Feedback Capacity of a Class of Symmetric Finite-State Markov Channels

Sen, Nevroz; Alajaji, Fady; Yüksel, Serdar

doi:10.1109/tit.2011.2146350

Cited by 17 publications

(11 citation statements)

References 30 publications

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“…Discrete noiseless channels and memoryless channels belong to this class; for such channels, feedback does not increase the capacity [4]. Class A type channels also include finite state stationary Markov channels which are indecomposable [33], and non-Markov channels which satisfy certain symmetry properties [37]. Further examples can be found in [5], [40].…”

Section: Iv1 Definitionmentioning

confidence: 99%

Metric and Topological Entropy Bounds for Optimal Coding of Stochastic Dynamical Systems

Kawan

Yüksel

2020

IEEE Trans. Automat. Contr.

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We consider the problem of optimal zero-delay coding and estimation of a stochastic dynamical system over a noisy communication channel under three estimation criteria concerned with the low-distortion regime. The criteria considered are (i) a strong and (ii) a weak form of almost sure stability of the estimation error as well as (ii) quadratic stability in expectation. For all three objectives, we derive lower bounds on the smallest channel capacity C0 above which the objective can be achieved with an arbitrarily small error. We first obtain bounds through a dynamical systems approach by constructing an infinite-dimensional dynamical system and relating the capacity with the topological and the metric entropy of this dynamical system. We also consider information-theoretic and probabilitytheoretic approaches to address the different criteria. Finally, we prove that a memoryless noisy channel in general constitutes no obstruction to asymptotic almost sure state estimation with arbitrarily small errors, when there is no noise in the system. The results provide new solution methods for the criteria introduced (e.g., standard information-theoretic bounds cannot be applied for some of the criteria) and establish further connections between dynamical systems, networked control, and information theory, and especially in the context of nonlinear stochastic systems.f w (x) = f (x, w), f x (w) = f (x, w).so that f w : X → X and f x : W → X.

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Section: Iv1 Definitionmentioning

confidence: 99%

Metric and Topological Entropy Bounds for Optimal Coding of Stochastic Dynamical Systems

Kawan

Yüksel

2020

IEEE Trans. Automat. Contr.

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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%

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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“…For such channels, it is known that feedback does not increase the capacity. Such a class also includes finite state stationary Markov channels which are indecomposable [72], and non-Markov channels which satisfies certain symmetry properties [82]. Further examples are studied in [87] and in [20].…”

Section: Channels With Memorymentioning

confidence: 99%

Characterization of Information Channels for Asymptotic Mean Stationarity and Stochastic Stability of Nonstationary/Unstable Linear Systems

Yüksel

2012

IEEE Trans. Inform. Theory

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Abstract-Stabilization of non-stationary linear systems over noisy communication channels is considered. Stochastically stable sources, and unstable but noise-free or bounded-noise systems have been extensively studied in information theory and control theory literature since 1970s, with a renewed interest in the past decade. There have also been studies on non-causal and causal coding of unstable/non-stationary linear Gaussian sources. In this paper, tight necessary and sufficient conditions for stochastic stabilizability of unstable (non-stationary) possibly multi-dimensional linear systems driven by Gaussian noise over discrete channels (possibly with memory and feedback) are presented. Stochastic stability notions include recurrence, asymptotic mean stationarity and sample path ergodicity, and the existence of finite second moments. Our constructive proof uses random-time state-dependent stochastic drift criteria for stabilization of Markov chains. For asymptotic mean stationarity (and thus sample path ergodicity), it is sufficient that the capacity of a channel is (strictly) greater than the sum of the logarithms of the unstable pole magnitudes for memoryless channels and a class of channels with memory. This condition is also necessary under a mild technical condition. Sufficient conditions for the existence of finite average second moments for such systems driven by unbounded noise are provided.Keywords: Stochastic stability, asymptotic mean stationarity, non-asymptotic information theory, Markov chains, stochastic control, feedback. I. PROBLEM FORMULATIONThis paper considers stochastic stabilization of linear systems controlled or estimated over discrete noisy channels with feedback. We consider first a scalar LTI discrete-time system (we consider multi-dimensional systems in Section IV) described byHere x t is the state at time t, u t is the control input, the initial condition x 0 is a second order random variable, and {d t } is a sequence of zero-mean independent, identically distributed (i.i.d.) Gaussian random variables. It is assumed that |a| ≥ 1 This system is connected over a Discrete Noisy Channel with a finite capacity to a controller, as shown in Figure 1.The controller has access to the information it has received through the channel. The controller in our model estimates the state and then applies its control. Remark 1.1: We note that the existence of the control can also be regarded as an estimation correction, and all results regarding stability may equivalently be viewed as the stability of the estimation error. Thus, the two problems are identical for such a controllable system and the reader unfamiliar with control theory can simply replace the stability of the state, with the stability of the estimation error.Recall the following definitions. Definition 1.1: A finite-alphabet channel with memory is characterized by a sequence of finite input alphabets M n+1 , finite output alphabets M ′ n+1 , and a sequence of conditional probability measures P n (qto R, with, Definition 1.2:A Discrete...

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Feedback Capacity of a Class of Symmetric Finite-State Markov Channels

Cited by 17 publications

References 30 publications

Metric and Topological Entropy Bounds for Optimal Coding of Stochastic Dynamical Systems

Metric and Topological Entropy Bounds for Optimal Coding of Stochastic Dynamical Systems

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

Characterization of Information Channels for Asymptotic Mean Stationarity and Stochastic Stability of Nonstationary/Unstable Linear Systems

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