A Novel Concatenation Decoding of Reed-Solomon Codes With SPC Product Codes

Xiaoling Liu, Wei Zhang, Yanyan Chang, Yanyan Liu

Abstract: This letter introduces a novel concatenation decoding of Reed-Solomon (RS) codes with single parity-check product codes (SPC-PCs), including the concatenation scheme and the decoding algorithm. The proposed scheme sequentially arranges SPC-PCs to form <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$K$</tex-math></inline-formula> information symbols, then encodes them into <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N$</tex-math></inline-formula> symbols using systematic RS code. A high-performance and low-complexity bit-iterative-update decoding (BIUD) algorithm is also proposed based on this scheme. We use the results of the parity-check to evaluate the reliability in each dimension and then iteratively update the reliability of each bit based on the structure of SPC-PCs. This way dramatically reduces the complexity of traditional reliability computation. Furthermore, the bit iterative update and the Berlekamp-Massey algorithm of RS codes can be well combined, resulting in more accurate results. The simulation and analysis results show that the proposed concatenation algorithm has significant performance improvement compared to the current RS-SPC concatenation decoding while having extremely low complexity.