A New Multi-Edge Metric-Constrained PEG Algorithm for Designing Binary LDPC Code With Improved Cycle-Structure

The progressive edge-growth (PEG) algorithm constructs an edge in each stage to maximize the variable node (VN) of interest's local girth in real time. Thus, this VN's local girths, after more than one edge is added to the current tanner graph (TG) setting, may not be maximized relative to that TG setting. To address this problem, we define the multi-edge local girth and edge-trial, and based on these definitions, propose a new multi-edge metric-constrained PEG algorithm (MM-PEGA) to improve the design at each VN. The MM-PEGA constructs an edge in each stage that, relative to the current TG setting, can potentially maximize the VN of interest's local girth after a certain number (up to the edge-trial) of edges are added to the TG setting. We first analyze the properties of the multi-edge local girth, and then propose an algorithm for calculating the multi-edge local girth. We also propose a method for accelerating the MM-PEGA. Moreover, we generalize the MM-PEGA for improving different PEG-like designs. According to the theoretical analysis, increasing the edge-trial of the MM-PEGA is expected to positively affect the cycle-structure and the error performance of resulting low-density parity-check (LDPC) code. This expectation is verified by simulations.