Decoding of low-density parity-check codes in non-Gaussian channels

This paper studies the performance of low-density parity-check codes decoded by the iterative message-passing algorithm (MPA) in heavy-tailed, non-Gaussian noise channels. Through detailed examination on the decoding procedure and observation on the decoding trajectory, impulsive noise is found to constitute a major channel impairment for the Gaussian-optimised MPA. Two main factors contributing to this non-robustness, which lead to error propagation and produce uncorrectable and undetected errors, are identified. To compensate for this shortfall, an effective countermeasure is outlined and a low-complexity robust MPA (RMPA) in both probability and log-domains is proposed. The RMPA can be implemented by appending the standard MPA with a nonlinear filter bank, thus requiring no major modifications. The nonlinear filter bank performs impulsive noise suppression and prevents the formation of overly strong priors. This gives room for performance improvements via iterative decoding. The nonlinear functions embedded in the filter bank can be stored as a lookup table or implemented efficiently using the CORDIC algorithm, which is very suitable for VLSI implementation. For severe impulsive noise, the RMPA significantly outperforms the MPA with performance gains typically exceeding 10 dB for bit error probabilities below 10^-2 with moderate codeword lengths. The performance of the sign-MPA (SMPA), which imposes a hard-limiting procedure on the received codewords, is also investigated.