Soft-Decision Decoding Using Ordered Recodings on the Most Reliable Basis

This correspondence investigates soft-decision decoding of binary linear block codes using ordered recodings of test error patterns on the so-called "most reliable basis." The analysis demonstrates the optimality of the most reliable basis by showing that, among all possible bases, the most reliable basis minimizes the list error probability for a very general (and well-defined) class of orderings for recoding operations. The correspondence then proposes a suboptimal algorithm which utilizes reprocessing ordering and incorporates two techniques that render it computationally very efficient: 1) an iterative reference recoding technique which simplifies the recoding operation required for each test error pattern, and 2) an adaptive skipping rule which significantly reduces the average number of recodings. Simulation results with codes of relatively large length show that the proposed algorithm is computationally very efficient in comparison to existing algorithms in the literature