科研之友
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摘要
An upper bound on the feedback capacity of unifilar finite-state channels (FSCs) is derived. A new technique, called the Q-context mapping, is based on a construction of a directed graph that is used for a sequential quantization of the receiver's output sequences to a finite set of contexts. For any choice of Q-graph, the feedback capacity is bounded by a single-letter expression, C-fb <= sup I (X, S; Y vertical bar Q), where the supremum is over p(x vertical bar s, q) and the distribution of (S, Q) is their stationary distribution. It is shown that 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 no-consecutive-ones input-constrained erasure channel, and the memoryless channel. Its efficiency is also demonstrated by deriving a new capacity result for the dicode erasure channel; the upper bound is obtained directly from the above-mentioned expression and its tightness is concluded with a general sufficient condition on the optimality of the upper bound. This sufficient condition is based on a fixed point principle of the BCJR equation and, indeed, formulated as a simple lower bound on feedback capacity of unifilar FSCs for arbitrary Q-graphs. This upper bound indicates that a single-letter expression might exist for the capacity of finite-state channels with or without feedback based on a construction of auxiliary random variable with specified structure, such as the Q-graph, and not with i.i.d distribution. The upper bound also serves as a non-trivial bound on the capacity of channels without feedback, a problem that is still open.
- 出版日期2017-3
