The feedback capacity of the binary erasure channel with a no-consecutive-ones input constraint

Oron Sabag, Haim H. Permuter, Navin Kashyap

Research output: Contribution to journalArticlepeer-review

27 Scopus citations


The input-constrained erasure channel with feedback is considered, where the binary input sequence contains no consecutive ones, i.e., it satisfies the (1,∞)-RLL constraint. We derive the capacity for this setting, which can be expressed as {equation presented}, where ∈ is the erasure probability and Hb(.) is the binary entropy function. Moreover, we prove that a priori knowledge of the erasure at the encoder does not increase the feedback capacity. The feedback capacity was calculated using an equivalent dynamic programming (DP) formulation with an optimal average-reward that is equal to the capacity. Furthermore, we obtained an optimal encoding procedure from the solution of the DP, leading to a capacity-achieving, zero-error coding scheme for our setting. DP is, thus, shown to be a tool not only for solving optimization problems, such as capacity calculation, but also for constructing optimal coding schemes. The derived capacity expression also serves as the only non-trivial upper bound known on the capacity of the input-constrained erasure channel without feedback, a problem that is still open.

Original languageEnglish
Article number7308065
Pages (from-to)8-22
Number of pages15
JournalIEEE Transactions on Information Theory
Issue number1
StatePublished - 1 Jan 2016


  • Binary erasure channel
  • Constrained coding
  • Dynamic
  • Feedback capacity
  • Programming
  • Runlength-limited (RLL) constraints

ASJC Scopus subject areas

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


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