A Comparative Performance Analysis of Regular LDPC Codes Over AWGN and Rayleigh Fading Channels

Abstract

In this paper, we provide a comparative performance analysis of regular Low Density Parity Check (LDPC) codes with rate ½ over uncorrelated Rayleigh fading channel and Additive White Gaussian Noise (AWGN) channel to find out to what extent a Rayleigh channel, in which the transmissions are interleaved, approximates the effect of an Additive White Gaussian Noise (AWGN) channel . We provide two performance metrics to quantify this comparative study, probability of bit error, and cross correlation of the bits as they travel across the two channels. We calculate cross correlation of the transmitted codewords while the bits are fully or partially interleaved and demonstrate that fully interleaving bits of LDPC encoded codewords (transmitted across Rayleigh fading channel) creates the most correlation with encoded codewords (transmitted across Additive White Gaussian Noise channel) by a factor of 7/5. Additionally, we show that the regular LDPC code used in this study generally performs better (or similar) over Gaussian channel. For two specific signal to noise ratios of 2 dB and 4 dB, probability of bit error associated with Rayleigh channel is approximately twice as much as probability of bit error associated with AWGN channel.