Improved Upper Bound on the Probability of Decoding Error for Codes of Complex Structure

Two methods without expurgation are proposed for constructing an upper bound of the probability of decoding error in a memoryless discrete channel, which is better than the random coding bound for low rates. Although in general the bounds obtained by these methods are worse than the expurgated bound, they are applicable to codes with structure constraints. We examine the application of these bounds to trellis codes, to codes for multiple access channels, to $(s,t)$-designs, and to $B_s$-codes.