Performance Bound for Finite-Length LDPC Coded Modulation

Coded modulation systems based on low density parity check (LDPC) codes of finite lengths are considered. The union bounds on the bit error probabilities of the maximum likelihood (ML) decoding are presented for both additive white Gaussian noise (AWGN) and flat Rayleigh fading channels. The tightness of the derived bound is verified by simulating the ML decoding of a very short LDPC code. For mediumlength codes, performance of the sum-product decoding can asymptotically approach the bounds. key words: LDPC codes, performance bound, coded modulation