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

We consider the effect of log-likelihood ratio saturation on the belief-propagation decoding of low-density parity-check codes. Saturation is commonly done in practice and is known to have a significant effect on the error-floor performance. Our focus is on threshold analysis and the 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 affected by saturation, and the asymptotic qualitative effect of saturation is similar to reduction by one of variable-node degree. We also describe conditions under which the block-error threshold for saturated belief-propagation decoding equals the bit-error threshold.

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