Modified OSD Algorithm with Reduced Gaussian Elimination
Marc Fossorier, Mahdi Shakiba-Herfeh, Huazi Zhang
TL;DR
This work targets soft-decision maximum likelihood decoding for short linear block codes by addressing the Gaussian elimination bottleneck in MRB/OSD decoding. It introduces a reduced GE framework that separates information and parity positions into MRB and LRB, performing GE on a smaller submatrix to achieve a complexity of $O(N^3 min{R,1-R}^3)$. The method is extended with multi-stage and restricted-complexity variants, including a bound on reprocessing with $B_{max}$, and demonstrated on BCH codes (e.g., $(127,113)$ and $(511,493)$) to approach MLD performance with manageable complexity. The approach offers significant efficiency improvements for near-MLD decoding in practical settings such as URLLC, with favorable software and hardware implications.
Abstract
In this paper, the OSD algorithm is modified to perform a limited GE with $O(N^3 \min\{R, 1-R\}^3)$ complexity for an $(N,K)$ linear block code of rate $R=K/N$.