The Feedback Capacity of the Binary Erasure Channel With a No-Consecutive-Ones Input Constraint

Sabag, Oron and Permuter, Haim H and Kashyap, Navin (2016) The Feedback Capacity of the Binary Erasure Channel With a No-Consecutive-Ones Input Constraint. In: IEEE TRANSACTIONS ON INFORMATION THEORY, 62 (1). pp. 8-22.

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Abstract

The input-constrained erasure channel with feedback is considered, where the binary input sequence contains no consecutive ones, i.e., it satisfies the (1, infinity)-RLL constraint. We derive the capacity for this setting, which can be expressed as C-is an element of = max(0 <= p <= 0.5) (1-is an element of) H-b (p)/1+(1-is an element of) p, where is an element of 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.

Item Type:	Journal Article
Publication:	IEEE TRANSACTIONS ON INFORMATION THEORY
Publisher:	IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
Additional Information:	Copy right for this article belongs to the IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 445 HOES LANE, PISCATAWAY, NJ 08855-4141 USA
Keywords:	Feedback capacity; constrained coding; dynamic programming; binary erasure channel; runlength-limited (RLL) constraints
Department/Centre:	Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited:	03 Mar 2016 05:44
Last Modified:	03 Mar 2016 05:44
URI:	http://eprints.iisc.ac.in/id/eprint/53366

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