Techniques of bounding the probability of decoding error for block coded modulation structures

Two techniques for upper bounding the average probability of decoding error in coded modulation structures are presented. The first bound, which is applicable to the additive white Gaussian noise (AWGN) channel, is tighter than the well-known union bound and the minimum distance bound, especially for low signal to noise ratio. It is shown that for the Leech lattice this upper bound is very close to a sphere lower bound. For the second upper bound, which is applicable to any memoryless channel (not necessarily AWGN), a method of random coset coding is presented. For the AWGN channel, a tighter upper bound is obtained by employing the method of random coset coding for calculating the average spectrum of distances of the code, which is required for the computation of the first upper bound.<>