Box and Match Techniques Applied to Soft-Decision Decoding

In this paper, we improve the ordered statistics decoding algorithm by using matching techniques. This allows us: to reduce the worst case complexity of decoding (the error performance being fixed) or to improve the error performance (for a same complexity); to reduce the ratio between average complexity and worst case complexity; to achieve practically optimal decoding of rate-1/2 codes of lengths up to 128 (rate-1/2 codes are a traditional benchmark, for coding rates different from 1/2, the decoding is easier); to achieve near-optimal decoding of a rate-1/2 code of length 192, which could never be performed before.