Multi-Edge-Type Low-Density Parity-Check Codes for Bandwidth-Efficient Modulation

A method of designing low-density parity-check codes for bandwidth-efficient high-order modulation is proposed. A multi-edge-type LDPC code ensemble is used to improve the correspondence between modulation bit-channel capacity and bit-level protection in a bit-interleaved coded modulation system. A key innovation is the development of a multi-dimensional extrinsic information transfer (EXIT) vector field technique for the analysis and design of multi-edge-type codes. A condition, sufficient for the decoder to converge, is derived on the multi-dimensional EXIT vector field, and this condition is used as a constraint in code optimization. Code designs indicate that the proposed method produces codes matching the performance of codes designed using best available methods in ensemble threshold, and is capable of achieving identical finite-length error rates with shorter block-lengths. In addition to simplified design complexity, the resulting codes allow for low-complexity implementation and rate-adaptivity, and hence are well-suited for adaptive modulation systems.