Computable Upper Bounds on the Capacity of Finite-State Channels

Huleihel, Bashar; Sabag, Oron; Permuter, Haim H.; Kashyap, Navin; Shitz, Shlomo Shamai

doi:10.1109/tit.2021.3091691

Cited by 11 publications

(15 citation statements)

References 46 publications

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“…trapdoor channel capacities ,respectively. Estimated feedforwad capacity is compared with upper and lower bounds from [19] and [46], respectively, and the estimated feedback capacity is compared with the analytical solution from [10]. Figure 7 compares of results to those from [47] for the POST and [36] for the NOST channel.…”

Section: Nost and Post Channelsmentioning

confidence: 99%

“…However, these approaches are only feasible under restrictive struc-tural assumptions on the channel that enable tensorizing the multi-letter DI objective, e.g., unifilar 1 finite-state channels (FSCs) with feedback and symmetric channels. For more general channels 2 , the capacity can be bounded using the machinery of Q-graphs [18,19], but tight bounds require an exhaustive search over an exponentially large space. Furthermore, all the aforementioned approaches require full knowledge of the channel probabilistic model, which is often unavailable in practice.…”

Section: Introductionmentioning

confidence: 99%

“…Figure 6: Figures (a) and (b) present DINE loss convergence to the feedback and feedforward trapdoor channel capacities ,respectively. Estimated feedforwad capacity is compared with upper and lower bounds from[19] and[46], respectively, and the estimated feedback capacity is compared with the analytical solution from[10].…”

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confidence: 99%

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Optimizing Estimated Directed Information over Discrete Alphabets

Tsur

Aharoni

Goldfeld

et al. 2022

2022 IEEE International Symposium on Information Theory (ISIT)

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Directed information (DI) is a fundamental measure for the study and analysis of sequential stochastic models. In particular, when optimized over input distributions it characterizes the capacity of general communication channels. However, analytic computation of DI is typically intractable and existing optimization techniques over discrete input alphabets require knowledge of the channel model, which renders them inapplicable when only samples are available. To overcome these limitations, we propose a novel estimation-optimization framework for DI over discrete input spaces. We formulate DI optimization as a Markov decision process and leverage reinforcement learning techniques to optimize a deep generative model of the input process probability mass function (PMF). Combining this optimizer with the recently developed DI neural estimator, we obtain an end-to-end estimation-optimization algorithm which is applied to estimating the (feedforward and feedback) capacity of various discrete channels with memory. Furthermore, we demonstrate how to use the optimized PMF model to (i) obtain theoretical bounds on the feedback capacity of unifilar finite-state channels; and (ii) perform probabilistic shaping of constellations in the peak power-constrained additive white Gaussian noise channel.

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Section: Nost and Post Channelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Optimizing Estimated Directed Information over Discrete Alphabets

Tsur

Aharoni

Goldfeld

et al. 2022

2022 IEEE International Symposium on Information Theory (ISIT)

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“…• Despite the extensive research efforts [12], [24]- [28] dedicated to the trapdoor channel [29], see Fig. 2, its feedforward capacity has remained an open problem for over sixty years.…”

Section: A Main Contributionsmentioning

confidence: 99%

Capacity of the Trapdoor Channel with Delayed Feedback

Huleihel

Sabag

Permuter

2022

2022 IEEE International Symposium on Information Theory (ISIT)

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In this paper, we investigate the capacity of finite-state channels (FSCs) in presence of delayed feedback. We show that the capacity of a FSC with delayed feedback can be computed as that of a new FSC with instantaneous feedback and an extended state. Consequently, graph-based methods to obtain computable upper and lower bounds on the delayed feedback capacity of unifilar FSCs are proposed. Based on these methods, we establish that the capacity of the trapdoor channel with delayed feedback of two time instances is given by log 2 3 2 . In addition, we derive an analytical upper bound on the delayed feedback capacity of the binary symmetric channel with a no consecutive ones input constraint. This bound also serves as a novel upper bound on its non-feedback capacity, which outperforms all previously known bounds. Lastly, we demonstrate that feedback does improve the capacity of the dicode erasure channel.This paper was presented in part at the 2022 IEEE International Symposium on Information Theory [1]. 1 The Q-graph is an auxiliary directed graph that is used to map channel output sequences onto one of the graph nodes (e.g. see Fig. 4).

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“…First of all, we know that an Ising channel can behave the same as a Z−channel [47] if Y 𝑡−1 = 0. This mean that if bit "0" is received at the receiver side, this mean that the receiver cannot harvest any energy.…”

Section: Appendix D Proof Of Propositionmentioning

confidence: 99%

SIC Error Towards the Packet Error Rate: Optimal Partitioning in OTFS-NOMA Systems

Zamanipour¹

2022

Preprint

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<p>\textit{A system including a lamp and a door, each of which has two possible states $1$ or $0$, i.e., ''on/open'' and ''off/closed'': the states of the door and the lamp are independent of each other and the total Markov chain is the one with memory of variable length with the context-tree $(\tau, \mathscr{p})$ with regard to the transition probability $\mathscr{p}$ and $\tau\stackrel{def}{=}\{1, 10, 100, \cdots\}\cup \{ 0^{\infty} \}$. Now, consider the lamp and the total system as the successive interference cancellation (SIC) error $-$ due to the imperfect SIC $-$ and the total packet error rate, respectively. How can we optimally determine the aforementioned variable length and adjust its variability in practice?} This paper technically explores orthogonal time-frequency-space (OTFS) modulation assisted non-orthogonal multiple access (NOMA) systems and the packet error rate mainly arising from the SIC imperfectness from an information-theoretic point of view. With a given prior distribution, we aim at marginalising over $\mathscr{SUFF}$ on all models $\mathscr{SUFF}$ of maximal depth $\mathscr{D}$ where according to the nature of the OTFS-NOMA principle, $\Big(\mathscr{SUFF}, \mathscr{D} \Big)=f\Big(\mathcal{T} (sec), \Delta f (Hz), \mathcal{N}^{(sample)}, \mathcal{M}^{(sample)}\Big)$ holds as a function of the OTFS-NOMA pair $\Big(\mathcal{N}^{(sample)}, \mathcal{M}^{(sample)}\Big)$. We theoretically make a solution to two scenarios of the availability and unavailability of the casual state-information (CSI) at the encoder, as well as an interpretation over e.g. enegy-level. </p>

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Computable Upper Bounds on the Capacity of Finite-State Channels

Cited by 11 publications

References 46 publications

Optimizing Estimated Directed Information over Discrete Alphabets

Optimizing Estimated Directed Information over Discrete Alphabets

Capacity of the Trapdoor Channel with Delayed Feedback

SIC Error Towards the Packet Error Rate: Optimal Partitioning in OTFS-NOMA Systems

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