The Benefit of Thresholding in LP Decoding of LDPC Codes

TL;DR

This paper investigates whether thresholding log-likelihood ratios improves LP decoding of LDPC codes over noisy channels, showing that for certain codes and high SNRs, truncation can enhance decoding performance.

Contribution

It proves that thresholding log-likelihood ratios can be beneficial for LP decoding in specific scenarios, a novel insight for suboptimal decoding strategies.

Findings

Thresholding can improve LP decoding performance for certain LDPC codes.

Optimal decoders are unaffected by thresholding, but suboptimal ones like LP decoding can benefit.

High SNR regimes favor the advantages of log-likelihood truncation.

Abstract

Consider data transmission over a binary-input additive white Gaussian noise channel using a binary low-density parity-check code. We ask the following question: Given a decoder that takes log-likelihood ratios as input, does it help to modify the log-likelihood ratios before decoding? If we use an optimal decoder then it is clear that modifying the log-likelihoods cannot possibly help the decoder's performance, and so the answer is "no." However, for a suboptimal decoder like the linear programming decoder, the answer might be "yes": In this paper we prove that for certain interesting classes of low-density parity-check codes and large enough SNRs, it is advantageous to truncate the log-likelihood ratios before passing them to the linear programming decoder.