On the performance of LT codes over BIAWGN channel

Abstract

Luby transform (LT) codes are defined by degree distribution functions of encoded symbols. In erasure channels, good degree distribution functions should prevent the ripple of degree-one symbols from vanishing until the successful termination of decoding process. In this paper, we show that for binary input additive white Gaussian noise (BIAWGN) channels, performance of LT codes also depends on the time at which source nodes in the decoding graph of the codes start receiving non-zero log-likelihood ratio (LLR) values. We show that source nodes can be categorized based on this time, and those in lower categories, i.e., those source nodes updated with non-zero LLR values at earlier iterations have higher probability of being decoded correctly. We theoretically derive formulas that can find the percentages of source nodes in each category for any given degree distribution function. We finally show that by increasing the number of source nodes in the lower categories, the bit error rate (BER) performance of LT codes can be drastically improved. This work provides a new perspective for the performance and design of such codes for BIAWGN channels.