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Capacity Bounds and Mapping Design for Binary Symmetric Relay Channels
School of Electrical Engineering and ACCESS Linnaeus Center, Royal Institute of Technology (KTH), Stockholm, 100 44, Sweden
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Received: 1 September 2012; in revised form: 4 December 2012 / Accepted: 6 December 2012 / Published: 17 December 2012
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
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Cite This Article
MDPI and ACS Style
Khormuji, M.N.; Skoglund, M. Capacity Bounds and Mapping Design for Binary Symmetric Relay Channels. Entropy 2012, 14, 2589-2610.
Khormuji MN, Skoglund M. Capacity Bounds and Mapping Design for Binary Symmetric Relay Channels. Entropy. 2012; 14(12):2589-2610.
Khormuji, Majid N.; Skoglund, Mikael. 2012. "Capacity Bounds and Mapping Design for Binary Symmetric Relay Channels." Entropy 14, no. 12: 2589-2610.