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Entropy 2012, 14(12), 2589-2610; doi:10.3390/e14122589
Article

Capacity Bounds and Mapping Design for Binary Symmetric Relay Channels

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Received: 1 September 2012; in revised form: 4 December 2012 / Accepted: 6 December 2012 / Published: 17 December 2012
(This article belongs to the Special Issue Information Theory Applied to Animal Communication)
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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.
Keywords: binary symmetric relay channel; decode-and-forward; compress-and-forward; linear relaying; capacity bounds; binary Fourier transform binary symmetric relay channel; decode-and-forward; compress-and-forward; linear relaying; capacity bounds; binary Fourier transform
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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MDPI and ACS Style

Khormuji, M.N.; Skoglund, M. Capacity Bounds and Mapping Design for Binary Symmetric Relay Channels. Entropy 2012, 14, 2589-2610.

AMA Style

Khormuji MN, Skoglund M. Capacity Bounds and Mapping Design for Binary Symmetric Relay Channels. Entropy. 2012; 14(12):2589-2610.

Chicago/Turabian Style

Khormuji, Majid N.; Skoglund, Mikael. 2012. "Capacity Bounds and Mapping Design for Binary Symmetric Relay Channels." Entropy 14, no. 12: 2589-2610.


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