The feedback capacity of the binary symmetric channel with a no-consecutive-ones input constraint

Sabag, Oron; Permuter, Haim H.; Kashyap, Navin

doi:10.1109/allerton.2015.7446999

Cited by 7 publications

(4 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Theorem 5.3 says that feedback may increase the capacity of input-constrained erasure channels even if there is no channel memory. These two theorems, together with the results in [38,44], suggest the intricacy of the interplay between feedback, memory and input constraints.…”

Section: Full Asymptoticsmentioning

confidence: 82%

“…Remark 5.5. Recently, Sabag et al [38] also computed an explicit asymptotic formula for the feedback capacity of a BSC(ε) with the input supported on the (1, ∞)-RLL constraint. By comparing the asymptotics of the feedback capacity with the that of non-feedback capacity [19], they showed that feedback does increase the channel capacity in the high SNR regime.…”

Section: Feedback With Input-constraintmentioning

confidence: 99%

See 1 more Smart Citation

Asymptotics of Input-Constrained Erasure Channel Capacity

Lü

Han

2018

IEEE Trans. Inform. Theory

View full text Add to dashboard Cite

In this paper, we examine an input-constrained erasure channel and we characterize the asymptotics of its capacity when the erasure rate is low. More specifically, for a general memoryless erasure channel with its input supported on an irreducible finite-type constraint, we derive partial asymptotics of its capacity, using some series expansion type formulas of its mutual information rate; and for a binary erasure channel with its first-order Markovian input supported on the (1, ∞)-RLL constraint, based on the concavity of its mutual information rate with respect to some parameterization of the input, we numerically evaluate its first-order Markov capacity and further derive its full asymptotics. The asymptotics obtained in this paper, when compared with the recently derived feedback capacity for a binary erasure channel with the same input constraint, enable us to draw the conclusion that feedback may increase the capacity of an input-constrained channel, even if the channel is memoryless.Index Terms: erasure channel, input constraint, capacity, feedback. * A preliminary version of this work has been presented in IEEE ISIT 2014.

show abstract

Section: Full Asymptoticsmentioning

confidence: 82%

Section: Feedback With Input-constraintmentioning

confidence: 99%

Asymptotics of Input-Constrained Erasure Channel Capacity

Lü

Han

2018

IEEE Trans. Inform. Theory

View full text Add to dashboard Cite

show abstract

“…As discussed in Section I, this gives a counterexample to a claim of Shannon's from [17]. A subsequent work [28] related to the conference version of our paper [29] used a novel technique to calculate upper bounds on the non-feedback capacity of the input-constrained BSC. The upper bound in [28] is a tighter upper bound than our feedback capacity, which shows that feedback increases capacity not only for small values of α, but actually for all α.…”

Section: B Feedback Increases Capacitymentioning

confidence: 95%

Feedback Capacity and Coding for the BIBO Channel With a No-Repeated-Ones Input Constraint

Sabag

Permuter

Kashyap

2018

IEEE Trans. Inform. Theory

Self Cite

View full text Add to dashboard Cite

In this paper, a general binary-input binary-output (BIBO) channel is investigated in the presence of feedback and input constraints. The feedback capacity and the optimal input distribution of this setting are calculated for the case of an (1, ∞)-RLL input constraint, that is, the input sequence contains no consecutive ones. These results are obtained via explicit solution of an equivalent dynamic programming optimization problem. A simple coding scheme is designed based on the principle of posterior matching, which was introduced by Shayevitz and Feder for memoryless channels. The posterior matching scheme for our input-constrained setting is shown to achieve capacity using two new ideas: history bits, which captures the memory embedded in our setting, and message-interval splitting, which eases the analysis of the scheme. Additionally, in the special case of an S-channel, we give a very simple zero-error coding scheme that is shown to achieve capacity. For the input-constrained BSC, we show using our capacity formula that feedback increases capacity when the cross-over probability is small.

show abstract

“…The feedback capacity was first formulated as a dynamic program for Markov channels without ISI in [12] and for a subclass of Markov channels in [16]. Modeling the feedback capacity as a dynamic program and implementing algorithms to solve the Bellman equation has also been used to compute the feedback capacity of the trapdoor channel [8], the binary Ising channel [17], the input-constrained BSC [18] and the input-constrained binary erasure channel [19]. In [20], reinforcement learning (RL) algorithms have been proposed to estimate the feedback capacity of a class of unifilar FSCs.…”

Section: Introductionmentioning

confidence: 99%

Capacity of Finite State Channels with Feedback: Algorithmic and Optimization Theoretic Properties

Grigorescu¹,

Boche²,

Schaefer³

et al. 2022

Preprint

View full text Add to dashboard Cite

The capacity of finite state channels (FSCs) with feedback has been shown to be a limit of a sequence of multiletter expressions. Despite many efforts, a closed-form singleletter capacity characterization is unknown to date. In this paper, the feedback capacity is studied from a fundamental algorithmic point of view by addressing the question of whether or not the capacity can be algorithmically computed. To this aim, the concept of Turing machines is used, which provides fundamental performance limits of digital computers. It is shown that the feedback capacity of FSCs is not Banach-Mazur computable and therefore not Borel-Turing computable. As a consequence, it is shown that either achievability or converse is not Banach-Mazur computable, which means that there are computable FSCs for which it is impossible to find computable tight upper and lower bounds. Furthermore, it is shown that the feedback capacity cannot be characterized as the maximization of a finite-letter formula of entropic quantities.

show abstract

The feedback capacity of the binary symmetric channel with a no-consecutive-ones input constraint

Cited by 7 publications

References 13 publications

Asymptotics of Input-Constrained Erasure Channel Capacity

Asymptotics of Input-Constrained Erasure Channel Capacity

Feedback Capacity and Coding for the BIBO Channel With a No-Repeated-Ones Input Constraint

Capacity of Finite State Channels with Feedback: Algorithmic and Optimization Theoretic Properties

Contact Info

Product

Resources

About