Reliable communication under channel uncertainty

Lapidoth, Amos; Narayan, Paresh Kumar

doi:10.1109/18.720535

Cited by 452 publications

(457 citation statements)

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“…A less powerful model is that of the compound channel where the jammer has a choice of strategies, but the chosen channel law does not change during the transmission of various symbols of the codeword. AVCs have been the subject of much research -the reader can find a good introduction to this topic as well as numerous pointers to the extensive literature in a survey by Lapidoth and Narayan [54]. To the author's understanding, it seems that much of the work has been of a non-constructive flavor, driven by the information-theoretic motivation of determining the capacity under different AVC variants.…”

Section: Remark 1 [Arbitrarily Varying Channel]mentioning

confidence: 99%

Algorithmic Results in List Decoding

Guruswami

2006

FNT in Theoretical Computer Science

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Error-correcting codes are used to cope with the corruption of data by noise during communication or storage. A code uses an encoding procedure that judiciously introduces redundancy into the data to produce an associated codeword. The redundancy built into the codewords enables one to decode the original data even from a somewhat distorted version of the codeword. The central trade-off in coding theory is the one between the data rate (amount of non-redundant information per bit of codeword) and the error rate (the fraction of symbols that could be corrupted while still enabling data recovery). The traditional decoding algorithms did as badly at correcting any error pattern as they would do for the worst possible error pattern. This severely limited the maximum fraction of errors those algorithms could tolerate. In turn, this was the source of a big hiatus between the error-correction performance known for probabilistic noise models (pioneered by Shannon) and what was thought to be the limit for the more powerful, worst-case noise models (suggested by Hamming).In the last decade or so, there has been much algorithmic progress in coding theory that has bridged this gap (and in fact nearly eliminated it for codes over large alphabets). These developments rely on an error-recovery model called "list decoding," wherein for the pathological error patterns, the decoder is permitted to output a small list of candidates that will include the original message. This book introduces and motivates the problem of list decoding, and discusses the central algorithmic results of the subject, culminating with the recent results on achieving "list decoding capacity." Part IGeneral Literature

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Section: Remark 1 [Arbitrarily Varying Channel]mentioning

confidence: 99%

Algorithmic Results in List Decoding

Guruswami

2006

FNT in Theoretical Computer Science

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“…In standard information-hiding problems with a compound DMC attack channel, deterministic codes are enough to achieve capacity; random coding is used as a method of proof to establish the existence of a deterministic code without actually specifying the code [37]. In our steganography problem, a randomized code is used to satisfy the perfect-undetectability condition of (2).…”

Section: Secret Keymentioning

confidence: 99%

Perfectly Secure Steganography: Capacity, Error Exponents, and Code Constructions

Wang

Moulin²

2008

IEEE Trans. Inform. Theory

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An analysis of steganographic systems subject to the following perfect undetectability condition is presented in this paper. Following embedding of the message into the covertext, the resulting stegotext is required to have exactly the same probability distribution as the covertext. Then no statistical test can reliably detect the presence of the hidden message. We refer to such steganographic schemes as perfectly secure. A few such schemes have been proposed in recent literature, but they have vanishing rate. We prove that communication performance can potentially be vastly improved; specifically, our basic setup assumes independently and identically distributed (i.i.d.) covertext, and we construct perfectly secure steganographic codes from public watermarking codes using binning methods and randomized permutations of the code. The permutation is a secret key shared between encoder and decoder. We derive (positive) capacity and random-coding exponents for perfectly-secure steganographic systems. The error exponents provide estimates of the code length required to achieve a target low error probability.In some applications, steganographic communication may be disrupted by an active warden, modelled here by a compound discrete memoryless channel. The transmitter and warden are subject to distortion constraints. We address the potential loss in communication performance due to the perfect-security requirement. This loss is the same as the loss obtained under a weaker order-1 steganographic requirement that would just require matching of first-order marginals of the covertext and stegotext distributions. Furthermore, no loss occurs if the covertext distribution is uniform and the distortion metric is cyclically symmetric; steganographic capacity is then achieved by randomized linear codes. Our framework may also be useful for developing computationally secure steganographic systems that have near-optimal communication performance.

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“…Fortunately, such things have long been studied in information theory in the context of unknown fading channels [2]. Medard in [3] examines the effect of imperfect channel knowledge on capacity, and Lapidoth and Shamai quantify the degradation in performance due to channel-state estimation errors by the receiver [4].…”

Section: Introductionmentioning

confidence: 99%

“…As just one example, control theorists are interested in knowing how networked control systems behave with or without acknowledgements of dropped packets since this is relevant for choosing among practical protocols like TCP vs. UDP [1]. Acknowledgements are a kind of sideinformation about control channel state, but as of now, there is no theoretical guidance for how to think about it in a principled way.Fortunately, such things have long been studied in information theory in the context of unknown fading channels [2]. Medard in [3] examines the effect of imperfect channel knowledge on capacity, and Lapidoth and Shamai quantify the degradation in performance due to channel-state estimation errors by the receiver [4].…”

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confidence: 99%

Side-information in control and estimation

Ramnarayan

Ranade

Sahai

2014

2014 IEEE International Symposium on Information Theory

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Abstract-As in portfolio theory, we can think of the value of side-information in a control system as the change in the "growth rate" due to side-information. A scalar counterexample (motivated by carry-free deterministic models) shows the value of side-information for control does not exactly parallel the value of side-information for portfolios. Mutual-information does not seem to be a bound here.The concept is further explored through a spinning vector control system that is re-oriented at each time so that the control or observation direction is partially unknown. The value of sideinformation can be calculated in this setup and it behaves quite differently in a control vs. estimation context. A second example considers the problem of vector control over a (scalar) erasure channel, the dual problem to the estimation problem of intermittent Kalman Filtering. The value of information here is measured through the change in the critical packet-drop probability for the system. While non-causal side-information regarding the packet arrivals does not affect the critical probability for the estimation problem, we find that it can generically be very valuable for the control problem -it seems to change the scaling behavior for the control counterpart to what would be considered the "high SNR limit" in communication problems. I. INTRODUCTIONParameter uncertainty has a long history in control theory -the very idea of robust control is about dealing with it. Recently, the advent of networked control systems has made stochastic uncertainty models more relevant. There is now a real need to have a theory capable of dealing with sideinformation in control. As just one example, control theorists are interested in knowing how networked control systems behave with or without acknowledgements of dropped packets since this is relevant for choosing among practical protocols like TCP vs. UDP [1]. Acknowledgements are a kind of sideinformation about control channel state, but as of now, there is no theoretical guidance for how to think about it in a principled way.Fortunately, such things have long been studied in information theory in the context of unknown fading channels [2]. Medard in [3] examines the effect of imperfect channel knowledge on capacity, and Lapidoth and Shamai quantify the degradation in performance due to channel-state estimation errors by the receiver [4]. Pradhan et al. show that the duality between source and channel coding in fact extends to the case with side-information under certain conditions [5]: this is particularly interesting given the well-known parallel between source coding and portfolio theory, which we will connect to here. Further, Kotagiri and Laneman [6] study the impact of non-causal knowledge of the state in a multiple-access setting. There are many more interesting results as well, but space precludes any serious discussion here.

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Reliable communication under channel uncertainty

Cited by 452 publications

References 108 publications

Algorithmic Results in List Decoding

Algorithmic Results in List Decoding

Perfectly Secure Steganography: Capacity, Error Exponents, and Code Constructions

Side-information in control and estimation

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