Efficient Ordered Statistics Decoding of BCH Codes Without Gaussian Elimination

Ordered statistics decoding (OSD) can achieve near maximum likelihood (ML) decoding performance for BCH codes. However, Gaussian elimination (GE) that delivers the systematic generator matrix of the code has an uncompromised latency. Addressing this challenge, this paper proposes a low-latency OSD (LLOSD) for BCH codes. Since BCH codes are binary subcodes of Reed-Solomon (RS) codes, codeword candidates can be produced using the RS systematic generator matrix, whose entries can be generated in parallel. By eliminating the non-binary codeword candidates and identifying the ML codeword, the LLOSD yields a lower latency as well as complexity than the OSD. It is shown that the LLOSD can be interpreted as generating the codeoword candidates through systematic encoding of a punctured BCH codeword, explaining its low-complexity feature. Moreover, the segmented variant is proposed to further facilitate the LLOSD. In order to decode long BCH codes, a hybrid soft decoding (HSD) is finally proposed. It integrates the LLOSD and the algebraic Chase decoding that can effectively provide extra TEPs for the LLOSD, enhancing the decoding performance. Both the complexity and performance of the proposed decoding are analyzed, demonstrating their advantage over the relevant state-of-the-art decoding.