Response to the following problem:
Consider the concatenation of a Reed-Solomon (31, 3) (q = 32-ary alphabet) as the outer code with a Hadamard (16, 5) binary code as the inner code in a DS spread spectrum system.
Assume that soft-decision decoding is performed on both codes. Determine an upper (union) bound on the probability of a bit error based on the minimum distance of the concatenated code.