A New Chase-type Soft-decision Decoding Algorithm for Reed-Solomon Codes

TL;DR

This paper introduces a novel tree-based Chase-type soft-decision decoding algorithm for Reed-Solomon codes that guarantees the most-likely codeword with efficient trials, improving decoding performance over existing methods.

Contribution

The paper extends Wu and Pados' binary decoding approach to q-ary codes, proposing a tree-structured Chase decoding method that enhances efficiency and accuracy.

Findings

Performs better than recent Chase algorithms with fewer trials

Guarantees the most-likely codeword if terminated early

Integrates seamlessly with Guruswami-Sudan decoding

Abstract

A new Chase-type soft-decision decoding algorithm for Reed-Solomon codes is proposed, referred to as tree-based Chase-type algorithm}. The proposed tree-based Chase-type algorithm takes the set of all vectors as the set of testing patterns, and hence definitely delivers the most-likely codeword provided that the computational resources are allowed. All the testing patterns are arranged in an ordered rooted tree according to the likelihood bounds of the possibly generated codewords, which is an extension of Wu and Pados' method from binary into $q$-ary linear block codes. While performing the algorithm, the ordered rooted tree is constructed progressively by adding at most two leafs at each trial. The ordered tree naturally induces a sufficient condition for the most-likely codeword. That is, whenever the tree-based Chase-type algorithm exits before a preset maximum number of trials is reached, the output codeword must be the most-likely one. But, in fact, the algorithm can be terminated by setting a discrepancy threshold instead of a maximum number of trials. When the tree-based Chase-type algorithm is combined with Guruswami-Sudan (GS) algorithm, each trial can be implement in an extremely simple way by removing from the gradually updated Grobner basis one old point and interpolating one new point. Simulation results show that the tree-based Chase-type algorithm performs better than the recently proposed Chase-type algorithm by Bellorado et al with less trials (on average) given that the maximum number of trials is the same.