Performance Bound for LDPC Coded Unitary Space–Time Modulation

Abstract

This paper is concerned with the bit error probability (BEP) of coded unitary space---time modulation systems based on finite-length low density parity check (LDPC) codes. The union bound on the BEP of the maximum likelihood (ML) decoding is derived for any code rate, unitary space---time constellation and mapping. The tightness of the bound is checked with simulation results of the ordered statistic decoding (OSD). Numerical and simulation results show that the union bound is also close to the error performance of the sum---product (SP) decoding at low BEP levels when Gray mapping is employed. The derived bound is useful to benchmark the error performance of finite-length coded unitary space---time modulation systems, especially for those that employ short-to-medium length LDPC codes.