The Feedback Capacity of the Binary Erasure Channel With a No-Consecutive-Ones Input Constraint
Data(s) |
2016
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Resumo |
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. |
Formato |
application/pdf |
Identificador |
http://eprints.iisc.ernet.in/53366/1/IEEE_Tra_Inf_The_62-1_8_2016.pdf 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. |
Publicador |
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC |
Relação |
http://dx.doi.org/10.1109/TIT.2015.2495239 http://eprints.iisc.ernet.in/53366/ |
Palavras-Chave | #Electrical Communication Engineering |
Tipo |
Journal Article PeerReviewed |