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

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

doi:10.1109/tit.2018.2809554

Cited by 25 publications

(24 citation statements)

References 37 publications

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“…A useful approach for computing the feedback capacity is via dynamic programming (DP) methods [11]- [13]. When the DP problem can be solved analytically, simple capacity expressions and optimal coding schemes can be determined [14]- [21]. However, in most cases analytical solutions are infeasible.…”

Section: Introductionmentioning

confidence: 99%

“…We will present a posterior matching (PM) scheme that achieves the lower bound for any graph-based encoder. The scheme is inspired by the PM principle for memoryless channels [23] that was extended to systems with memory [21]. Thus, any graph-based encoder implies a simple coding scheme that achieves I(X, S; Y |Q) even if the lower bound does not attain the capacity.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Graph-Based Encoders and Their Performance for Finite-State Channels With Feedback

Sabag

Huleihel

Permuter

2020

IEEE Trans. Commun.

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The capacity of unifilar finite-state channels in the presence of feedback is investigated. We derive a new evaluation method to extract graph-based encoders with their achievable rates, and to compute upper bounds to examine their performance. The evaluation method is built upon a recent methodology to derive simple bounds on the capacity using auxiliary directed graphs. While it is not clear whether the upper bound is convex, we manage to formulate it as a convex optimization problem using transformation of the argument with proper constraints. The lower bound is formulated as a non-convex optimization problem, yet, any feasible point to the optimization problem induces a graph-based encoders. In all examples, the numerical results show near-tight upper and lower bounds that can be easily converted to analytic results. For the non-symmetric Trapdoor channel and binary fading channels (BFCs), new capacity results are eastablished by computing the corresponding bounds. For all other instances, including the Ising channel, the near-tightness of the achievable rates is shown via a comparison with corresponding upper bounds. Finally, we show that any graph-based encoder implies a simple coding scheme that is based on the posterior matching principle and achieves the lower bound.where the joint distribution is π S,Q P X|S,Q P Y |X,S , and π S,Q denotes a stationary distribution. For DRAFT

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Graph-Based Encoders and Their Performance for Finite-State Channels With Feedback

Sabag

Huleihel

Permuter

2020

IEEE Trans. Commun.

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“…where the feedback capacity is explicitly determined include the ANC [17], the finite-state channel with states known at both transmitter and receiver [31], the trapdoor channel [32], the Ising channel [33], the symmetric finite-state Markov channel [34], and the BEC [10] and the binary-input binary-output channel [35] with both channels subjected to a no consecutive ones input constraint.…”

Section: Single-letter Expressions or Exact Values Of Such Capacitiesmentioning

confidence: 99%

“…where (35) holds since X 1 = V 1 , (36) follows from (6), (37) follows form (1) and the fact that the noise process is independent of the message, (38) holds since X 2 = f * (V 2 , Z 1 ) and (39) is obtained by repeating the steps (35)- (38). To analyze the first term in (34), we consider Pr(Y i = y i |Y i−1 = y i−1 ) for two cases:…”

Section: Nec Capacity-cost Function With Feedbackmentioning

confidence: 99%

Capacity of Burst Noise-Erasure Channels With and Without Feedback and Input Cost

Song

Alajaji

Linder

2019

IEEE Trans. Inform. Theory

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A class of burst noise-erasure channels which incorporate both errors and erasures during transmission is studied. The channel, whose output is explicitly expressed in terms of its input and a stationary ergodic noise-erasure process, is shown to have a so-called "quasi-symmetry" property under certain invertibility conditions. As a result, it is proved that a uniformly distributed input process maximizes the channel's block mutual information, resulting in a closed-form formula for its non-feedback capacity in terms of the noise-erasure entropy rate and the entropy rate of an auxiliary erasure process. The feedback channel capacity is also characterized, showing that feedback does not increase capacity and generalizing prior related results. The capacity-cost function of the channel with and without feedback is also investigated. A sequence of finite-letter upper bounds for the capacity-cost function without feedback is derived. Finite-letter lower bonds for the capacity-cost function with feedback are obtained using a specific encoding rule. Based on these bounds, it is demonstrated both numerically and analytically that feedback can increase the capacity-cost function for a class of channels with Markov noise-erasure processes. Index TermsChannels with burst errors and erasures, channels with memory, channel symmetry, non-feedback and feedback capacities, non-feedback and feedback capacity-cost functions, input cost constraints, stationary ergodic and Markov processes.The authors are with the

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“…To facilitate this analysis, the convex analytic method [32] was used, e.g., in [8] and [33], while in [26], [34], [35], [36], [27], [37], and [38] the average cost optimality equation was used (typically through the vanishing discount method). In particular, [34], [37], and [38] use this latter approach to solve dynamic programs that provide explicit channel capacity expressions. In this paper (unlike in our earlier work [8]), we also use the average cost optimality equation approach, but here certain technical subtleties complicate…”

Section: B Literature Reviewmentioning

confidence: 99%

Optimal Zero Delay Coding of Markov Sources: Stationary and Finite Memory Codes

Wood

Linder

Yiksel

2017

IEEE Trans. Inform. Theory

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The optimal zero delay coding of a finite state Markov source is considered. The existence and structure of optimal codes are studied using a stochastic control formulation. Prior results in the literature established the optimality of deterministic Markov (Walrand-Varaiya type) coding policies for the finite time horizon problem, and the optimality of both deterministic nonstationary and randomized stationary policies for the infinite time horizon problem. Our main result here shows that for any irreducible and aperiodic Markov source with a finite alphabet, deterministic and stationary Markov coding policies are optimal for the infinite horizon problem. In addition, the finite blocklength (time horizon) performance on an optimal (stationary and Markov) coding policy is shown to approach the infinite time horizon optimum at a rate O(1/T ). The results are extended to systems where zero delay communication takes place across a noisy channel with noiseless feedback.

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

Cited by 25 publications

References 37 publications

Graph-Based Encoders and Their Performance for Finite-State Channels With Feedback

Graph-Based Encoders and Their Performance for Finite-State Channels With Feedback

Capacity of Burst Noise-Erasure Channels With and Without Feedback and Input Cost

Optimal Zero Delay Coding of Markov Sources: Stationary and Finite Memory Codes

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