A framework for low-complexity communication over channels with feedback

This thesis develops a framework for low-complexity communication over channels with feedback. In this framework, which is referred to in the thesis as the compressed-error-cancellation framework, data are sent via a sequence of messages: the first message contains the original data; each subsequent message contains a source-coded description of the channel distortions introduced on the message preceding it. The usefulness and flexibility of the framework is demonstrated by applying it to a number of fundamental feedback communication problems. The framework is first used for coding over known single-user channels. For discrete memoryless channels with complete, noiseless feedback (DMCf's), a coding scheme exploiting lowcomplexity lossless source coding algorithms is developed, and the associated encoder and decoder are shown to use a number of computations growing only linearly with the number of channel inputs used (linear complexity). The associated error exponent is shown to be optimal in an appropriate sense and implies that capacity is achievable. Simulations confirm the analytically predicted behavior. For the class of channels with memory known as discrete finite-state channels with complete, noiseless feedback (DFSCf' s), the framework is used to develop linear-complexity coding schemes performing analogously in terms of rate and reliability to the schemes developed for DMCf' s. The framework is then used for coding over unknown DFSCf's. A linear-complexity universal communication scheme whose rate varies with the quality of the realized channel is developed and analyzed. The asymptotic rate and reliability characteristics of this universal scheme are shown to be similar to those of the schemes developed for known channels. An extension of the compressed-error-cancellation framework is developed for discrete memoryless multiple-access channels with complete, noiseless feedback and leads to linear-complexity coding schemes achieving rates on the frontier of the feedback-free capacity region. Finally, the compressed-error-cancellation framework is applied to the problem of coding for channels with noisy and partial feedback. The scheme developed for DMCf's is modified to incorporate Slepian-Wolf coded feedback, resulting in a linear-complexity, capacity-achieving coding scheme with partial, noiseless feedback. This modified scheme, of which the ARQ protocol is shown to be a special case, is then used as an outer code in a concatenated coding arrangement; with a forward error-correcting (FEC) code used as the inner code, a framework emerges for integrating FEC coding with feedback coding, leading to a broad class of coding schemes using various amounts of noiseless feedback. Preliminary investigations on partial-feedback multiple-access scenarios and noisy feedback scenarios are also discussed. Thesis Supervisor: Gregory W. Wornell Title: Associate Professor of Electrical Engineering