Matched Quantized Min-Sum Decoding of Low-Density Parity-Check Codes

TL;DR

This paper introduces a quantized message passing decoding algorithm for LDPC codes that nearly matches the performance of the sum-product algorithm, using a novel min-sum approximation and stability analysis.

Contribution

It proposes a new quantized min-sum decoding algorithm for LDPC codes, with performance close to sum-product and a stability analysis emphasizing degree-3 variable nodes.

Findings

Algorithm nearly closes the gap with sum-product decoding.

Density evolution analysis confirms large performance gains.

Finite-length simulations validate asymptotic results.

Abstract

A quantized message passing decoding algorithm for low-density parity-check codes is presented. The algorithm relies on the min approximation at the check nodes, and on modelling the variable node inbound messages as observations of an extrinsic discrete memoryless channel. The performance of the algorithm is analyzed and compared to quantized min-sum decoding by means of density evolution, and almost closes the gap with the performance of the sum-product algorithm. A stability analysis is derived, which highlights the role played by degree-$3$ variable nodes in the stability condition. Finite-length simulation results confirm large gains predicted by the asymptotic analysis.