Unique and Minimum Distance Decoding of Linear Codes with Reduced Complexity

TL;DR

This paper presents a new decoding algorithm for linear codes that reduces computational complexity by systematically inspecting error patterns within the information set, improving decoding efficiency.

Contribution

It introduces a novel decoding method with reduced complexity for unique and minimum distance decoding of linear codes, based on error pattern inspection.

Findings

Decoding complexity for unique decoding is O(n^{2}q^{nRH(delta/2/R)}).

Decoding complexity for minimum distance decoding is O(n^{2}q^{nRH(delta/R)}).

Algorithm inspects all error patterns of certain weights in the information set.

Abstract

We show that for (systematic) linear codes the time complexity of unique decoding is O(n^{2}q^{nRH(delta/2/R)}) and the time complexity of minimum distance decoding is O(n^{2}q^{nRH(delta/R)}). The proposed algorithm inspects all error patterns in the information set of the received message of weight less than d/2 or d, respectively.