Successive Maximization for Systematic Design of Universally Capacity Approaching Rate-Compatible Sequences of LDPC Code Ensembles over Binary-Input Output-Symmetric Memoryless Channels

A systematic construction of capacity achieving low-density parity-check (LDPC) code ensemble sequences over the Binary Erasure Channel (BEC) has been proposed by Saeedi et al. based on a method, here referred to as Successive Maximization (SM). In SM, the fraction of degree-i nodes are successively maximized starting from i = 2 with the constraint that the ensemble remains convergent over the channel. In this paper, we propose SM to design universally capacity approaching rate-compatible LDPC code ensemble sequences over the general class of Binary-Input Output-Symmetric Memoryless (BIOSM) channels. This is achieved by first generalizing the SM method to other BIOSM channels to design a sequence of capacity approaching ensembles called the parent sequence. The SM principle is then applied to each ensemble within the parent sequence, this time to design rate-compatible puncturing schemes. As part of our results, we extend the stability condition which was previously derived for degree-2 variable nodes to other variable node degrees as well as to the case of rate-compatible codes. Consequently, we prove that using the SM principle, one is able to design universally capacity achieving rate-compatible LDPC code ensemble sequences over the BEC. Unlike the previous results in the literature, the proposed SM approach is naturally extendable to other BIOSM channels. The performance of the rate-compatible schemes designed based on our method is comparable to those designed by optimization.