Analysis of Saturated Belief Propagation Decoding of Low-Density Parity-Check Codes

TL;DR

This paper investigates how log-likelihood ratio saturation impacts belief propagation decoding of LDPC codes, revealing that while error floor performance degrades gracefully, stability is significantly affected, akin to reducing variable node degree.

Contribution

It provides a detailed analysis of the effects of saturation on threshold and stability in belief propagation decoding of LDPC codes, including conditions linking block and bit thresholds.

Findings

Saturation causes graceful degradation in decoding performance.

Stability of density evolution is strongly affected by saturation.

Block threshold can match bit threshold under certain conditions.

Abstract

We consider the effect of log-likelihood ratio saturation on belief propagation decoder low-density parity-check codes. Saturation is commonly done in practice and is known to have a significant effect on error floor performance. Our focus is on threshold analysis and stability of density evolution. We analyze the decoder for standard low-density parity-check code ensembles and show that belief propagation decoding generally degrades gracefully with saturation. Stability of density evolution is, on the other hand, rather strongly effected by saturation and the asymptotic qualitative effect of saturation is similar to reduction by one of variable node degree. We also show under what conditions the block threshold for the saturated belief propagation corresponds with the bit threshold.