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Sasidharan et al., 2015 - Google Patents

A high-rate MSR code with polynomial sub-packetization level

Sasidharan et al., 2015

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Document ID
7437163749939777624
Author
Sasidharan B
Agarwal G
Kumar P
Publication year
Publication venue
2015 IEEE International Symposium on Information Theory (ISIT)

External Links

Snippet

We present a high-rate (n, k, d= n− 1)-MSR code with a sub-packetization level that is polynomial in the dimension k of the code. While polynomial sub-packetization level was achieved earlier for vector MDS codes that repair systematic nodes optimally, no such MSR …
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Classifications

    • H—ELECTRICITY
    • H03—BASIC ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
    • H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
    • H03M13/13—Linear codes
    • H03M13/15—Cyclic codes, i.e. cyclic shifts of codewords produce other codewords, e.g. codes defined by a generator polynomial, Bose-Chaudhuri-Hocquenghem [BCH] codes
    • H03M13/151—Cyclic codes, i.e. cyclic shifts of codewords produce other codewords, e.g. codes defined by a generator polynomial, Bose-Chaudhuri-Hocquenghem [BCH] codes using error location or error correction polynomials
    • H03M13/1515—Reed-Solomon codes
    • H—ELECTRICITY
    • H03—BASIC ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
    • H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
    • H03M13/11—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits using multiple parity bits
    • H03M13/1102—Codes on graphs and decoding on graphs, e.g. low-density parity check [LDPC] codes
    • H03M13/1148—Structural properties of the code parity-check or generator matrix
    • H03M13/116—Quasi-cyclic LDPC [QC-LDPC] codes, i.e. the parity-check matrix being composed of permutation or circulant sub-matrices
    • H—ELECTRICITY
    • H03—BASIC ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
    • H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
    • H03M13/11—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits using multiple parity bits
    • H03M13/1102—Codes on graphs and decoding on graphs, e.g. low-density parity check [LDPC] codes
    • H03M13/1105—Decoding
    • H03M13/1131—Scheduling of bit node or check node processing
    • H03M13/1137—Partly parallel processing, i.e. sub-blocks or sub-groups of nodes being processed in parallel
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING; COUNTING
    • G06F—ELECTRICAL DIGITAL DATA PROCESSING
    • G06F11/00—Error detection; Error correction; Monitoring
    • G06F11/07—Error detection; Error correction; Monitoring responding to the occurence of a fault, e.g. fault tolerance
    • G06F11/08—Error detection or correction by redundancy in data representation, e.g. by using checking codes
    • G06F11/10—Adding special bits or symbols to the coded information, e.g. parity check, casting out 9's or 11's
    • G06F11/1008—Adding special bits or symbols to the coded information, e.g. parity check, casting out 9's or 11's in individual solid state devices
    • G06F11/1012—Adding special bits or symbols to the coded information, e.g. parity check, casting out 9's or 11's in individual solid state devices using codes or arrangements adapted for a specific type of error
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING; COUNTING
    • G06F—ELECTRICAL DIGITAL DATA PROCESSING
    • G06F11/00—Error detection; Error correction; Monitoring
    • G06F11/07—Error detection; Error correction; Monitoring responding to the occurence of a fault, e.g. fault tolerance
    • G06F11/08—Error detection or correction by redundancy in data representation, e.g. by using checking codes
    • G06F11/10—Adding special bits or symbols to the coded information, e.g. parity check, casting out 9's or 11's
    • G06F11/1076—Parity data used in redundant arrays of independent storages, e.g. in RAID systems
    • H—ELECTRICITY
    • H03—BASIC ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/29—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes combining two or more codes or code structures, e.g. product codes, generalised product codes, concatenated codes, inner and outer codes
    • H03M13/2906—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes combining two or more codes or code structures, e.g. product codes, generalised product codes, concatenated codes, inner and outer codes using block codes
    • H03M13/2909—Product codes
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00—Arrangements for detecting or preventing errors in the information received
    • H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
    • H04L1/0056—Systems characterized by the type of code used
    • H04L1/0057—Block codes
    • H—ELECTRICITY
    • H03—BASIC ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/65—Purpose and implementation aspects

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