378 9209 3163 20232 6690 16518 716 735310 4588 6709 20202 10905 915 4317 11073 13576 16433 368 3508 2117111 14072 4033 19959 12608 631 19494 14160 8249 10223 21504 12395 432 212 13800 1416113 2948 964714 14693 1602715 20506 1108216 1143 902017 13501 401418 1548 219019 12216 2155620 2095 1989721 4189 795822 15940 1004823 515 1261424 8501 845025 17595 1678426 5913 849527 16394 1042328 7409 698129 6678 1593930 20344 1298731 2510 1458832 17918 665533 6703 1945134 496 421735 7290 576636 10521 8925
 37 20379 1190538 4090 583839 19082 1704040 20233 1235241 19365 1954642 6249 1903043 11037 1919344 19760 1177245 19644 742846 16076 352147 11779 2106248 13062 968249 8934 521750 11087 331951 18892 435652 7894 389853 5963 436054 7346 1172655 5182 560956 2412 1729557 9845 2049458 6687 186459 20564 52160 18226 172071 9380 82662 7073 30653 18252 134374 9161 156425 10714 10153
 6 11585 90787 5359 94188 9024 95159 1206 1635410 14994 110211 9375 2079612 15964 602713 14789 645214 8002 1859115 14742 1408916 253 304517 1274 1928618 14777 204419 13920 990020 452 737421 18206 992122 6131 541423 10077 972624 12045 547925 4322 799026 15616 555027 15561 1066128 20718 738729 2518 1880430 8984 260031 6516 1790932 11148 9833 20559 370434 7510 1569
 35 16000 1169236 9147 1030337 16650 19138 15577 1868539 17167 2091740 4256 339141 20092 1721942 9218 505643 18429 847244 12093 2075345 16345 1274846 16023 1109547 5048 1759548 18995 481749 16483 353650 1439 1614851 3661 303952 19010 1812153 8968 1179354 13427 1800355 5303 308356 531 1666857 4771 672258 5695 796059 3589 14630
表3
    奇偶校验比特累加器的地址(比率5/6)
 0 4362 416 8909 4156 3216 3112 2560 2912 6405 8593 4969 67231 2479 1786 8978 30114339 9313 6397 2957 7288 5484 6031 102172 10175 9009 9889 3091 4985 7267 4092 8874 5671 2777 2189 87163 9052 4795 3924 3370 10058 1128 9996 10165 9360 4297 434 51384 2379 7834 4835 2327 9843 804 329 8353 7167 3070 1528 73115 3435 7871 348 3693 1876 6585 10340 7144 5870 2084 4052 27806 3917 3111 3476 1304 10331 5939 5199 1611 1991 699 8316 99607 6883 3237 1717 10752 7891 9764 4745 3888 10009 4176 4614 15678 10587 2195 1689 2968 5420 2580 2883 6496 111 6023 1024 44499 3786 8593 2074 3321 5057 1450 3840 5444 6572 3094 9892 151210 8548 1848 10372 4585 7313 6536 6379 1766 9462 2456 5606 997511 8204 10593 7935 3636 3882 394 5968 8561 2395 7289 9267 997812 7795 74 1633 9542 6867 7352 6417 7568 10623 725 2531 911513 7151 2482 4260 5003 10105 7419 9203 6691 8798 2092 8263 375514 3600 570 4527 200 9718 6771 1995 8902 5446 768 1103 652015 6304 762116 6498 920917 7293 678618 5950 170819 8521 179320 6174 785421 9773 119022 9517 1026823 2181 934924 1949 556025 1556 55526 8600 382727 5072 105728 7928 3542
 29 3226 37620 7045 24201 9645 26412 2774 24523 5331 20314 9400 75035 1850 23386 10456 97747 1692 92768 10037 40389 3964 33810 2640 508711 858 347312 5582 568313 9523 91614 4107 155915 4506 349116 8191 418217 10192 615718 5668 330519 3449 154020 4766 269721 4069 667522 1117 101623 5619 308524 8483 840025 8255 39426 6338 504227 6174 5119
 28 7203 198929 1781 51740 1464 35591 3376 42142 7238 673 10595 88314 1221 65135 5300 46526 1429 97497 7878 51318 4435 102849 6331 550710 6662 494111 9614 1023812 8400 802513 9156 563014 7067 887815 9027 341516 1690 386617 2854 846918 6206 63019 363 545320 4125 700821 1612 670222 9069 922623 5767 406024 3743 923725 7018 557226 8892 4536
 27 853 606428 8069 589329 2051 28850 10691 31531 3602 40552 328 17173 2219 92994 1939 78985 617 2066 8544 13747 10676 32408 6672 94899 3170 745710 7868 573111 6121 1073212 4843 913213 580 959114 6267 929015 3009 226816 195 241917 8016 155718 1516 919519 8062 906420 2095 896821 753 732622 6291 383323 2614 784424 2303 64625 2075 611
 26 4687 36227 8684 994028 4830 206529 7038 13630 1769 78371 3801 16892 10070 23593 3667 99184 1914 69205 4244 56696 10245 78217 7648 39448 3310 54889 6346 966610 7088 612211 1291 782712 10592 894513 3609 712014 9168 911215 6203 805216 3330 289517 4264 1056318 10556 649619 8807 764520 1999 453021 9202 681822 3403 173423 2106 902324 6881 3883
 25 3895 217126 4062 642427 3755 953628 4683 213129 7347 8027
表4
     奇偶校验比特累加器的地址(比率1/2)
 54 9318 14392 27561 26909 10219 2534 859755 7263 4635 2530 28130 3033 23830 365156 24731 23583 26036 17299 5750 792 916957 5811 26154 18653 11551 15447 13685 1626458 12610 11347 28768 2792 3174 29371 1299759 16789 16018 21449 6165 21202 15850 318660 31016 21449 17618 6213 12166 8334 1821261 22836 14213 11327 5896 718 11727 930862 2091 24941 29966 23634 9013 15587 544463 22207 3983 16904 28534 21415 27524 2591264 25687 450122193 14665 14798 16158 549165 4520 17094 23397 42 64 22370 16941 2152666 10490 6182 32370 9597 30841 25954 276267 22120 22865 29870 15147 13668 14955 1923568 6689 18408 18346 9918 25746 5443 2064569 29982 12529 13858 4746 30370 10023 2482870 1262 28032 29888 13063 24033 21951786371 6594 29642 31451 14831 9509 9335 3155272 1358 6454 16633 20354 24598 624 526573 19529 295 18011 3080 13364 8032 15323
 74 11981 1510 7960 21462 9129 11370 2574175 9276 29656 4543 30699 20646 21921 2805076 15975 25634 5520 31119 13715 21949 1960577 18688 4608 31755 30165 13103 10706 2922478 21514 23117 12245 26035 31656 25631 3069979 9674 24966 31285 29908 17042 24588 3185780 21856 27777 29919 27000 14897 11409 712281 29773 23310 263 4877 28622 20545 2209282 15605 5651 21864 3967 14419 22757 1589683 30145 1759 10139 29223 26086 10556 509884 18815 16575 2936 24457 26738 6030 50585 30326 22298 27562 2013126390 6247 2479186 928 29246 21246 12400 15311 32309 1860887 20314 6025 26689 16302 2296 3244 1961388 6237 11943 22851 15642 23857 15112 2094789 26403 25168 19038 18384 8882 12719 70930 14567 249651 3908 1002 10279 2403 24102 7644 12383 41735 13861 159186 21327 10467 5288 145798 28158 80699 16583 1109810 16681 2836311 13980 2472512 32169 17989
  13 10907 276714 21557 381815 26676 1242216 7676 875417 14905 2023218 15719 2464619 31942 858920 19978 2719721 27060 1507122 6071 2664923 10393 1117624 9597 1337025 7081 1767726 1433 1951327 26925 901428 19202 890029 18152 3064730 20803 173731 11804 2522132 31683 1778333 29694 934534 12280 2661135 6526 2612236 26165 1124137 7666 2696238 16290 848039 11774 1012040 30051 3042641 1335 15424
 42 6865 1774243 31779 1248944 32120 2100145 14508 699646 979 2502447 4554 2189648 7989 2177749 4972 2066150 6612 273051 12742 441852 29194 59553 19267 20113
表5
                奇偶校验比特累加器的地址(比率3/4)
 0 6385 7901 14611 13389 11200 3252 5243 2504 2722 821 73741 11359 2698 357 13824 12772 7244 6752 15310 852 2001 114172 7862 7977 6321 13612 12197 14449 15137 13860 1708 6399 134443 1560 11804 6975 13292 3646 3812 8772 7306 5795 14327 78664 7626 11407 14599 9689 1628 2113 10809 9283 1230 1524148705 1610 5699 15876 9446 12515 1400 6303 5411 14181 13925 73586 4059 8836 3405 7853 7992 15336 5970 10368 10278 9675 46517 4441 3963 9153 2109 12683 7459 12030 12221 629 15212 4068 6007 8411 5771 3497 543 14202 875 9186 6235 13908 35639 3232 6625 4795 546 9781 2071 7312 3399 7250 4932 1265210 8820 10088 11090 7069 6585 13134 10158 7183 488 7455 923811 1903 10818 119 215 7558 11046 10615 11545 14784 7961 15619
  12 3655 8736 4917 15874 5129 2134 15944 14768 7150 2692 146913 8316 3820 505 8923 6757 806 7957 4216 15589 13244 262214 14463 4852 15733 3041 11193 12860 13673 8152 6551 15108 875815 3149 1198116 13416 690617 13098 1335218 2009 1446019 7207 431420 3312 394521 4418 624822 2669 1397523 7571 902324 14172 296725 7271 713826 6135 1367027 7490 1455928 8657 246629 8599 1283430 3470 315231 13917 436532 6024 1373033 10973 1418234 2464 1316735 5281 1504936 1103 184937 2058 106938 9654 609539 14311 766740 15617 8146
 41 4588 1121842 13660 624343 8578 787444 1174126860 1022 12641 12604 99652 8217 27073 3156 117934 354 15145 6978 140586 7922 160797 15087 121388 5053 64709 12687 1493210 15458 176311 8121 172112 12431 54913 4129 709114 1426 841515 9783 760416 6295 1132917 1409 1206118 8065 908719 2918 843820 1293 1411521 3922 1385122 3851400023 5865 176824 2655 14957
 25 5565 633226 4303 1263127 11653 1223628 16025 763229 4655 1412830 9584 1312331 13987 959732 15409 1211033 8754 1549034 7416 1532535 2909 1554936 2995 825737 9406 479138 11111 485439 2812 852140 8476 1471741 7820 1536042 1179 793943 2357 867844 7703 62160 3477 70671 3931 138452 7675 128993 1754 81874 7785 14005 9213 58916 2494 77037 2576 79028 4821 15682
 9 10426 1193510 1810 90411 11332 926412 11312 357013 14916 265014 7679 784215 6089 1308416 3938 275117 8509 464818 12204 891719 5749 1244320 12613 443121 1344 401422 8488 1385023 1730 1489624 14942 712625 14983 886326 6578 856427 4947 39628 297 1280529 13878 669230 11857 1118631 14395 1149332 16145 1225133 13462 742834 14526 1311935 2535 1124336 6465 1269037 6872 9334
 38 15371 1402339 8101 1018740 11963 484841 15125 611942 8051 1446543 11139 516744 2883 14521
表6
            奇偶校验比特累加器的地址(比率4/5)
 0 149 11212 5575 6360 12559 8108 8505 408 10026 128281 5237 490 10677 4998 3869 3734 3092 3509 7703 103052 8742 5553 2820 7085 12116 10485 564 7795 2972 21573 2699 4304 8350 712 2841 3250 4731 10105 517 75164 12067 1351 11992 12191 11267 5161537 6166 4246 23635 6828 7107 2127 3724 5743 11040 10756 4073 1011 34226 11259 1216 9526 1466 10816 940 3744 2815 11506 115737 4549 11507 1118 1274 11751 5207 7854 12803 4047 64848 8430 4115 9440 413 4455 2262 7915 12402 8579 70529 3885 9126 5665 4505 2343 253 4707 3742 4166 155610 1704 8936 6775 8639 8179 7954 8234 7850 8883 871311 11716 4344 9087 11264 2274 8832 9147 11930 6054 545512 7323 3970 10329 2170 8262 3854 2087 12899 9497 1170013 4418 1467 2490 5841 817 11453 533 11217 11 962 525114 1541 4525 7976 3457 9536 7725 3788 2982 6307 599715 11484 2739 4023 12107 6516 551 2572 6628 8150 985216 6070 1761 4627 6534 7913 3730 11866 1813 12306 824917 12441 5489 8748 7837 7660 2102 11341 2936 6712 11977
  18 10155 421019 10101048320 8900 1025021 10243 1227822 7070 439723 12271 388724 11980 683625 9514 435626 7137 1028127 11881 252628 1969 1147729 3044 1092130 2236 872431 9104 634032 7342 858233 11675 1040534 6467 1277535 3186 121980 9621 114451 7486 56112 4319 48793 2196 3444 7527 66505 10693 24406 6755 27067 5144 59988 11043 80339 4846 443510 4157 9228
  11 12270 656212 11954 759213 7420 259214 8810 963615 689 543016 920 130417 1253 1193418 9559 601619 312 758920 4439 419721 4002 955522 12232 777923 1494 878224 10749 396925 4368 347926 6316 534227 2455 349328 12157 740529 6598 1149530 11805 445531 9625 209032 4731 232133 3578 260834 8504 184935 4027 11510 5647 49351 4219 18702 10968 80543 6970 5447
 4 3217 56385 8972 6696 5618 124727 1457 12808 8868 38839 8866 122410 8371 597211 266 440512 3706 324413 6039 584414 7200 328315 1502 1128216 12318 220217 4523 96518 9587 701119 2552 205120 12045 1030621 11070 510422 6627 690623 9889 212124 829 970125 2201 181926 6689 1292527 2139 875728 12004 594829 8704 319130 8171 1093331 6297 711632 616 7146
 33 5142 976134 10377 813835 7616 58110 7285 98631 7764 108672 12343 90193 4414 83314 3464 6425 6960 20396 786 30217 710 20868 7423 56019 8120 488510 12385 1199011 9739 1003412 424 1016213 1347 759714 1450 11215 7965 847816 8945 739717 6590 831618 6838 901119 6174 941020 255 11321 6197 583522 12902 384423 4377 350524 5478 867225 4453 2132
 26 9724 138027 12131 1152628 12323 951129 8231 175230 497 902231 9288 308032 2481751533 2696 26834 4023 1234135 7108 5553
表7
                      奇偶校验比特累加器的地址(比率3/5)
 22422 10282 11626 19997 11161 2922 3122 99 5625 17064 8270 17925087 16218 17015 828 20041 25656 4186 11629 22599 17305 22515 646311049 22853 25706 14388 5500 19245 8732 2177 13555 11346 17265 306916581 22225 12563 19717 23577 11555 25496 6853 25403 5218 15925 2176616529 14487 7643 10715 17442 11119 5679 14155 24213 21000 1116 156205340 8636 16693 1434 5635 6516 9482 20189 1066 15013 25361 1424318506 22236 20912 8952 5421 15691 6126 21595 500 6904 13059 68028433 4694 5524 14216 3685 19721 25420 9937 23813 9047 25651 1682621500 24814 6344 17382 7064 13929 4004 16552 12818 8720 5286 220622517 2429 19065 2921 21611 1873 7507 5661 23006 23128 20543 197771770 4636 20900 14931 9247 12340 11008 12966 4471 2731 16445 7916635 14556 18865 22421 22124 12697 9803 25485 7744 18254 11313 900419982 23963 18912 7206 12500 4382 20067 6177 21007 1195 23547 24837756 11158 14646 20534 3647 17728 11676 11843 12937 4402 8261 229449306 24009 10012 11081 3746 24325 8060 19826 842 8836 2898 5019
 7575 7455 25244 4736 14400 22981 5543 8006 24203 13053 1120 51283482 9270 13059 15825 7453 23747 3656 24585 16542 17507 22462 1467015627 15290 4198 22748 5842 13395 23918 16985 14929 3726 25350 2415724896 16365 16423 13461 16615 8107 24741 3604 25904 8 716 9604 203653729 17245 18448 9862 20831 25326 20517 24618 13282 5099 14183 880416455 17646 15376 18194 25528 1777 6066 21855 14372 12517 4488 174901400 8135 23375 20879 8476 4084 12936 25536 22309 16582 6402 2436025119 23586 128 4761 10443 22536 8607 9752 25446 15053 1856 4040377 21160 13474 5451 17170 5938 10256 11972 24210 17833 22047 1610813075 9648 24546 13150 23867 7309 19798 2988 16858 4825 23950 1512520526 3553 11525 23366 245217626 19265 20172 18060 24593 13255 155218839 21132 20119 15214 14705 7096 10174 5663 18651 19700 12524 140334127 2971 17499 16287 22368 21463 7943 18880 5567 8047 23363 679710651 24471 14325 4081 7258 4949 7044 1078 797 22910 20474 431821374 13231 22985 5056 3821 23718 14178 9978 19030 23594 8895 253586199 22056 7749 13310 3999 23697 16445 22636 5225 22437 24153 94427978 12177 2893 20778 3175 8645 11863 24623 10311 25767 17057 369120473 11294 9914 22815 2574 8439 3699 5431 24840 21908 16088 182448208 5755 19059 8541 24924 6454 11234 10492 16406 10831 11436 964916264 11275 24953 2347 12667 19190 7257 7174 24819 2938 2522 117493627 5969 13862 1538 23176 6353 2855 17720 2472 7428 573 150360 18539 186611 10502 30022 9368 107613 12299 78284 15048 133625 18444 246406 20775 191757 18970 10971
 8 5329 199829 11296 1865510 15046 2065911 7300 2214012 22029 1447713 11129 74214 13254 1381315 19234 1327316 6079 2112217 22782 582818 19775 424719 1660 1941320 4403 364921 13371 2585122 22770 2178423 10757 1413124 16071 2161725 6393 372526 597 1996827 5743 808428 6770 954829 4285 1754230 13568 2259931 1786 461732 23238 1164833 19627 203034 13601 1345835 13740 1732836 25012 13944
 37 22513 668738 4934 1258739 21197 513340 22705 693841 7534 2463342 24400 1279743 21911 2571244 12039 114045 24306 102146 14012 2074747 11265 1521948 4670 1553149 9417 1435950 2415 650451 24964 2469052 14443 881653 6926 129154 6209 2080655 13915 407956 24410 1319657 13505 611758 9869 822059 1570 604460 25780 1738761 20671 2491362 24558 2059163 12402 370264 8314 135765 20071 14616
 66 17014 368867 19837 94668 15195 1213669 7758 2280870 3564 292571 3434 7769
表8
    奇偶校验比特累加器的地址(比率8/9)
  0 6235 2848 32221 5800 3492 53482 2757 927 903 6961 4516 47394 1172 3237 62645 1927 2425 36836 3714 6309 24957 3070 6342 71548 2428 613 37619 2906 264 592710 1716 1950 427311 4613 6179 349112 4865 3286 600513 1343 5923 352914 4589 4035 213215 1579 3920 673716 1644 1191 599817 1482 2381 462018 6791 6014 6596
 19 2738 5918 37860 5156 61661 1504 43562 130 19043 6027 31874 6718 7595 6240 28706 2343 13117 1039 54658 6617 25139 1588 522210 6561 53511 4765 205412 5966 689213 1969 386914 3571 242015 4632 98116 3215 416317 973 311718 3802 619819 3794 39480 3196 61261 573 19092 850 40343 5622 16014 6005 5245 5251 57836 172 20327 1875 2475
 8 497 12919 2566 343010 1249 74011 2944 194812 6528 289913 2243 361614 867 373315 1374 470216 4698 228517 4760 391718 1859 405819 6141 35270 2148 50661 1306 1452 2319 8713 3463 10614 5554 66475 5837 3396 5821 49327 6356 47568 3930 4189 211 309410 1007 492811 3584 123512 6982 286913 1612 101314 953 496415 4555 441016 4925 4842
  17 5778 60018 6509 241719 1260 49030 3369 30311 3557 32242 3028 5833 3258 4404 6226 66555 4895 10946 1481 68477 4433 19328 2107 16499 2119 206510 4003 638811 6720 362212 3694 452113 1164 705014 1965 361315 4331 6616 2970 179617 4652 321818 1762 477719 5736 13990 970 25721 2062 65992 4597 48703 1228 69134 4159 10375 2916 2362
  6 395 12267 6911 45488 4618 22419 4120 428010 5825 47411 2154 555812 3793 547113 5707 159514 1403 32515 6601 518316 6369 456917 4846 89618 7092 618419 6764 71270 6358 19511 3117 69602 2710 70623 1133 36044 3694 6575 1355 1106 3329 67367 2505 34078 2462 48069 4216 21410 5348 561911 6627 624312 2644 507313 4212 508814 3463 3889
 15 5306 47816 4320 612117 3961 112518 5699 119519 6511 7920 3934 27781 3238 65872 1111 65963 1457 62264 1446 38855 3907 40436 6839 28737 1733 56158 5202 42699 3024 472210 5445 637211 370 182812 4695 160013 680 207414 1801 669015 2669 137716 2463 168117 5972 517118 5728 428419 1696 1459
表9
    奇偶校验比特累加器的地址(比率9/10)
 0 5611 2563 29001 5220 3143 48132 2481 834 813 6265 4064 42654 1055 2914 56385 1734 2182 33156 3342 5678 22467 2185 552 33858 2615 236 53349 1546 1755 384610 4154 5561 314211 4382 2957 540012 1209 5329 317913 1421 3528 606314 1480 1072 539815 3843 1777 436916 1334 2145 416317 2368 5055 2600 6118 54051 2994 43702 3405 16693 4640 55504 1354 39215 117 17136 5425 28667 6047 6838 5616 25829 2108 117910 933 4921
  11 5953 226112 1430 469913 5905 48014 4289 184615 5374 620816 1775 347617 3216 21780 4165 8841 2896 37442 874 28013 3423 55794 3404 35525 2876 55156 516 17197 765 36318 5059 14419 5629 59810 5405 47311 4724 521012 155 183213 1689 222914 449 116415 2308 308816 1122 66917 2268 57580 5878 26091 782 33592 1231 42313 4225 2052
 4 4286 35175 5531 31846 1935 45607 1174 1318 3115 9569 3129 108810 5238 444011 5722 428012 3540 37513 191 278214 906 443215 3225 111116 6296 258317 1457 9030 855 44751 4097 39702 4433 43613 5198 5414 1146 44265 3202 29026 2724 5257 1083 41248 2326 60039 5605 599010 4376 157911 4407 98412 1332 616313 5359 397514 1907 1854
 15 3601 574816 6056 326617 3322 40850 1768 32441 2149 1442 1589 42913 5154 12524 1855 59395 4820 27066 1475 33607 4266 6938 4156 20189 2103 75210 3710 385311 5123 93112 6146 332313 1939 500214 5140 143715 1263 29316 5949 466517 4548 63800 3171 46901 5204 21142 6384 55653 5722 17574 2805 62645 1202 26166 1018 32447 4018 5289
 8 2257 30679 2483 307310 1196 532911 649 391812 3791458113 5028 380314 3119 350615 4779 43116 3888 551017 4387 40840 5836 16921 5126 10782 5721 61653 3540 24994 2225 63485 1044 14846 6323 40427 1313 56038 1303 34969 3516 363910 5161229311 4682 384512 3045 64313 2818 261614 3267 64915 6236 59316 646 294817 4213 14420 5779 1596
  1 2403 12372 2217 15143 5609 7164 5155 38585 1517 13126 2554 31587 5280 26438 4990 13539 5648 117010 1152 436611 3561 536812 3581 141113 5647 466114 1542 540115 5078 268716 316 175517 3392 1991
表10
对于BCH编码器211，在表11中列举了BCH码参数。
  LDPC编码率   BCH未编码分组长度kbch   BCH编码分组长度nbch   BCH纠错(比特)
  1/2   32208   32400   12
  2/3   43040   43200   10
  3/4   48408   48600   12
  4/5   51648   51840   12
  5/6   53840   54000   10
  3/5   38688   38880   12
  8/9   57472   57600   8
  9/10   58192   58320   8
表11
应当注意，在前面的表格中，nbch＝kldpc。
通过相乘下面表12的列表中的第一t多项式，得到t纠错BCH编码器211的生成多项式：
    g1(x)   1+x2+x3+x5+x16
    g2(x)   1+x+x4+x5+x6+x8+x16
    g3(x)   1+x2+x3+x4+x5+x7+x8+x9+x10+x11+x16
    g4(x)   1+x2+x4+x6+x9+x11+x12+x14+x16
    g5(x)   1+x+x2+x3+x5+x8+x9+x10+x11+x12+x16
    g6(x)   1+x2+x4+x5+x7+x8+x9+x10+x12+x13+x14+x15+x16
    g7(x)   1+x2+x5+x6+x8+x9+x10+x11+x13+x15+x16
    g8(x)   1+x+x2+x5+x6+x8+x9+x12+x13+x14+x16
    g9(x)   1+x5+x7+x9+x10+x11+x16
    g10(x)   1+x+x2+x5+x7+x8+x10+x12+x13+x14+x16
    g11(x)   1+x2+x3+x5+x9+x11+x12+x13+x16
    g12(x)   1+x+x5+x6+x7+x9+x11+x12+x16
表12
按照以下方式将信息比特 m = ( m k bch - 1 , m k bch - 2 , . . . , m 1 , m 0 ) BCH编码成码字 c = ( m k bch - 1 , m k bch - 2 , . . . , m 1 , m 0 , d n bch - k bch - 1 , d n bch - k bch - 2 , . . . , d 1 , d 0 ) . 信息多项式 m ( x ) = m k bch - 1 x k bch - 1 + m k bch - 2 x k bch - 2 + . . . + m 1 x + m 0 乘以xnbch-kbch。接着，xnbch-kbchm(x)除以g(x)。以 d ( x ) = d n bch - k bch - 1 x n bch - k bch - 1 + . . . + d 1 x + d 0 为余数，码字多项式被设置如下： c ( x ) = x n bch - k bch m ( x ) + d ( x ) .
在示例性实施例中，以上LDPC码可以用于各种数字视频应用，例如MPEG(运动图象专家组)分组传输。
图3是图1的系统中的示例性接收器的图例。在接收端，接收器300包含解调器301，解调器301对从发送器200接收的信号执行解调。在接收天线303上接收这些信号以进行解调。在解调之后，接收信号被传送到解码器305，解码器305通过结合比特度量产生器307来产生信息X′，从而重构初始源信息。通过非Gray映射，比特度量产生器307在解码处理期间与解码器305来回(迭代)交换概率信息，如图10所示。可选地，如果使用Gray映射(根据本发明的一个实施例)，比特度量产生器执行一遍就足够了，其中每次LDPC解码器迭代之后进一步的比特度量产生的尝试可能产生有限的性能改进；这里参照图11更加全面地描述了这个方案。为理解本发明的优点，如图4所示，查看如何产生LDPC码是有用的。
[49]图4的图例根据本发明的实施例示出了稀疏奇偶校验矩阵的图例。LDPC码是具有稀疏奇偶校验矩阵H(n-k)xn的长线性分组码。通常，分组长度n的范围为数千到数万比特。例如，图4示出了具有长度n＝8和比率1/2的LDPC码的奇偶校验矩阵。图5的双向图可以等价表示相同的码。
图5是图4中矩阵的LDPC码的双向图的图例。奇偶校验公式意味着，对于每个校验节点，所有相邻比特节点的累加和(在GF(伽罗瓦域)(2)上)等于零。如附图所示，比特节点占据图表的左边，并且根据预定关系与一或多个校验节点相关。例如，对应于校验节点m1，相对于比特节点存在以下表达式n1+n4+n5+n8＝0。
回到接收器303，LDPC解码器305被认为是信息通过解码器，其中解码器305的目标是寻找比特节点的数值。为完成这个任务，比特节点和校验节点迭代地彼此通信。这个通信的性质如下所述。
从校验节点到比特节点，每个校验节点为一个相邻比特节点提供有关该比特节点的数值的估测(″评价″)，该估测基于来自其它相邻比特节点的信息。例如，在前面的例子中，如果n4，n5和n8的累加和对于m1而言″看上去象″0，则m1向n1指示：n1的数值相信为0(由于n1+n4+n5+n8＝0)；否则m1向n1指示：n1的数值相信为1。另外，对于软判决解码，增加可靠性测量。
从比特节点到校验节点，每个比特节点向相邻校验节点传递有关其自身数值的估测，该估测基于来自它的其它相邻校验节点的反馈。在前面的例子中，n1只具有两个相邻校验节点m1和m3。如果从m3向n1的反馈表明n1的数值可能为0，则n1会通知m1：n1自身数值的估测为0。对于比特节点具有超过两个的相邻校验节点的情况，比特节点在向与其通信的校验节点报告判决之前，对来自它的其它相邻校验节点的反馈执行多数表决(软判决)。以上处理被重复，直到所有比特节点被认为是正确的(即满足所有奇偶校验公式)，或者直到到达迭代的预定最大数量，从而声明解码失败。
图6的图例根据本发明的实施例示出了稀疏奇偶校验矩阵的子矩阵，其中子矩阵包含限制到下三角区的奇偶校验值。如前所述的，通过限制奇偶校验矩阵的下三角区的数值，编码器203(图2A和2B)可以使用简单编码技术。根据本发明的实施例，施加于奇偶校验矩阵的限制具有以下形式：
H(n-k)xn＝[A(n-k)xkB(n-k)x(n-k)]，其中B是下三角。
使用Hc T＝0将任何信息分组i＝(i0，i1...，ik-1)编码成码字c＝(i0，i1，...，ik-1，p0，p1，...，pn-k-1)，并且递归地对奇偶校验比特求解；例如，
a00i0+a01i1+...+a0，k-1ik-1+p0＝0＝＞  求解p0，
a10i0+a11i1+...+a1，k-1ik-1+b10p0+p1＝0＝＞  求解p1
并且类似地对p2，p3，...，pn-k-1求解。
图7的图表示出了利用非限制奇偶校验矩阵(H矩阵)的码和利用具有图6的限制H矩阵的码之间的性能对比。该图表示出了两种LDPC码之间的性能比较：具有通用奇偶校验矩阵的LDPC码，和奇偶校验矩阵被限制为下三角以简化编码的LDPC码。对于这个模拟，调制方案为8-PSK。性能损失在0.1dB以内。因此，由于下三角H矩阵的限制，性能损失是微小的，而在编码技术的简化方面的效果是显著的。因此，等价于下三角或行和/或列置换后的上三角的任何奇偶校验矩阵，可以用于相同的目的。
图8A和8B的图例分别示出了均可以在图1的系统中使用的非Gray 8-PSK调制方案和Gray 8-PSK调制方案。可以在图3的接收器中使用图8A的非Gray 8-PSK方案，以提供需要极低帧消除率(FER)的系统。通过结合例如博斯-乔赫里-霍克文黑姆码(BCH)，汉明码或里德-索罗蒙(RS)码的外码而使用图8B所示的Gray 8-PSK方案，也可以满足这个要求。
在这个可以使用8-PSK调制的方案下，不必在LDPC解码器305(图3)和比特度量产生器307之间进行迭代。在没有外码的情况下，如下面图9所示，使用Gray标记的LDPC解码器305表现出较早的差错平台(error floor)。
图9的图表示出了利用图8A和8B的Gray标记和非Gray标记的码之间的性能对比。差错平台源于这样的事实：假定来自LDPC解码器305的反馈正确，则对于非Gray标记而言，8-PSK比特度量的再生更加精确，因为具有已知2比特的两个8-PSK符号与非Gray标记进一步分离。这可以等价地视为以更高的信噪比(SNR)工作。因此，即使使用Gray或非Gray标记的相同LDPC码的差错渐近线具有相同的斜率(即彼此平行)，具有非Gray标记的LDPC码的差错渐近线会在任何SNR上穿过较低的FER。
另一方面，对于不需要极低FER的系统，在LDPC解码器305和8-PSK比特度量产生器307之间没有任何迭代的Gray标记可能更加适用，由于在每次LDPC解码器迭代之前再生8-PSK比特度量会导致额外的复杂度。此外，当使用Gray标记时，在每次LDPC解码器迭代之前再生8-PSK比特度量只产生非常轻微的性能改进。如上所述，没有迭代的Gray标记可以被用于需要极低FER的系统，假定实现外码。
Gray标记和非Gray标记之间的选择还取决于LDPC码的特征。通常，比特或校验节点度数(degree)越高，则越适用于Gray标记，由于对于更高的节点度数，就非Gray标记而言，从LDPC解码器305到8-PSK(或类似的更高阶调制)比特度量产生器307的初始反馈退化得更加厉害。
当8-PSK(或类似的更高阶)调制被用于二进制解码器时，发现没有″等噪声″地接收符号的3个(或更多)比特。例如，对于Gray 8-PSK标记，认为符号的第3个比特给解码器带来的噪声多于其它2比特。因此，LDPC码设计没有为8-PSK符号的″含更多噪声″的第3比特所表示的那些比特节点分配少量的边(edge)，使得那些比特没有被双倍惩罚。
图10的流程图根据本发明的实施例示出了使用非Gray映射的LDPC解码器的操作。在这个方案中，LDPC解码器和比特度量产生器逐个进行迭代。在这个例子中，使用8-PSK调制；然而相同原理也适用于其它更高级的调制方案。在这种情况下，假定解调器301输出距离向量d，向比特度量产生器307指示接收的有噪声符号点和8-PSK符号点之间的距离，因而向量分量如下所示：
d i = - E s N o { ( r x - s i , x ) 2 + ( r y - s i , y ) 2 } - - - i = 0,1 , . . . , 7 .
8-PSK比特度量产生器307与LDPC解码器305通信以交换先验概率信息和后验概率信息，其中先验概率信息和后验概率信息分别被表示成u和a。也就是说，向量u和a分别表示编码比特的对数似然比的先验和后验概率。
8-PSK比特度量产生器307按如下方式产生每组3个比特的先验似然比。首先，获得有关编码比特的非本征信息：
ej＝aj-uj          j＝0，1，2。
接着确定8-PSK符号概率pi，i＝0，1，...，7。
*yj＝-f(0，ej)     j＝0，1，2其中f(a，b)＝max(a，b)+LUTf(a，b)，LUTf(a，b)＝ln(1+e-|a-b|)
*xj＝yj+ej        j＝0，1，2
*p0＝x0+x1+x2     p4＝y0+x1+x2
p1＝x0+x1+y2      p5＝y0+x1+y2
p2＝x0+y1+x2      p6＝y0+y1+x2
p3＝x0+y1+y2      p7＝y0+y1+y2
接着，比特度量产生器307按照如下方式确定编码比特的先验对数似然比以作为LDPC解码器305的输入：
u0＝f(d0+p0，d1+p1，d2+p2，d3+p3)-f(d4+p4，d5+p5，d6+p6，d7+p7)-e0
u1＝f(d0+p0，d1+p1，d4+p4，d5+p5)-f(d2+p2，d3+p3，d6+p6，d7+p7)-e1
u2＝f(d0+p0，d2+p2，d4+p4，d6+p6)-f(d1+p1，d3+p3，d5+p5，d7+p7)-e2
应当注意，具有超过两个的变量的函数j(.)可以被递归评估；例如f(a，b，c)＝f(f(a，b)，c)。
现在描述使用非Gray映射的LDPC解码器305的操作。在步骤1001，LDPC解码器305根据以下公式(和图12A所示的)在第一次迭代之前初始化编码比特的对数似然比v：
v n → k i = u n , n＝0，1，...，N-1，i＝1，2，...，deg(比特节点n)
这里，vn→ki表示从比特节点n到其相邻校验节点ki的信息，un表示比特n的解调器输出，N是码字长度。
在步骤1003，更新校验节点k，其中输入v产生输出w。如图12B所示，从其dc个相邻比特节点到校验节点k的传入信息被表示成vn1→k，vn2→k，...，vndc→k。目标是计算从校验节点k回到dc个相邻比特节点的传出信息。这些信息被表示成wk→n1，wk→n2，...，wk→ndc，其中
w k → n i = g ( v n 1 → k , v n 2 → k , . . . , v n i - 1 → k , v n i + 1 → k , . . . , v n dc → k )
函数g()被定义如下：
g(a，b)＝sign(a)×sign(b)×{min(|a|，|b|)}+LUTg(a，b)，
其中LUTg(a，b)＝ln(1+e-|a+b|)-ln(1+e-|a-b|)。类似于函数f，具有超过两个的变量的函数g可以递归评估。
接着，解码器305在步骤1205输出后验概率信息(图12C)，使得：
a n = u n + Σ j w k j → n .
在步骤1007，确定是否满足所有的奇偶校验公式。如果不满足这些奇偶校验公式，则象在步骤1009中那样，解码器305重新导出8-PSK比特度量和信道输入un。接着象在步骤1011中那样，更新比特节点。
如图14C所示，从其dv个相邻校验节点到比特节点n的传入信息被表示成wk1→n，wk2→n，...，wkdv→n。计算从比特节点n回到dv个相邻校验节点的传出信息；这种信息被表示成vn→k1，vn→k2，...，vn→kdv，并且计算如下：
v n → k i = u n + Σ j ≠ i w k j → n
在步骤1013，解码器305输出硬判决(在满足所有奇偶校验公式的情况下)：
如果 H c ^ T = 0 , 则停止
当使用非Gray标记时，以上方案是合适的。然而当实现Gray标记时，执行图11的处理。
图11的流程图根据本发明的实施例示出了图3的使用Gray映射的LDPC解码器的操作。当使用Gray标记时，只在LDPC解码器之前一次性产生比特度量会更加有利，因为在每次LDPC解码器迭代之后再生比特度量只产生微小的性能改进。象图10的步骤1001和1003那样，执行编码比特v的对数似然比的初始化，并且在步骤1101和1103更新校验节点。接着象在步骤1105中那样，更新比特节点n。此后，解码器输出后验概率信息(步骤1107)。在步骤1109，确定是否满足所有的奇偶校验公式；如果全部满足，解码器输出硬判决(步骤1111)。否则重复步骤1103-1107。
图13A的流程图根据本发明的各个实施例示出了使用正反向方案计算校验节点和比特节点之间的传出消息的处理。对于具有dc个相邻边的校验节点，执行dc(dc-1)和许多g(.，.)函数的计算。然而，正反向方案将计算复杂度缩减到3(dc-2)，其中存储dc-1个变量。
参照图12B，从dc个相邻比特节点到校验节点k的传入信息被表示成vn1→k，vn2→k，...，vndc→k。期望计算从校验节点k回到dc个相邻比特节点的传出信息；这些传出信息被表示成wk→n1，wk→n2，...，wk→ndc。
在计算这些传出信息的正反向方案中，正向变量f1，f2，...，fdc被定义如下：
f1＝v1→k
f2＝g(f1，v2→k)
f3＝g(f2，v3→k)
.  .  .
.  .  .
fdc＝g(fdc-1，vdc→k)
在步骤1301，计算这些正向变量，并且在步骤1303存储这些正向变量。
类似地，反向变量b1，b2，...，bdc被定义如下：
bdc＝vdc→k
bdc-1＝g(bdc，vdc-1→k)
b1＝g(b2，v1→k)
在步骤1305，计算这些反向变量。此后象在步骤1307中那样，根据存储的正向变量和计算的反向变量计算传出信息。传出信息被计算如下：
wk→1＝b2
wk→i＝g(fi-1，bi+1)    i＝2，3，...，dc-1
wk→dc＝fdc-1
在这个方案中，只需要存储正向变量f2，f3，...，fdc。当计算反向变量bi时，同时计算传出信息wk→i，从而不必存储反向变量。
如下面讨论的，通过并行方案可以进一步增强计算负载。
图13B的流程图根据本发明的各个实施例示出了使用并行方案计算校验节点和比特节点之间的传出消息的处理。对于具有来自dc个相邻比特节点的输入vn1→k，vn2→k，...，vndc→k的校验节点k，象在步骤1311中那样计算以下参数：
γ k = g ( v n 1 → k , v n 2 → k , . . . , v n dc → k )
应当注意，g(.，.)函数也可以被表示成以下形式：
g ( a , b ) = ln 1 + e a + b e a + e b
[821通过使用g(.，.)函数的回归性质，得到以下表达式：
γ k = ln 1 + e g ( v n 1 → k , . . . , v n i - 1 → k , v n i + 1 → k , . . . , v n dc → k ) + v n i → k e g ( v n 1 → k , . . . , v n i - 1 → k , v n i + 1 → k , . . . , v n dc → k ) + e v n i → k = ln 1 + e w k → n i + v n i → k e w k → n i + e v n i → k
因此，可以按照下面的方式对wk→ni求解：
w k → n i = ln e v n i → k + γ k - 1 e v n i → k - γ k - 1 - γ k
使用表示函数ln|ex-1|的查找表LUTx可以获得以上公式的ln(.)项(步骤1313)。不同于其它查找表LUTf或LUTg，表LUTx需要的表项的数量最好与量化等级的数量一样多。一旦获得γk，可以在步骤1315使用以上公式并行地针对所有ni计算wk→ni。
γk的计算延迟为log2(dc)会更加有利。
图14A-14C的图表示出了根据本发明的各个实施例产生的LDPC码的模拟结果。尤其是，图14A-14C示出了具有更高阶调制和编码率3/4(QPSK，1.485比特/符号)，2/3(8-PSK，1.980比特/符号)和5/6(8-PSK，2.474比特/符号)的LDPC码的性能。
存在两个通用方案以实现校验节点和比特节点之间的互连：(1)完全并行方案和(2)部分并行方案。在完全并行体系结构中，物理实现所有节点及其互连。这个体系结构的优点是速度。
然而在实现所有节点及其连接时，完全并行体系结构会导致更大的复杂度。因此，对于完全并行体系结构，需要使用更小的分组长度以降低复杂度。在这种情况下，对于相同的时钟频率，会导致成比例的吞吐率降低，和FER-Es/No性能的某种退化。
实现LDPC码的第二个方案是只物理实现全部节点的一个子集，并且只使用这些有限数量的″物理″节点来处理码的所有″功能″节点。尽管可以使LDPC解码器的操作非常简单，并且能够并行执行，然而进一步的设计问题是如何在″随机″分布的比特节点和校验节点之间建立通信。根据本发明的一个实施例，解码器305(图3)通过以结构化方式访问存储器来解决这个问题，从而实现表面上随机的码。参照图15A和15B说明这个方案。
图15A和15B的图例根据本发明的实施例分别示出了存储器的上边和下边，所述存储器被组织成支持结构化访问，以实现LDPC编码中的随机性。通过聚焦于奇偶校验矩阵的生成，可以实现结构化访问而无需破坏真正随机码的性能。通常，可以通过校验节点与比特节点的连接规定奇偶校验矩阵。例如，比特节点可以被分成具有固定尺寸的组，出于图解的目的，该尺寸为392。另外，假定连接到度数3的第一比特节点的校验节点被编号为例如a，b和c，则连接到第二比特节点的校验节点被编号为a+p，b+p和c+p，连接到第三比特节点的校验节点被编号为a+2p，b+2p和c+2p等等；其中p＝(校验节点的编号)/392。对于具有392个比特节点的下一个组，连接到第一比特节点的校验节点不同于a，b，c，使得通过适用选择p，所有校验节点具有相同的度数。在自由常数(free constants)上执行随机搜索，使得所得到的LDPC码没有cycle-4和cycle-6。由于本发明的奇偶校验矩阵的结构特征，可以存储边信息，以允许在解码期间并行访问一组相关边值。
换言之，本发明的方案利于在校验节点和比特节点处理期间进行存储器访问。双向图中边的数值可以被存储在例如随机访问存储器(RAM)的存储介质中。应当注意，对于校验节点和比特节点处理期间的真正随机LDPC码，需要以随机方式逐个访问边的数值。然而这种常规访问方案对于高数据速率应用而言速度过慢。以这样的方式组织图15A和15B的RAM，其中可以在一个时钟周期内获取较大的相关边的组；因此，根据预定方案或结构，这些数值在存储器中被放置在″一起″。可以发现，实际上，即使具有真正随机码，对于一组校验节点(和分别地，比特节点)而言，相关边可以在RAM中放置在彼此之后，但是与一组比特节点(分别地，校验节点)相邻的相关边会随机散布在RAM中。因此，本发明所说的″一起″源于奇偶校验矩阵本身的设计。也就是说，校验矩阵设计保证一组比特节点和校验节点的相关边在RAM中同时放置在一起。
如图15A和15B所示，每个框包含边的数值，为多个比特(例如6个)。根据本发明的一个实施例，边RAM被分成两个部分：上边RAM1501(图15A)和下边RAM 1503(图15B)。下边RAM 1503包含例如度数2的比特节点和校验节点之间的边。上边RAM 1503包含例如度数大于2的比特节点和校验节点之间的边。因此，对于每个校验节点，2个相邻边被存储在下边RAM 1503中，其余边被存储在上边RAM 1501中。例如，表14指定了各个编码率下上边RAM 1501和下边RAM 1503的尺寸：
  1/2   2/3   3/4   5/6
 上边RAM   400×392   440×392   504×392   520×392
  下边RAM   160×392   110×392   72×392   52×392
表14
根据表14，具有尺寸576×392的边RAM足以存储所有编码率1/2，2/3，3/4和5/6的边度量。
如上所述，在这个示例性情况下，一次选择一组392个比特节点和392个校验节点进行处理。对于392个校验节点的处理，从上边RAM1501访问q＝dc-2个连续行，并且从下边RAM 1503访问2个连续行。dc的数值取决于具体的码，例如针对上述的码，对于比率1/2，dc＝7；对于比率2/3，dc＝10；对于比率3/4，dc＝16；对于比率5/6，dc＝22。当然，可以针对其它的码采用其它的dc数值。在这种情况下，q+2为每个校验节点的度数。
对于比特节点处理，如果392个比特节点的组具有度数2，其边位于下边RAM 1503的2个连续行中。如果比特节点具有度数d＞2，其边位于上边RAM 1501的d个行中。这d个行的地址可以被存储在例如只读存储器(ROM)的非易失存储器中。这些行中的一个内的边对应于392个比特节点的第一边，另一个行内的边对应于392个比特节点的第二边，等等。此外，对于每个行，属于392个节点的组中的第一比特节点的边的列索引也可以被存储在ROM中。对应于第二，第三比特节点等等的边以″回绕″方式跟随在开始列索引之后。例如，如果行中第j个边属于第一比特节点，则第(j+1)个边属于第二比特节点，第(j+2)个边属于第三比特节点，...，而第(j-1)个边属于第392个比特节点。
通过图15A和15B示出的组织，在LDPC编码期间大大增强了存储器访问的速度。
图16图解了一种计算机系统，通过该计算机系统可以实现基于本发明的实施例。计算机系统1600包含总线1601或用于传送信息的其它通信机构，和连接到总线1601以处理信息的处理器1603。计算机系统1600也包含例如随机访问存储器(RAM)的主存储器1605或其它动态存储设备，其连接到总线1601以存储信息和将由处理器1603执行指令。主存储器1605也可以被用来在处理器1603执行的指令的执行期间存储临时变量或其它中间信息。计算机系统1600还包含只读存储器(ROM)1607或其它静态存储设备，其连接到总线1601以存储处理器1603的静态信息和指令。例如磁盘或光盘的存储设备1609还被连接到总线1601以存储信息和指令。
计算机系统1600可以通过总线1601连接到显示器1611，例如阴极射线管(CRT)，液晶显示器，有效矩阵显示器或等离子体显示器以向计算机用户显示信息。输入设备1613，例如包含字符和其它按键的键盘被连接到总线1601，以向处理器1603传送信息和命令选择。另一种用户输入设备是光标控制器1615，例如鼠标，轨迹球或光标方向键，用于向处理器1603传送方向信息和命令选择，并且用于控制光标在显示器1611上的移动。
根据本发明的一个实施例，计算机系统1600响应处理器1603执行主存储器1605中包含的指令序列而提供LDPC码的生成。可以从例如存储设备1609的另一个计算机可读介质将这种指令读取到主存储器1605中。主存储器1605中包含的指令序列的执行导致处理器1603执行这里描述的处理步骤。多处理结构中的一或多个处理器也可以被用来执行主存储器1605中包含的指令。在可选实施例中，可以使用硬连线电路取代软件指令或与之结合，以实现本发明的实施例。于是，本发明的实施例不局限于硬件电路和软件的任何特定组合。
计算机系统1600还包含连接到总线1601的通信接口1617。通信接口1617提供连接到网络链路1619的双向数据通信，所述网络链路1619连接到局域网1621。例如，通信接口1617可以是数字用户线路(DSL)卡或调制解调器，综合业务数字网络(ISDN)卡，电缆调制解调器或电话调制解调器，用于提供针对相应类型的电话线的数据通信连接。作为另一个例子，通信接口1617可以是局域网(LAN)卡(例如EthemetTM或异步传送模式(ATM)网络的局域网(LAN)卡)，用于提供针对兼容LAN的数据通信连接。也可以实现无线链路。在任何这种实现中，通信接口1617发送和接收电气，电磁或光学信号，这些信号传递表示各种信息的数字数据流。此外，通信接口1617可以包含外设接口设备，例如通用串行总线(USB)接口，PCMCIA(个人计算机存储器卡国际协会)接口等等。
网络链路1619通常通过一或多个网络提供到其它数据设备的数据通信。例如，网络链路1619可以提供通过局域网1621到主计算机1623的连接，主计算机1623具有到网络1625(例如广域网(WAN)或全球分组数据通信网络，现在通常被称作″因特网″)或到服务提供商操作的数据设备的连接。局域网1621和网络1625使用电气，电磁或光学信号传送信息和指令。通过各个网络传送的信号，和通过通信接口1617在网络链路1619上传送的信号是传递信息和指令的载波的示例性形式，其中通信接口1617与计算机系统1600之间传送数字数据。
计算机系统1600可以通过网络，网络链路1619和通信接口1617发送信息和接收包含程序代码的数据。在因特网例子中，服务器(未示出)可以通过网络1625，局域网1621和通信接口1617发送所请求的代码，所述的代码属于用来实现本发明的实施例的应用程序。处理器1603可以执行发送的代码(同时被接收)，并且/或者在存储设备169或其它非易失存储器中存储此代码，以便以后执行。通过这种方式，计算机系统1600可以获得载波形式的应用代码。
这里使用的术语″计算机可读介质″是指参与向处理器1603提供指令以便执行的任何介质。这种介质可以采用许多形式，包含但不局限于非易失介质，易失介质和传输介质。非易失介质包含例如光盘或磁盘，例如存储设备1609。易失介质包含动态存储器，例如主存储器1605。传输介质包含同轴电缆，铜线和光纤，包含有包括总线1601的导线。传输介质也可以具有声波，光波或电磁波，例如在射频(RF)和红外(IR)数据通信期间产生的波的形式。计算机可读介质的常见形式包含例如软盘，柔性盘(flexible disk)，硬盘，磁带，任何其他磁介质，CD-ROM，CDRW，DVD，任何其他光学介质，打孔卡，纸带，光学标记卡片，任何其他具有孔图案或其它光学可识别标记的物理介质，RAM，PROM和EPROM，快擦写EPROM，任何其他存储器芯片或盒，载波，或任何其他计算机可以读取的介质。
各种形式的计算机可读介质可以用来向处理器提供指令以便执行。例如，最初可以在远程计算机的磁盘上携带用于执行至少部分本发明的指令。在这种情况下，远程计算机将指令加载到主存储器中，使用调制解调器并通过电话线发送指令。本地计算机系统的调制解调器接收电话线上的数据，使用红外发送器将数据转换成红外信号，并且将红外信号发送到便携计算设备，例如个人数字助理(PDA)和膝上型电脑。便携计算设备上的红外探测器接收红外信号传递的信息和指令，并且将数据放在总线上。总线将数据传送到主存储器，而处理器从主存储器检索和执行指令。可选地，在被处理器执行之前或之后，主存储器接收的指令可以被存储在存储设备上。
因此，本发明的各个实施例提供了用于对结构化低密度奇偶校验(LDPC)码进行编码的方案。通过将奇偶校验矩阵的部分限制为下三角，并且/或者满足其它要求以简化解码器的比特节点和校验节点之间的通信，提供LDPC码的结构。访问存储表示结构化奇偶校验矩阵的信息的存储器。信息被组织成表格形式，其中每个行表示数值1在奇偶校验矩阵的列组的第一列内的存在。各个行对应于奇偶校验矩阵的各个列组，其中根据预定操作(例如循环移位，相加等等)导出每个组内的后续列。LDPC编码信号基于所存储的表示奇偶校验矩阵的信息。根据本发明的一个实施例，利用博斯-乔赫里-霍克文黑姆码(BCH)编码器，发送器使用BCH码对输入信号进行编码，其中对应于输入信号的输出LDPC编码信号表示具有外BCH码和内LDPC码的码。此外，提供循环冗余校验(CRC)编码器以便根据CRC码对输入信号进行编码。以上方案有利的是，以上方案降低了复杂度，但没有牺牲性能。
虽然已经结合若干实施例和实现描述了本发明，然而本发明不限于，但是覆盖了在所附权利要求书的范围内的各种明显的修改和等价方案。

Claims (33)

1.一种编码方法，包括：
访问存储有表示低密度奇偶校验(LDPC)码的结构化奇偶校验矩阵的信息的存储器(1605，1607)，所述信息被组织成表格形式，其中每个行表示数值1在奇偶校验矩阵的列组的第一列中的存在，各个行对应于奇偶校验矩阵的各个列组，其中根据预定操作导出每个组内的后续列；和
根据所存储的表示奇偶校验矩阵的信息输出LDPC编码信号。
2.如权利要求1所述的方法，其中所述预定操作指定以下步骤中的一个：
在每个组的第一列上执行循环移位；和
将常数加到每个组的第一列上，所述常数取决于LDPC码的编码率。
3.如权利要求1所述的方法，其中顺序确定奇偶校验比特，所述方法还包括：
如果奇偶校验矩阵的第i个行中的第j个项为1，通过相加第(i-1)个奇偶校验比特和第j个信息比特，确定第i个奇偶校验比特。
4.如权利要求1所述的方法，还包括：
将奇偶校验比特累加器初始化为零；
如果奇偶校验矩阵的第(jM)个列中的第i个项为1，则在第i个奇偶校验比特累加器中累加具有M个信息比特的第j个组中的第一信息比特，其中j＝0，1，2，3，...，kldpc/M-1；
根据{x+m mod M×q}mod(nldpc-kldpc)在奇偶校验比特累加器中累加第j个组的其余(M-1)个信息比特m＝jM+1，jM+2，jM+3，...，(j+1)M-1，其中x表示对应于组中第一比特jM的奇偶校验比特累加器的地址，q是编码率相关常数；和
在处理完所有信息比特之后，根据pi＝pi_Pi-1，i＝1，2，...，nldpc-kldpc-1从i＝1开始执行操作，其中pi，i＝0，1，..，nldpc-kldpc-1的最终内容等于奇偶校验比特pi。
5.如权利要求4所述的方法，其中M＝360。
6.如权利要求4所述的方法，其中对于编码率2/3，5/6，1/2，3/4，4/5，3/5，8/9和9/10，码相关常数q是分别是60，30，90，45，36，72，20和18。
7.如权利要求1所述的方法，还包括：
根据信号群集调制LDPC编码信号，所述信号群集包含8-PSK(相移键控)，16-QAM(正交振幅调制)，QPSK(正交相移键控)，16-APSK(幅度相移键控)和32-APSK中的一个。
8.如权利要求1所述的方法，还包括：
根据博斯-乔赫里-霍克文黑姆(BCH)码对输入信号进行编码，其中对应于输入信号的输出LDPC编码信号表示具有外BCH码和内LDPC码的码。
9.如权利要求8所述的方法，其中冗余BCH比特的数量为nBCH-kBCH＝16*t，其中t表示BCH码的纠错能力。
10.如权利要求8所述的方法，其中当结合比率1/2，3/4，4/5和3/5的LDPC码使用时，BCH码的纠错能力为12比特，当结合比率2/3和5/6的LDPC码使用时，能力纠错为10比特，当结合比率8/9和9/10的LDPC码使用时，纠错能力为8比特。
11.如权利要求1所述的方法，其中根据表1-8中的一个，在第j个行上指定奇偶校验矩阵的列索引 j * 360 ( j = 0,1,2,3 , . . . , k ldpc 360 - 1 ) 中1的行索引：                 奇偶校验比特累加器的地址(比率2/3)  0 10491 16043 506 12826 8065 8226 2767 240 18673 9279 10579 209281 17819 8313 6433 6224 5120 5824 12812 17187 9940 13447 13825 184832 17957 6024 8681 18628 12794 5915 14576 10970 12064 20437 4455 71513 19777 6183 9972 14536 8182 17749 11341 5556 4379 17434 15477 185324 4651 19689 1608 659 16707 14335 6143 3058 14618 178 94 20684 53065 9778 2552 12096 12369 15198 16890 4851 3109 1700 18725 1997 15882
6 486 6111 13743 11537 5591 7433 15227 14145 1483 3887 17431 124307 20647 14311 11734 4180 8110 5525 12141 15761 18661 18441 10569 81928 3791 14759 15264 19918 10132 9062 10010 12786 10675 9682 19246 54549 19525 9485 7777 19999 8378 9209 3163 20232 6690 16518 716 735310 4588 6709 20202 10905 915 4317 11073 13576 16433 368 3508 2117111 14072 4033 19959 12608 631 19494 14160 8249 10223 21504 12395 432212 13800 1416113 2948 964714 14693 1602715 20506 1108216 1143 902017 13501 401418 1548 219019 12216 2155620 2095 1989721 4189 795822 15940 1004823 515 1261424 8501 845025 17595 1678426 5913 849527 16394 1042328 7409 698129 6678 1593930 20344 1298731 2510 1458832 17918 665533 6703 1945134 496 4217
 35 7290 576636 10521 892537 20379 1190538 4090 583839 19082 1704040 20233 1235241 19365 1954642 6249 1903043 11037 1919344 19760 1177245 19644 742846 16076 352147 11779 2106248 13062 968249 8934 521750 11087 331951 18892 435652 7894 389853 5963 436054 7346 1172655 5182 560956 2412 1729557 9845 2049458 6687 186459 20564 52160 18226 172071 9380  82662 7073  30653 18252 13437
 4 9161 156425 10714 101536 11585 90787 5359 94188 9024 95159 1206 1635410 14994 110211 9375 2079612 15964 602713 14789 645214 8002 1859115 14742 1408916 253 304517 1274 1928618 14777 204419 13920 990020 452 737421 18206 992122 6131 541423 10077 972624 12045 547925 4322 799026 15616 555027 15561 1066128 20718 738729 2518 1880430 8984 260031 6516 1790932 11148 98
 33 20559 370434 7510 156935 16000 1169236 9147 1030337 16650 19138 15577 1868539 17167 2091740 4256 339141 20092 1721942 9218 505643 18429 847244 12093 2075345 16345 1274846 16023 1109547 5048 1759548 18995 481749 16483 353650 1439 1614851 3661 303952 19010 1812153 8968 1179354 13427 1800355 5303 308356 531 1666857 4771 672258 5695 796059 3589 14630
表1               奇偶校验比特累加器的地址(比率5/6)   0 4362 416 8909 4156 3216 3112 2560 2912 6405 8593 4969 67231 2479 1786 8978 3011 4339 9313 6397 2957 7288 5484 6031 102172 10175 9009 9889 3091 4985 7267 4092 8874 5671 2777 2189 87163 9052 4795 3924 3370 10058 1128 9996 10165 9360 4297 434 51384 2379 7834 4835 2327 9843 804 329 8353 7167 3070 1528 73115 3435 7871 348 3693 1876 6585 10340 7144 5870 2084 4052 27806 3917 3111 3476 1304 10331 5939 5199 1611 1991 699 8316 99607 6883 3237 1717 10752 7891 9764 4745 3888 10009 4176 4614 15678 10587 2195 1689 2968 5420 25 80 2883 6496 111 6023 1024 44499 3786 8593 2074 3321 5057 1450 3840 5444 6572 3094 9892 151210 8548 1848 10372 4585 7313 6536 6379 1766 9462 2456 5606 997511 8204 10593 7935 3636 3882 394 5968 8561 2395 7289 9267 997812 7795 74 1633 9542 6867 7352 6417 7568 10623 725 2531 911513 7151 2482 4260 5003 10105 7419 9203 6691 8798 2092 8263 375514 3600 570 4527 200 9718 6771 1995 8902 5446 768 1103 652015 6304 762116 6498 920917 7293 678618 5950 170819 8521 179320 6174 785421 9773 119022 9517 1026823 2181 934924 1949 556025 1556 55526 8600 3827
 27 5072 105728 7928 354229 3226 37620 7045 24201 9645 26412 2774 24523 5331 20314 9400 75035 1850 23386 10456 97747 1692 92768 10037 40389 3964 33810 2640 508711 858 347312 5582 568313 9523 91614 4107 155915 4506 349116 8191 418217 10192 615718 5668 330519 3449 154020 4766 269721 4069 667522 1117 101623 5619 308524 8483 840025 8255 394
 26 6338 504227 6174 511928 7203 198929 1781 51740 1464 35591 3376 42142 7238 673 10595 88314 1221 65135 5300 46526 1429 97497 7878 51318 4435 102849 6331 550710 6662 494111 9614 1023812 8400 802513 9156 563014 7067 887815 9027 341516 1690 386617 2854 846918 6206 63019 363 545320 4125 700821 1612 670222 9069 922623 5767 406024 3743 9237
  25 7018 557226 8892 453627 853 606428 8069 589329 2051 28850 10691 31531 3602 40552 328 17173 2219 92994 1939 78985 617 2066 8544 13747 10676 32408 6672 94899 3170 745710 7868 573111 6121 1073212 4843 913213 580 959114 6267 929015 3009 226816 195 241917 8016 155718 1516 919519 8062 906420 2095 896821 753 732622 6291 383323 2614 7844
  24 2303 64625 2075 61126 4687 36227 8684 994028 4830 206529 7038 13630 1769 78371 3801 16892 10070 23593 3667 99184 1914 69205 4244 56696 10245 78217 7648 39448 3310 54889 6346 966610 7088 612211 1291 782712 10592 894513 3609 712014 9168 911215 6203 805216 3330 289517 4264 1056318 10556 649619 8807 764520 1999 453021 9202 681822 3403 1734
 23 2106 902324 6881 388325 3895 217126 4062 642427 3755 953628 4683 213129 7347 8027
表2        奇偶校验比特累加器的地址(比率1/2)  54 9318 14392 27561 26909 10219 2534 859755 7263 4635 2530 28130 3033 23830 365156 24731 23583 26036 17299 5750 792 9 16957 5811 26154 18653 11551 15447 13685 1626458 12610 11347 28768 2792 3174 29371 1299759 16789 16018 21449 6165 21202 15850 318660 31016 21449 17618 6213 12166 8334 1821261 22836 14213 11327 5896 718 11727 930862 2091 24941 29966 23634 9013 15587 5 44463 22207 3983 16904 28534 21415 27524 2591264 25687 450122193 14665 14798 16158 549165 4520 17094 23397 4264 22370 16941 2152666 10490 6182 32370 9597 30841 25954 276267 22120 22865 29870 15147 13668 14955 1923568 6689 18408 18346 9918 25746 5443 2064569 29982 12529 13858 4746 30370 10023 2482870 1262 28032 29888 13063 24033 21951786371 6594 29642 31451 14831 9509 9335 31552
 72 1358 6454 16633 20354 24598 624 526573 19529 295 18011 3080 13364 8032 1532374 11981 1510 7960 21462 9129 11370 2574175 9276 29656 4543 30699 20646 21921 2805076 15975 25634 5520 31119 13715 21949 1960577 18688 4608 31755 30165 13103 10706 2922478 21514 23117 12245 26035 31656 25631 3069979 9674 24966 31285 29908 17042 24588 3185780 21856 27777 29919 27000 14897 11 409 712281 29773 23310 263 4877 28622 20545 2209282 15605 5651 21864 3967 14419 22757 1589683 30145 1759 10139 29223 26086 10556 509884 18815 16575 2936 24457 26738 6030 50585 30326 22298 27562 2013126390 6247 2479186 928 29246 21246 12400 15311 3230 9 1860887 20314 6025 26689 16302 2296 3244 1961388 6237 11943 22851 15642 23857 15112 2094789 26403 25168 19038 18384 8882 12719 70930 14567 249651 3908 1002 10279 2403 24102 7644 12383 41735 13861 159186 21327 10467 5288 145798 28158 80699 16583 1109810 16681 28363
  11 13980 2472512 32169 1798913 10907 276714 21557 381815 26676 1242216 7676 875417 14905 2023218 15719 2464619 31942 858920 19978 2719721 27060 1507122 6071 2664923 10393 1117624 9597 1337025 7081 1767726 1433 1951327 26925 901428 19202 890029 18152 3064730 20803 173731 11804 2522132 31683 1778333 29694 934534 12280 2661135 6526 2612236 26165 1124137 7666 2696238 16290 848039 11774 10120
 40 30051 3042641 1335 1542442 6865 1774243 31779 1248944 32120 2100145 14508 699646 979 2502447 4554 2189648 7989 2177749 4972 2066150 6612 273051 12742 441852 29194 59553 19267 20113
表3             奇偶校验比特累加器的地址(比率3/4)   0 6385 7901 14611 13389 11200 3252 5243 2504 2722 821 73741 11359 2698 357 13824 12772 7244 6752 1 5310 852 2001 114172 7862 7977 6321 13612 12197 14449 15137 13860 1708 6399 134443 1560 11804 6975 13292 3646 3812 8772 7306 5795 14327 78664 7626 11407 14599 9689 1628 2113 10809 9283 1230 1524148705 1610 5699 15876 9446 12515 1400 6303 5411 14181 139 25 73586 4059 8836 3405 7853 7992 15336 5970 10368 10278 9675 46517 4441 3963 9153 2109 12683 7459 12030 12221 629 15212 4068 6007 8411 5771 3497 543 14202 875 9186 6235 13908 35639 3232 6625 4795 546 9781 2071 7312 3399 7250 4932 12652
  10 8820 10088 11090 7069 6585 13134 10158 7183 488 7455 923811 1903 10818 119 215 7558 11046 10615 11545 14784 7961 1561912 3655 8736 4917 15874 5129 2134 15944 14768 7150 2692 146913 8316 3820 505 8923 6757 806 7957 4216 15589 13244 262214 14463 4852 15733 3041 11193 12860 13673 8152 6551 15108 875815 3149 1198116 13416 690617 13098 1335218 2009 1446019 7207 431420 3312 394521 4418 624822 2669 1397523 7571 902324 14172 296725 7271 713826 6135 1367027 7490 1455928 8657 246629 8599 1283430 3470 315231 13917 436532 6024 1373033 10973 1418234 2464 1316735 5281 1504936 1103 184937 2058 106938 9654 6095
 39 14311 766740 15617 814641 4588 1121842 13660 624343 8578 787444 1174126860 1022 12641 12604 99652 8217 27073 3156 117934 354 15145 6978 140586 7922 160797 15087 121388 5053 64709 12687 1493210 15458 176311 8121 172112 12431 54913 4129 709114 1426 841515 9783 760416 6295 1132917 1409 1206118 8065 908719 2918 843820 1293 1411521 3922 1385122 38514000
 23 5865 176824 2655 1495725 5565 633226 4303 1263127 11653 1223628 16025 763229 4655 1412830 9584 1312331 13987 959732 15409 1211033 8754 1549034 7416 1532535 2909 1554936 2995 825737 9406 479138 11111 485439 2812 852140 8476 1471741 7820 1536042 1179 793943 2357 867844 7703 62160 3477 70671 3931 138452 7675 128993 1754 81874 7785 14005 9213 58916 2494 7703
  7 2576 79028 4821 156829 10426 1193510 1810 90411 11332 926412 11312 357013 14916 265014 7679 784215 6089 1308416 3938 275117 8509464818 12204 891719 5749 1244320 12613 443121 1344 401422 8488 1385023 1730 1489624 14942 712625 14983 886326 6578 856427 4947 39628 297 1280529 13878 669230 11857 1118631 14395 1149332 16145 1225133 13462 742834 14526 1311935 2535 11243
 36 6465 1269037 6872 933438 15371 1402339 8101 1018740 11963 484841 15125 611942 8051 1446543 11139 516744 2883 14521
表4          奇偶校验比特累加器的地址(比率4/5)   0 149 11212 5575 6360 12559 8108 8505 408 10026 128281 5237 490 10677 4998 3869 3734 3092 3509 7703 103052 8742 5553 2820 7085 12116 10485 564 7795 2972 21573 2699 4304 8350 712 2841 3250 4731 10105 517 75164 12067 1351 11992 1 2191 11267 5161537 6166 4246 23635 6828 7107 2127 3724 5743 11040 10756 4073 1011 34226 11259 1216 9526 1466 10816 940 3744 2815 11506 115737 4549 11507 1118 1274 11751 5207 7854 12803 4047 64848 8430 4115 9440 413 4455 2262 7915 12402 8579 70529 3885 9126 5665 4505 2343 253 4707 3742 4166 155610 1704 8936 6775 8639 8179 7954 8234 7850 8883 871311 11716 4344 9087 11264 2274 8832 9147 11930 6054 545512 7323 3970 10329 2170 8262 3854 2087 12899 9497 1170013 4418 1467 2490 5841 817 11453 533 11217 119 62 525114 1541 4525 7976 3457 9536 7725 3788 2982 6307 599715 11484 2739 4023 12107 6516 551 2572 6628 8150 9852
  16 6070 1761 4627 6534 7913 3730 11866 1813 12306 824917 12441 5489 8748 7837 7660 2102 11341 2936 6712 1197718 10155 421019 10101048320 8900 1025021 10243 1227822 7070 439723 12271 388724 11980 683625 9514 435626 7137 1028127 11881 252628 1969 1147729 3044 1092130 2236 872431 9104 634032 7342 858233 11675 1040534 6467 1277535 3186 121980 9621 114451 7486 56112 4319 48793 2196 3444 7527 66505 10693 24406 6755 27067 5144 59988 11043 8033
 9 4846 443510 4157 922811 12270 656212 11954 759213 7420 259214 8810 963615 689 543016 920 130417 1253 1193418 9559 601619 312 758920 4439 4197214002 955522 12232 777923 1494 878224 10749 396925 4368 347926 6316 534227 2455 349328 12157 740529 6598 1149530 11805 445531 9625 209032 4731 232133 3578 260834 8504 184935 4027 11510 5647 49351 4219 1870
 2 10968 80543 6970 54474 3217 56385 8972 6696 5618 124727 1457 12808 8868 38839 8866 122410 8371 597211 266 440512 3706 324413 6039 584414 7200 328315 1502 1128216 12318 220217 4523 96518 9587 701119 2552 205120 12045 1030621 11070 510422 6627 690623 9889 212124 829 970125 2201 181926 6689 1292527 2139 875728 12004 594829 8704 319130 8171 10933
 31 6297 711632 616 714633 5142 976134 10377 813835 7616 58110 7285 98631 7764 108672 12343 90193 4414 83314 3464 6425 6960 20396 786 30217 710 20868 7423 56019 8120 488510 12385 1199011 9739 1003412 424 1016213 1347 759714 1450 11215 7965 847816 8945 739717 6590 831618 6838 901119 6174 941020 255 11321 6197 583522 12902 384423 4377 3505
 24 5478 867225 4453 213226 9724 138027 12131 1152628 12323 951129 8231 175230 497 902231 9288 308032 2481751533 2696 26834 4023 1234135 7108 5553
表5                   奇偶校验比特累加器的地址(比率3/5)   22422 10282 11626 19997 11161 2922 3122 99 5625 17064 8270 17925087 16218 17015 828 20041 25656 4186 11629 22599 17305 22515 646311049 22853 25706 14388 5500 19245 8732 2177 13555 11346 17265 306916581 22225 12563 19717 23577 11 555 25496 6853 25403 5218 15925 2176616529 14487 7643 10715 17442 11119 5679 14155 24213 21000 1116 156205340 8636 16693 1434 5635 6516 9482 20189 1066 15013 25361 1424318506 22236 20912 8952 5421 15691 6126 21595 500 6904 13059 68028433 4694 5524 14216 3685 19721 25420 9937 23813 9047 25651 1682621500 24814 6344 17382 7064 13929 4004 16552 12818 8720 5286 220622517 2429 19065 2921 21611 1873 7507 5661 23006 23128 20543 197771770 4636 20900 14931 9247 12340 11008 12966 4471 2731 16445 7916635 14556 18865 22421 22124 12697 9803 25485 7744 18254 11313 900419982 23963 18912 7206 12500 4382 20067 6177 21007 1195 23547 24837
 756 11158 14646 20534 3647 17728 11676 11843 12937 4402 8261 229449306 24009 10012 11081 3746 24325 8060 19826 842 8836 2898 50197575 7455 25244 4736 14400 22981 5543 8006 24203 13053 1120 51283482 9270 13059 15825 7453 23747 3656 24585 16542 17507 22462 1467015627 15290 4198 22748 5842 13395 23918 16985 14929 3726 25350 2415724896 16365 16423 13461 16615 8107 24741 3604 25904 87 16 9604 203653729 17245 18448 9862 20831 25326 20517 24618 13282 5099 14183 880416455 17646 15376 18194 25528 1777 6066 21855 14372 12517 4488 174901400 8135 23375 20879 8476 4084 12936 25536 22309 16582 6402 2436025119 23586 128 4761 10443 22536 8607 9752 25446 15053 1856 4040377 21160 13474 5451 17170 5938 10256 11972 24210 17833 22047 1610813075 9648 24546 13150 23867 7309 19798 2988 16858 4825 23950 1512520526 3553 11525 23366 245217626 19265 20172 18060 24593 13255 155218839 21132 20119 15214 1 4705 7096 10174 5663 18651 19700 12524 140334127 2971 17499 16287 22368 21463 7943 18880 5567 8047 23363 679710651 24471 14325 4081 7258 4949 7044 1078 797 22910 20474 431821374 13231 22985 5056 3821 23718 14178 9978 19030 23594 8895 253586199 22056 7749 13310 3999 23697 16445 22636 5225 22437 24153 94427978 12177 2893 20778 3175 8645 11863 24623 10311 25767 17057 369120473 11294 9914 22815 2574 8439 3699 5431 24840 21908 16088 182448208 5755 19059 8541 24924 6454 11234 10492 16406 10831 11436 964916264 11275 24953 2347 12667 19190 7257 7174 24819 2938 2522 117493627 5969 13862 1538 23176 6353 2855 17720 2472 7428 573 150360 18539 186611 10502 30022 9368 107613 12299 78284 15048 133625 18444 24640
 6 20775 191757 18970 109718 5329 199829 11296 1865510 15046 2065911 7300 2214012 22029 1447713 11129 74214 13254 1381315 19234 1327316 6079 2112217 22782 582818 19775 424719 1660 1941320 4403 364921 13371 2585122 22770 2178423 10757 1413124 16071 2161725 6393 372526 597 1996827 5743 808428 6770 954829 4285 1754230 13568 2259931 1786461732 23238 1164833 19627 203034 13601 13458
 35 13740 1732836 25012 1394437 22513 668738 4934 1258739 21197 513340 22705 693841 7534 2463342 24400 1279743 21911 2571244 12039 114045 24306 102146 14012 2074747 11265 1521948 4670 1553149 9417 1435950 2415 650451 24964 2469052 14443 881653 6926 129154 6209 2080655 13915 407956 24410 1319657 13505 611758 9869 822059 1570 604460 25780 1738761 20671 2491362 24558 2059163 12402 3702
 64 8314 135765 20071 1461666 17014 368867 19837 94668 15195 1213669 7758 2280870 3564 292571 3434 7769
表6    奇偶校验比特累加器的地址(比率8/9)   0 6235 2848 32221 5800 3492 53482 2757 927 903 6961 4516 47394 1172 3237 62645 1927 2425 36836 3714 6309 24957 3070 6342 71548 2428 613 37619 2906 264 592710 1716 1950 427311 4613 6179 349112 4865 3286 600513 1343 5923 352914 4589 4035 213215 1579 3920 673716 1644 1191 5998
  17 1482 2381 462018 6791 6014 659619 2738 5918 37860 5156 61661 1504 43562 130 19043 6027 31874 6718 7595 6240 28706 2343 13117 1039 54658 6617 25139 1588 522210 6561 53511 4765 205412 5966 689213 1969 386914 3571 242015 4632 98116 3215 416317 973 311718 3802 619819 3794 39480 3196 61261 573 19092 850 40343 5622 16014 6005 5245 5251 5783
  6 172 20327 1875 24758 497 12919 2566 343010 1249 74011 2944 194812 6528 289913 2243 361614 867 373315 1374 470216 4698 228517 4760 391718 1859 405819 6141 35270 2148 50661 1306 1452 2319 8713 3463 10614 5554 66475 5837 3396 5821 49327 6356 47568 3930 4189 211 309410 1007 492811 3584 123512 6982 286913 1612 101314 953 4964
 15 4555 441016 4925 484217 5778 60018 6509 241719 1260 49030 3369 30311 3557 32242 3028 5833 3258 4404 6226 66555 4895 10946 1481 68477 4433 19328 2107 16499 2119 206510 4003 638811 6720 362212 3694 452113 1164 705014 1965 361315 4331 6616 2970 179617 4652 321818 1762 477719 5736 13990 970 25721 2062 65992 4597 48703 1228 6913
 4 4159 10375 2916 23626 395 12267 6911 45488 4618 22419 4120 428010 5825 47411 2154 555812 3793 547113 5707 159514 1403 32515 6601 518316 6369 456917 4846 89618 7092 618419 6764 71270 6358 19511 3117 69602 2710 70623 1133 36044 3694 6575 1355 1106 3329 67367 2505 34078 2462 48069 4216 21410 5348 561911 6627 624312 2644 5073
 13 4212 508814 3463 388915 5306 47816 4320 612117 3961 112518 5699 119519 6511 7920 3934 27781 3238 65872 1111 65963 1457 62264 1446 38855 3907 40436 6839 28737 1733 56158 5202 42699 3024 472210 5445 637211 370 182812 4695 160013 680 207414 1801 669015 2669 137716 2463 168117 5972 517118 5728 428419 1696 1459
表7    奇偶校验比特累加器的地址(比率9/10)   0 5611 2563 29001 5220 3143 48132 2481 834 813 6265 4064 42654 1055 2914 56385 1734 2182 33156 3342 5678 22467 2185 552 33858 2615 236 53349 1546 1755 384610 4154 5561 314211 4382 2957 540012 1209 5329 317913 1421 3528 606314 1480 1072 539815 3843 1777 436916 1334 2145 416317 2368 5055 2600 6118 54051 2994 43702 3405 16693 4640 55504 1354 39215 117 17136 5425 28667 6047 6838 5616 2582
 9 2108 117910 933 492111 5953 226112 1430 469913 5905 48014 4289 184615 5374 620816 1775 347617 3216 21780 4165 8841 2896 37442 874 28013 3423 55794 3404 35525 2876 55156 516 17197 765 36318 5059 14419 5629 59810 5405 47311 4724 521012 155 183213 1689 222914 449 116415 2308 308816 1122 66917 2268 57580 5878 26091 782 3359
 2 1231 42313 4225 20524 4286 35175 5531 31846 1935 45607 1174 1318 3115 9569 3129 108810 5238 444011 5722 428012 3540 37513 191 278214 906 443215 3225 111116 6296 258317 1457 9030 855 44751 4097 39702 4433 43613 5198 5414 1146 44265 3202 29026 2724 5257 1083 41248 2326 60039 5605 599010 4376 157911 4407 98412 1332 6163
 13 5359 397514 1907 185415 3601 574816 6056 326617 3322 40850 1768 32441 2149 1442 1589 42913 5154 12524 1855 59395 4820 27066 1475 33607 4266 6938 4156 20189 2103 75210 3710 385311 5123 93112 6146 332313 1939 500214 5140 143715 1263 29316 5949 466517 4548 63800 3171 46901 5204 21142 6384 55653 5722 17574 2805 62645 1202 2616
 6 1018 32447 4018 52898 2257 30679 2483 307310 1196 532911 649 391812 3791458113 5028 380314 3119 350615 4779 43116 3888 551017 4387 40840 5836 16921 5126 10782 5721 61653 3540 24994 2225 63485 1044 14846 6323 40427 1313 56038 1303 34969 3516 363910 5161229311 4682 384512 3045 64313 2818 261614 3267 64915 6236 59316 646 2948
 17 4213 14420 5779 15961 2403 12372 2217 15143 5609 7164 5155 38585 1517 13126 2554 31587 5280 26438 4990 13539 5648 117010 1152 436611 3561 536812 3581 141113 5647 466114 1542 540115 5078 268716 316 175517 3392 1991
表8
12.如权利要求11所述的方法，其中通过{x+m mod 360 × q}mod(nldpc-kldpc)指定奇偶校验矩阵的其它列索引m(m mod 360≠0并且m＜kldpc)中1的行索引，其中对于比率2/3 LDPC码，q＝60；对于比率5/6LDPC码，q＝30；对于比率1/2 LDPC码，q＝90；对于比率3/4 LDPC码，q＝45；对于比率4/5 LDPC码，q＝36；对于比率3/5 LDPC码，q＝72；对于比率8/9 LDPC码，q＝20；对于比率9/10 LDPC码，q＝18，其中x表示表1-7的第j个行上的项，j＝int{m/360}，int{.}表示整数函数，通过j和j+1指定奇偶校验矩阵的列索引m＝kIdpc+j(j＝0，1，2，...，nldpc-kldpc-2)中1的行索引，通过nldpc-kldpc-1指定奇偶校验矩阵的列索引nldpc-1中1的行索引。
13.一种携带用于编码的指令的计算机可读介质，所述指令被配置成当执行时使得一或多个处理器执行如权利要求1所述的方法。
14.一种用于产生低密度奇偶校验(LDPC)码的编码器，包括：
存储有表示LDPC码的结构化奇偶校验矩阵的信息的存储器(1605，1607)，所述信息被组织成表格形式，其中每个行表示数值1在奇偶校验矩阵的列组的第一列中的存在，各个行对应于奇偶校验矩阵的各个列组，其中根据预定操作导出每个组内的后续列；和
用于取出所存储的用于表示奇偶校验矩阵的信息，以输出LDPC编码信号的装置。
15.如权利要求14所述的编码器，其中所述预定操作指定以下操作中的一个：在每个组的第一列上的循环移位，和将常数加到每个组的第一列上，所述常数取决于LDPC码的编码率。
16.如权利要求14所述的编码器，其中如果奇偶校验矩阵的第i个行中的第j个项为1，通过相加第(i-1)个奇偶校验比特和第j个信息比特，确定第i个奇偶校验比特。
17.如权利要求14所述的编码器，其中将奇偶校验比特累加器初始化为零，如果奇偶校验矩阵的第(jM)个列中的第i个项为1，则在第i个奇偶校验比特累加器中累加具有M个信息比特的第j个组中的第一信息比特，其中j＝0，1，2，3，...，kldpc/M-1，根据{x+m mod M×q}mod(nldpc-kldpc)在奇偶校验比特累加器中累加第j个组的其余(M-1)个信息比特m＝jM+1，jM+2，jM+3，...，(j+1)M-1，其中x表示对应于组中第一比特jM的奇偶校验比特累加器的地址，q是编码率相关常数，在处理完所有信息比特之后，根据pi＝pi_pi-1，i＝1，2，...，nldpc-kldpc-1从i＝1开始执行操作，其中pi，i＝0，1，...，nldpc-kldpc-1的最终内容等于奇偶校验比特pi。
18.如权利要求17所述的编码器，其中M＝360。
19.如权利要求14所述的编码器，其中对于编码率2/3，5/6，1/2，3/4，4/5，3/5，8/9和9/10，码相关常数q是分别是60，30，90，45，36，72，20和18。
20.如权利要求11所述的编码器，其中根据信号群集调制LDPC编码信号，所述信号群集包含8-PSK(相移键控)，16-QAM(正交振幅调制)，QPSK(正交相移键控)，16-APSK(幅度相移键控)和32-APSK中的一个。
21.如权利要求14所述的编码器，还包括：
博斯-乔赫里-霍克文黑姆(BCH)编码器，其被构造成使用BCH码对输入信号进行编码，其中对应于输入信号的输出LDPC编码信号表示具有外BCH码和内LDPC码的码。
22.如权利要求21所述的编码器，其中冗余BCH比特的数量为nBCH-kBCH＝16*t，其中t表示BCH码的纠错能力。
23.如权利要求21所述的编码器，其中当结合比率1/2，3/4，4/5和3/5的LDPC码使用时，BCH码的纠错能力为12比特，当结合比率2/3和5/6的LDPC码使用时，能力纠错为10比特，当结合比率8/9和9/10的LDPC码使用时，纠错能力为8比特。
24.一种使用低密度奇偶校验(LDPC)编码的发送器，包括：
存储有表示LDPC码的结构化奇偶校验矩阵的信息的存储器(1605，1607)，所述信息被组织成表格形式，其中每个行表示数值1在奇偶校验矩阵的列组的第一列中的存在，各个行对应于奇偶校验矩阵的各个列组，其中根据预定操作导出每个组内的后续列；和LDPC编码器(203)，被构造成从存储器(1605，1607)中访问所存储的信息，以输出LDPC编码信号。
25.如权利要求24所述的发送器，其中所述预定操作指定以下操作中的一个：在每个组的第一列上的循环移位，和将常数加到每个组的第一列上，所述常数取决于LDPC码的编码率。
26.如权利要求24所述的发送器，其中如果奇偶校验矩阵的第i个行中的第j个项为1，通过相加第(i-1)个奇偶校验比特和第j个信息比特，确定第i个奇偶校验比特。
27.如权利要求24所述的发送器，其中将奇偶校验比特累加器初始化为零，如果奇偶校验矩阵的第(jM)个列中的第i个项为1，则在第i个奇偶校验比特累加器中累加具有M个信息比特的第j个组中的第一信息比特，其中j＝0，1，2，3，...，kldpc/M-1，根据{x+m mod M×q}mod(nldpc-kldpc)在奇偶校验比特累加器中累加第j个组的其余(M-1)个信息比特m＝jM+1，jM+2，jM+3，...，(j+1)M-1，其中x表示对应于组中第一比特jM的奇偶校验比特累加器的地址，q是编码率相关常数，在处理完所有信息比特之后，根据pi＝pi_pi-1，i＝1，2，...，nldpc-kldpc-1从i＝1开始执行操作，其中pi，i＝0，1，..，nldpc-Kldpc-1的最终内容等于奇偶校验比特pi。
28.如权利要求27所述的发送器，其中M＝360。
29.如权利要求24所述的发送器，其中对于编码率2/3，5/6，1/2，3/4，4/5，3/5，8/9和9/10，码相关常数q是分别是60，30，90，45，36，72，20和18。
30.如权利要求24所述的发送器，其中根据信号群集调制LDPC编码信号，所述信号群集包含8-PSK(相移键控)，16-QAM(正交振幅调制)，QPSK(正交相移键控)，16-APSK(幅度相移键控)和32-APSK中的一个。
31.如权利要求24所述的发送器，还包括：
博斯-乔赫里-霍克文黑姆(BCH)发送器，其被构造成使用BCH码对输入信号进行编码，其中对应于输入信号的输出LDPC编码信号表示具有外BCH码和内LDPC码的码。
32.如权利要求31所述的发送器，其中冗余BCH比特的数量为nBCH-kBCH＝16*t，其中t表示BCH码的纠错能力。
33.如权利要求31所述的发送器，其中当结合比率1/2，3/4，4/5和3/5的LDPC码使用时，BCH码的纠错能力为12比特，当结合比率2/3和5/6的LDPC码使用时，能力纠错为10比特，当结合比率8/9和9/10的LDPC码使用时，纠错能力为8比特。
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CN100385796C (zh) * 2004-11-25 2008-04-30 上海交通大学 低密度校验码的信道编码方法
CN101147326B (zh) * 2005-03-31 2010-08-18 三菱电机株式会社 纠错编码装置
CN103609025A (zh) * 2011-04-28 2014-02-26 索尼公司 数据处理装置和数据处理方法
CN110545109A (zh) * 2014-02-19 2019-12-06 索尼公司 接收方法与接收装置
CN110545109B (zh) * 2014-02-19 2023-02-24 索尼公司 接收方法与接收装置
CN111684725A (zh) * 2018-02-09 2020-09-18 高通股份有限公司 用于冗余版本的低密度奇偶校验(ldpc)奇偶校验比特存储
CN111684725B (zh) * 2018-02-09 2023-08-18 高通股份有限公司 用于冗余版本的低密度奇偶校验(ldpc)奇偶校验比特存储
CN118227372A (zh) * 2024-05-23 2024-06-21 深圳市领存技术有限公司 一种基于秩度量纠错码的存储方法及相关产品

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