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# On Körner-Marton's sum modulo two problem

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Sefidgaran, M
; Sharif University of Technology
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2015

481
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- Type of Document: Article
- DOI: 10.1109/IWCIT.2015.7140207
- Publisher: Institute of Electrical and Electronics Engineers Inc , 2015
- Abstract:
- In this paper we study the sum modulo two problem proposed by Körner and Marton. In this source coding problem, two transmitters who observe binary sources X and Y, send messages of limited rate to a receiver whose goal is to compute the sum modulo of X and Y. This problem has been solved for the two special cases of independent and symmetric sources. In both of these cases, the rate pair (H(X|Y), H(Y|X)) is achievable. The best known outer bound for this problem is a conventional cut-set bound, and the best known inner bound is derived by Ahlswede and Han using a combination of Slepian-Wolf and Körner-Marton's coding schemes. In this paper, we propose a new outer bound which is strictly better than the cut-set bound. In particular, we show that the rate pair (H(X|Y), H(Y|X)) is not achievable for any binary sources other than independent and symmetric sources. Then, we study the minimum achievable sum-rate using Ahlswede-Han's region and propose a conjecture that this amount is not less than minimum of Slepian-Wolf and Körner-Marton's achievable sum-rates. We provide some evidences for this conjecture
- Keywords:
- Bins ; Communication channels (information theory) ; Image coding ; Achievable sum rates ; Binary sources ; Coding scheme ; Cut-set bound ; Outer bounds ; Slepian-wolf ; Source-coding ; Information theory
- Source: IWCIT 2015 - Iran Workshop on Communication and Information Theory, 6 May 2015 through 7 May 2015 ; May , 2015 ; 9781479982356 (ISBN)
- URL: http://ieeexplore.ieee.org/document/7140207/?arnumber=7140207