Symbol-level iterative information set decoding of RS codes

Abstract

This paper presents the implementation of a low-complex iterative symbol-level decoding scheme for Reed-Solomon codes. Most soft-decision iterative decoders for Reed-Solomon codes work on a bit level due to the efficient passing of soft information due to the sparsity of the binary parity check matrix. These decoders yield a good error correction performance, but this comes at the cost of an increased computational complexity resulting from working at a bit-level. This study aims to lower the computational complexity of iterative decoding of Reed-Solomon codes by introducing a high-performance soft-decision iterative Reed-Solomon decoder that works on a symbol-level, in contrast to the bit-level implementation used in most iterative Reed-Solomon decoders. The proposed algorithm utilises soft information to decode while applying information set decoding techniques to an extended parity check matrix. The use of the extended parity check matrix provides additional parity check equations which assist the algorithm in determining the correct information set of symbols used in the decoding process. For a given (n,k) Reed-Solomon code, the algorithm converges to a valid codeword by correctly decoding a specified information set of k symbols from the received vector. Simulations run show the proposed algorithm performs favourably when compared to other symbol-level iterative decoders while working at a relatively lower complexity.