Asymptotics of Input-Constrained Erasure Channel Capacity

Lü, Yonglong; Han, Guangyue

doi:10.1109/tit.2017.2742498

Cited by 12 publications

(13 citation statements)

References 40 publications

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“…Interestingly, our techniques recover the lower bounds given in [7], for the (d, k)-RIC BSC, for k < ∞. For the (1, ∞)-RIC BSC and BEC, the analytical lower bounds thus found compare favourably with asymptotic lower bounds given in [8], [9], and extend to all values of the channel parameters.…”

Section: Introductionsupporting

confidence: 68%

“…Analytical lower bounds were derived by Zehavi and Wolf [7] for binary symmetric channels with a (d, k)-runlength-limited (RLL) constraint -see Definition V.1 -at the input. Later works gave capacity lower bounds for input-constrained binary symmetric and binary erasure channels in the asymptotic (very low or very high noise) regimes [8], [9], [10]. Our work applies to a larger class of channels, and provides bounds for all values of the channel parameters.…”

Section: Introductionmentioning

confidence: 92%

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Computable Lower Bounds for Capacities of Input-Driven Finite-State Channels

Rameshwar

Kashyap

2020

2020 IEEE International Symposium on Information Theory (ISIT)

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This paper studies the capacities of input-driven finitestate channels, i.e., channels whose current state is a time-invariant deterministic function of the previous state and the current input. We lower bound the capacity of such a channel using a dynamic programming formulation of a bound on the maximum reverse directed information rate. We show that the dynamic programmingbased bounds can be simplified by solving the corresponding Bellman equation explicitly. In particular, we provide analytical lower bounds on the capacities of (d, k)-runlength-limited inputconstrained binary symmetric and binary erasure channels. Furthermore, we provide a single-letter lower bound based on a class of input distributions with memory.

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Section: Introductionsupporting

confidence: 68%

Section: Introductionmentioning

confidence: 92%

Computable Lower Bounds for Capacities of Input-Driven Finite-State Channels

Rameshwar

Kashyap

2020

2020 IEEE International Symposium on Information Theory (ISIT)

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“…least d 0s between any pair of successive 1s. As was shown in the works [7], [8], and [9], the capacities of the (1, ∞)-RLL inputconstrained binary erasure and binary symmetric channels are strictly larger than their respective non-feedback capacities, for at least some values of the channel parameters. Hence, Shannon's argument does not apply to DMCs with constrained inputs, and special tools are required to determine the feedback capacities of such channels.…”

Section: Introductionmentioning

confidence: 66%

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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“…It then follows that (13). Recursively applying the above inequality, we infer that there exist 0 < ξ < 1 and M ′ > 0 such that…”

Section: Convergence Analysismentioning

confidence: 83%

A Deterministic Algorithm for the Capacity of Finite-State Channels

Han

Marcus

2019

2019 IEEE International Symposium on Information Theory (ISIT)

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We propose a modified version of the classical gradient descent method to compute the capacity of finite-state channels with Markovian input. Under some concavity assumption, our algorithm proves to achieve a polynomial accuracy in a polynomial time for general finite-state channels. Moreover, for some special families of finite-state channels, our algorithm can achieve an exponential accuracy in a polynomial time.

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Asymptotics of Input-Constrained Erasure Channel Capacity

Cited by 12 publications

References 40 publications

Computable Lower Bounds for Capacities of Input-Driven Finite-State Channels

Computable Lower Bounds for Capacities of Input-Driven Finite-State Channels

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

A Deterministic Algorithm for the Capacity of Finite-State Channels

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