Browse Theses

Cyclic codes and modified cyclic codes are widely used because they can be decoded efficiently. These codes are usually decoded with hard-decision decoders that take advantage of the algebraic properties of the codes. In this dissertation algorithms are presented which use the algebraic structure of cyclic codes to provide efficient soft decision decoding of Reed-Solomon codes. These algorithms provide better error correction performance than existing hard-decision decoding algorithms, and more efficient decoding than existing soft decision decoding techniques.

Reed-Solomon codes are powerful codes, but they are limited to certain code lengths. For codes with lengths that cannot be Reed-Solomon lengths, nonbinary BCH codes are used. These codes can be decoded using the same hard-decision decoding techniques that are used with Reed-Solomon codes, but can only decode up to their design distance. The design distance of a nonbinary BCH code is generally less than the minimum distance of a cyclic code of the same dimensions. Cyclic codes and shortened cyclic codes are presented which have better minimum distances than corresponding nonbinary BCH codes. These cyclic codes do not have efficient hard-decision decoding algorithms. However, efficient algorithms for soft-decision decoding of these codes are presented.

Normally, for error control in a communication system using M -ary orthogonal signaling, a Reed-Solomon code of length M is used. To achieve good error performance, a large value of M may be desired, but this results in a complex receiver system. A method is presented for using a smaller signal constellation size, n , while maintaining system performance. Systems are developed which have constant bandwidth and improve error performance while decreasing system complexity. These systems use Reed-Solomon and cyclic codes, and they use soft-decision decoding techniques.