Capacity and coding for the ising channel with feedback

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36 Scopus citations


The Ising channel, which was introduced in 1990, is a channel with memory that models intersymbol 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=(2Hb(a)/3+a) ≈ 0.575522 , where (a) is a particular root of a fourth-degree polynomial and (Hbx) denotes the binary entropy function. Simultaneously, (a=arg max0≤x≤1(2H b(x)/3+x). Finally, an error-free, capacity-achieving coding scheme is provided together with the outlining of a strong connection between the DP results and the coding scheme.

Original languageEnglish
Article number6840313
Pages (from-to)5138-5149
Number of pages12
JournalIEEE Transactions on Information Theory
Issue number9
StatePublished - 19 Jun 2014


  • Bellman Equation
  • Ising channel
  • dynamic program
  • feedback capacity
  • infinite-horizon
  • value iteration

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


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