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

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.