Math @ Duke

Publications [#325508] of Henry Pfister
Papers Published
 Sabag, O; Permuter, HH; Pfister, HD, Singleletter bounds on the feedback capacity of unifilar finitestate channels,
2016 Ieee International Conference on the Science of Electrical Engineering, Icsee 2016
(January, 2017), IEEE, ISBN 9781509021529 [doi]
(last updated on 2019/07/15)
Abstract: © 2016 IEEE. Upper and lower bounds on the feedback capacity of unifilar finitestate channels (FSCs) are derived. The upper bound is derived using a new technique, called the Qcontexts, which is based on a construction of a directed graph that is used to quantize recursively the receiver's output sequences to a finite set of contexts. For any choice of Qgraph, the feedback capacity is bounded by a singleletter expression, Cfb ≤ sup I (X, S; Y Q), where the supremum is over Pxs,q and the distribution of (S, Q) is their stationary distribution. The bound is tight for all unifilar FSCs where feedback capacity is known: channels where the state is a function of the outputs, the trapdoor channel, Ising channels, the noconsecutiveones inputconstrained erasure channel and for the memoryless channel. The upper bound indicates that a singleletter expression might exist for the capacity of finitestate channels with or without feedback which are based on a construction of auxiliary random variable with memory, such as Qgraph, and not with i.i.d distribution. The lower bound provides a sufficient condition for the optimality of the upper bound, however, it is formulated such that independent lower bounds on feedback capacity may be calculated. The efficiency of these bounds is demonstrated by deriving a new capacity result for the dicode erasure channel (DEC). The upper bound also serves as a nontrivial bound on the capacity of channels without feedback, a problem that is still open.


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