Extrinsic Dispersion Transfer Chart for Finite Length LDPC Codes Design
Ahmed Attia Abotabl, Aria Nosratinia · 2016
The most popular methods for the analysis of LDPC codes, e.g. density evolution and EXIT charts, apply to infinite length ensembles. Finite length analysis is less common, among the notable examples are scaling law analysis and the EXIT band chart. The scaling law is limited to the waterfall region and furthermore is limited to the final error rates and does not give insight into the progression and dynamics of belief propagation decoding. The EXIT band chart was based on empirical considerations and does not enjoy a strong underlying theory. The developments of this paper are motivated by the recent results by Polyanskiy, Poor and Verdu showing that the rate penalty due to finite blocklength depends on the channel dispersion. We propose tracking the dispersion between the transmitted bits and the log-likelihood ratio across the decoder iterations to capture the effect of the codeword length. Based on the proposed analysis, a simple lower bound on the block error probability as a function of the blocklength is derived. The bound is corroborated by simulation.