Power- and bandwidth-efficient communications using LDPC codes

We apply low-density parity-check (LDPC) codes to a bandwidth-efficient modulation scheme using multilevel coding, multistage decoding, and trellis-based signal shaping. Performance results based on density evolution and simulations are presented. Using irregular LDPC component codes of block length 10⁵ and a 64-quadrature amplitude modulation signal constellation operating at 2 bits/dimension, a bit-error rate of 10^-5 is achieved at an E_b/N₀ of 6.55 dB. At this value of E_b/N₀, the Shannon channel capacity, computed assuming equally likely signaling, is below 2 bits/dimension.