Random Coding Bounds for Noncoherent mFSK Multiple-Access Channels

Abstract

We investigate a time-varying trellis coded multiple-access scheme using noncoherent mFSK signals. Techniques similar to this were originally proposed by Cohen, Heller, and Viterbi and more recently in a mFSK form by Viterbi. In these multiple-access systems van der Muelen Ahlswede Liao, Gaarder and Wolf , Kasami and Lin, Weldon and Wolf have shown that the decoded symbols of one user can be used to reduce the "multiple-access noise" to other users and thus allow for a larger achievable rate region than one would expect with conventional time division multiple-access techniques. In some cases, specific codes were investigated. Peterson and Costello and Chevillat have extended these earlier works to convolutional and trellis codes. In this case the decoder is designed as a "super" Viterbi decoder that regards all transmitter trellis codes combined to form a single "super" trellis encoder. In this paper we investigate the noncoherent mFSK scheme discussed by Viterbi and generalize to single level and multi-level energy detectors with a single "super" Viterbi decoder at the receiver. The main results are random coding bounds for the general case where L users each have remotely located time-varying trellis encoders of constraint length K. We assume throughout that the channel is noiseless, and symbol timing synchronization is maintained among the L users. These assumptions are being relaxed in the thesis research of Sorace.