Soft Decision Decoding with Cyclic Information Set and the Decoder Architecture for Cyclic Codes

Abstract

The soft decision decoding algorithm for cyclic codes, especially the maximum likelihood (ML) decoding algorithm, can obtain significant performance superior to that of algebraic decoding, but the complexity is much higher. To deal with this problem, an improved soft decision decoding algorithm based on a cyclic information set and its efficient implementation architecture are proposed. This algorithm employs the property of the cyclic codes to generate a series of cyclic information sequences by circularly shifting, constructing the cyclic information set. Then, a limited number of candidate information sequences are efficiently generated using an iterative computation method, and the candidate codewords are generated using the very concise encoding method of the cyclic codes. Furthermore, the efficient hardware architecture based on systolic arrays is also proposed to generate candidate information sequences and to select the optimal candidate codewords. An emulation platform is constructed to verify the error correction performance and to determine the optimal decoder parameters. Emulation results indicate that, with appropriate parameter selection, the proposed decoding algorithm can achieve a bit error rate approaching the ML performance while maintaining low complexity.