Capacity and Coding for the Ising Channel With Feedback

DOI10.1109/TIT.2014.2331951zbMATH Open1360.94187arXiv1205.4674OpenAlexW2964209511MaRDI QIDQ2986134

Ohad Elishco, Haim Permuter

Publication date: 16 May 2017

Published in: IEEE Transactions on Information Theory (Search for Journal in Brave)

Abstract: The Ising channel, which was introduced in 1990, is a channel with memory that models Inter-Symbol interference. In this paper we consider the Ising channel with feedback and find the capacity of the channel together with a capacity-achieving coding scheme. To calculate the channel capacity, an equivalent dynamic programming (DP) problem is formulated and solved. Using the DP solution, we establish that the feedback capacity is the expression $C=(frac2H_b(a)3+a)approx0.575522$ where $a$ is a particular root of a fourth-degree polynomial and $H_b(x)$ denotes the binary entropy function. Simultaneously, $a=argma{x}_{0leqxleq1}(frac2H_b(x)3+x)$. Finally, a simple, error-free, capacity-achieving coding scheme is provided together with outlining a strong connection between the DP results and the coding scheme.

Full work available at URL: https://arxiv.org/abs/1205.4674

Mathematics Subject Classification ID

Measures of information, entropy (94A17) Coding theorems (Shannon theory) (94A24)

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