Lowering the error floor of short-to-medium length LDPC codes using optimal low-correlated-edge density (OED) PEG Tanner graphs

摘要

We propose a simple modification to the progressive edge-growth (PEG) algorithm in order to control the girth of low-density parity-check (LDPC) code Tanner graphs constructed. Using the modified algorithm, the edge densities in short irregular rate-% LDPC code graphs can be increased without increasing the correlation between edges in graphs by creating cycles of undesired length. Density evolution (DE) optimized symbol node degree distributions used for constructing short-to-medium length codes were further optimized (slightly altered) while maintaining the maximum edge correlation (minimum local girths) that exists in graphs constructed using the unaltered DE optimized distributions. As a result of improved degree sequences (and graph densities) which were derived, short-to-medium length LDPC codes with lower error floors than published for LDPC codes of identical length and rate were found. These slightly denser codes have lower error floor than codes constructed using DE optimized degree distributions in PEG algorithms modified for improved approximate cycle extrinsic message degrees (ACE). Simulation results show that, at a code length of 512, efficient irregular rate-% PEG codes have significantly lower error floors than a rate-% IEEE 802.16e (WiMAX) LDPC code of length 576.