Analytic Techniques for Periodic Trellis Codes Richard

This paper presents analytical techniques for trellis codes on AWGN channels with periodic fading. The paper begins with an asymptotically tight union bound on the bit error rate of a trellis code on such a channel and a procedure for eeciently computing the required transfer function for any trellis code, including those that do not satisfy regularity properties that simplify the task. Periodic erasures can cause an encoder that is non-catastrophic for the regular AWGN channel to display catastrophic behavior. Two techniques identify erasure patterns that will cause this behavior. One technique applies the traditional catastrophic test to a strictly equivalent multiple trellis code after removing columns corresponding to erased symbols. The second technique eeciently searches for zero distance loops in the state diagram.