A single-letter upper bound on the feedback capacity of unifilar finite-state channels

Sabag, Oron; Permuter, Haim H.; Pfister, Henry D.

doi:10.1109/isit.2016.7541311

Cited by 15 publications

(47 citation statements)

References 11 publications

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“…We shall make use of the following single-letter bounds on feedback capacity (specialized to input-constrained DMCs) of [12]. The theorem below provides a lower bound on C fb DM C by considering input distributions that are BCJR-invariant.…”

Section: Bounds On Feedback Capacitymentioning

confidence: 99%

“…Theorem II.1 ( [12], Theorem 3). The feedback capacity, C fb DM C , of input-constrained DMCs is lower bounded as…”

Section: Bounds On Feedback Capacitymentioning

confidence: 99%

“…The next theorem, which is a specialization of Theorem 2 of [12], provides a single-letter upper bound on C fb DMC , when the presentation of the input constraint is assumed to be irreducible: for all irreducible Q-graphs with q 0 such that (s 0 , q 0 ) lies in an aperiodic closed communicating class.…”

Section: Bounds On Feedback Capacitymentioning

confidence: 99%

“…Our techniques involve the use of the single-letter bounding techniques of Sabag et al in [12], and we come up with a specific Q-graph (or a Q-context mapping) and a choice of a specific "BCJR-invariant" input distribution, which gives rise to an achievable rate.…”

Section: Introductionmentioning

confidence: 99%

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Bounds on the Feedback Capacity of the $(d,\infty)$-RLL Input-Constrained Binary Erasure Channel

Rameshwar¹,

Kashyap²

2021

Preprint

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The paper considers the input-constrained binary erasure channel (BEC) with causal, noiseless feedback. The channel input sequence respects the (d, ∞)-runlength limited (RLL) constraint, i.e., any pair of successive 1s must be separated by at least d 0s. We derive upper and lower bounds on the feedback capacity of this channel, for all d ≥ 1, given by: max, where the functiondδ+ 1 1− , with ∈ [0, 1] denoting the channel erasure probability, and h b (•) being the binary entropy function. We note that our bounds are tight for the case when d = 1 (see Sabag et al. (2016)), and, in addition, we demonstrate that for the case when d = 2, the feedback capacity is equal to the capacity with noncausal knowledge of erasures, for ∈ [0, 1 − 1 2 log(3/2) ]. For d > 1, our bounds differ from the non-causal capacities (which serve as upper bounds on the feedback capacity) derived in Peled et al. (2019) in only the domains of maximization. The approach in this paper follows Sabag et al. (2017), by deriving single-letter bounds on the feedback capacity, based on output distributions supported on a finite Q-graph, which is a directed graph with edges labelled by output symbols.

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Section: Bounds On Feedback Capacitymentioning

confidence: 99%

“…Theorem II.1 ( [12], Theorem 3). The feedback capacity, C fb DM C , of input-constrained DMCs is lower bounded as…”

Section: Bounds On Feedback Capacitymentioning

confidence: 99%

Section: Bounds On Feedback Capacitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Bounds on the Feedback Capacity of the $(d,\infty)$-RLL Input-Constrained Binary Erasure Channel

Rameshwar¹,

Kashyap²

2021

Preprint

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“…For a sub-family of unifilar FSCs where the channel state is a deterministic function of the channel output, a single-letter feedback capacity expression was derived and formulated as a DP optimization problem in [41]. Another method to compute explicit capacity expressions is the Q-graph that was introduced and utilized in [48],…”

Section: Introductionmentioning

confidence: 99%

The Feedback Capacity of Noisy Output is the STate (NOST) Channels

Shemuel¹,

Sabag²,

Permuter³

2021

Preprint

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We consider finite-state channels (FSCs) where the channel state is stochastically dependent on the previous channel output. We refer to these as Noisy Output is the STate (NOST) channels. We derive the feedback capacity of NOST channels in two scenarios: with and without causal state information (CSI) available at the encoder. If CSI is unavailable, the feedback capacity iswhile if it is available at the encoder, the feedback capacity iswhere U is an auxiliary random variable with finite cardinality. In both formulas, the output process is a Markov process with stationary distribution. The derived formulas generalize special known instances from the literature, such as where the state is distributed i.i.d. and where it is a deterministic function of the output. C FB and C FB-CSI are also shown to be computable via concave optimization problem formulations. Finally, we give a sufficient condition under which CSI available at the encoder does not increase the feedback capacity, and we present an interesting example that demonstrates this.

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