Trellis Coding for the Two-User Multiple-Access Channel, Part II: A Free Distance Lower Bound

Random trellis codes for the two-user discrete memoryless multiple-access channel are considered. An upper bound on the maximum likelihood decoding error probability is derived and a two-user random trellis coding error exponent is derived. The error exponent is identical to the analogous result for tree codes. The known two-user random block coding error exponent is derived by considering the class of terminated trellis code pairs having the same constraint length. Unit-memory codes for the two-user channel are considered. It is shown that the two-user unit-memory coding error exponent is at least as large as the two-user conventional trellis coding error exponent. A lower bound on the free distance of two-user random trellis codes is derived. It is shown that for the noiseless channel case the lower bound is strictly positive for any rate pair within the two-user capacity region, whereas in the noisy channel case the bound extends beyond this region--namely, to the two-user identification region. For the noiseless binary adder channel case the new bound is better than Peterson and Costello''s lower bound. Unit-memory codes for the single-user continuous phase modulated channel are considered. Heuristic design rules are used for defining the subsets of codes within which an exhaustive search is conducted. The coding gains of the best codes within these subsets are better than those of the best previously known multi-memory codes.