Abstract
Capacity bounds for a three-node binary symmetric relay channel with orthogonal components at the destination are studied. The cut-set upper bound and the rates achievable using decode-and-forward (DF), partial DF and compress-and-forward (CF) relaying are first evaluated. Then relaying strategies with finite memory-length are considered. An efficient algorithm for optimizing the relay functions is presented. The Boolean Fourier transform is then employed to unveil the structure of the optimized mappings. Interestingly, the optimized relay functions exhibit a simple structure. Numerical results illustrate that the rates achieved using the optimized low-dimensional functions are either comparable to those achieved by CF or superior to those achieved by DF relaying. In particular, the optimized low-dimensional relaying scheme can improve on DF relaying when the quality of the source-relay link is worse than or comparable to that of other links.
Highlights
We focus on a relay network in which each link is a binary symmetric channel
We study decode-and-forward (DF), partial decode-and-forward (PDF), compress-and-forward (CF) and general finite-memory relay mappings
We show that one can improve on the result presented in [14] and illustrate that it is possible to approach the capacity upper bound for some cases by using the proposed low-dimensional mappings
Summary
This channel is considered in [1,2]. We desire to quantify the supremum of the set of rates, R, for which the average message error probability at the destination can be made to approach zero as the number of channel uses n goes to infinity. This number is the capacity, C, in the communication between the source and destination.
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