Guessing What, Noise or Codeword?

TL;DR

This paper compares two guessing algorithms for decoding binary linear codes, proving the optimality of one and proposing variants to balance complexity and performance for high SNR scenarios.

Contribution

It introduces and analyzes the guessing codeword decoding (GCD) as an ML decoding method and proposes variants of ordered statistic decoding to optimize decoding complexity.

Findings

GCD is proven to be a maximum likelihood decoding algorithm.

GCD is more efficient than GND in most practical cases.

Variants of OSD can balance decoding complexity and performance.

Abstract

In this paper, we distinguish two guessing algorithms for decoding binary linear codes. One is the guessing noise decoding (GND) algorithm, and the other is the guessing codeword decoding (GCD) algorithm. We prove that the GCD is a maximum likelihood (ML) decoding algorithm and that the GCD is more efficient than GND for most practical applications. We also introduce several variants of ordered statistic decoding (OSD) to trade off the complexity of the Gaussian elimination (GE) and that of the guessing, which may find applications in decoding short block codes in the high signal-to-noise ratio (SNR) region.