Finite Length Analysis of Low-Density Parity-Check Codes on Impulsive Noise Channels

Low-density parity-check (LDPC) codes with very long block lengths are well known for their powerful error correction, but it is not always desirable to employ long codes in communication systems, where latency is a serious issue, such as voice and video communication between multiple users. Finite length analyses of LDPC codes have already been presented in the literature for the additive white Gaussian noise channel, but in this paper, we consider the finite length analysis of LDPC codes for channels that exhibit impulsive noise. First, an exact uncoded bit error probability (BEP) of an impulsive noise channel, modeled as a symmetric α-stable (SαS) distribution, is derived. Then, to obtain the LDPC-coded performance, density evolution is applied to evaluate the asymptotic performance of LDPC codes on SαS channels and determine the threshold signal-to-noise ratio. Finally, we derive closed-form expressions for the BEP and block error probability of short LDPC codes on these channels, which are shown to match closely with simulated results on channels with different levels of impulsiveness, even for block lengths as low as 1000 b.