Summary: This paper presents a method for evaluating the bit-error probability of a concatenated coding system for BPSK transmission over the AWGN channel. In the concatenated system, a linear binary block code is used as the inner code and is decoded with the soft-decision maximum likelihood decoding, and a maximum distance separable code (or its interleaved code) is used as the outer code and is decoded with a bounded distance decoding. The method is illustrated through a specific example in which the inner code is a binary \((64.40.8)\) Reed-Muller subcode and the outer code is the NASA standard \((255.223.33)\) Reed-Solomon code over \(\text{GF} (2^8)\) interleaved to a depth of 5. This specific concatenated system is being considered for NASA's high-speed satellite communications. The bit-error performance is evaluated by a combination of simulation and analysis. The split weight enumerators for the maximum distance separable codes are derived and used for the analysis.