Performance Bounds and Estimates for Quantized LDPC Decoders

TL;DR

This paper establishes a code-independent lower bound on the error rate of LDPC decoders based on problematic sub-graphs, providing a way to estimate performance limits of quantized decoding algorithms across various code structures.

Contribution

It introduces a novel, code-independent lower bound on LDPC decoder error rates based on sub-graph analysis, applicable to quantized message passing algorithms.

Findings

The bounds are consistent with simulated performance of quantized SPA and MSA decoders.

The approach applies to both structured and random LDPC codes.

Performance estimates derived from the bounds are robust across different code classes.

Abstract

The performance of low-density parity-check (LDPC) codes at high signal-to-noise ratios (SNRs) is known to be limited by the presence of certain sub-graphs that exist in the Tanner graph representation of the code, for example trapping sets and absorbing sets. This paper derives a lower bound on the frame error rate (FER) of any LDPC code containing a given problematic sub-graph, assuming a particular message passing decoder and decoder quantization. A crucial aspect of the lower bound is that it is code-independent, in the sense that it can be derived based only on a problematic sub-graph and then applied to any code containing it. Due to the complexity of evaluating the exact bound, assumptions are proposed to approximate it, from which we can estimate decoder performance. Simulated results obtained for both the quantized sum-product algorithm (SPA) and the quantized min-sum algorithm (MSA) are shown to be consistent with the approximate bound and the corresponding performance estimates. Different classes of LDPC codes, including both structured and randomly constructed codes, are used to demonstrate the robustness of the approach.