Performance Study of a Class of Irregular Near Capacity Achieving LDPC Codes

Abstract

This paper investigates the performance of a class of irregular low-density parity-check (LDPC) codes through a recently published low complexity upper bound on their beliefpropagation decoding thresholds. Moreover, their performance analysis is carried out through a recently published algorithmic method, presented in Babich et al. 2017 paper. In particular, the class considered is characterized by variable node degree distributions $\lambda(x)$ of minimum degree $i_1 \gt 2$: being, in this case, $\lambda^{'} (0)=\lambda_2=0$, this is useful to design LDPC codes presenting a linear minimum distance growth with the block length with probability 1, as shown in Di et al.’s 2006 paper. These codes unfortunately cannot reach capacity under iterative decoding, since the achievement of capacity requires $\lambda_2 \neq 0$. However, in this latter case, the block error probability might converge to a constant, as shown in the aforementioned paper.