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50th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

作者： Torbatian, Mehdi Yang, En-hui Univ Waterloo Dept Elect & Comp Engn Waterloo ON N2L 3G1 Canada

ISBN: (纸本)9781467345392;9781467345378

We consider causal coding of three jointly Gaussian correlated sources, X-1, X-2, X-3, with a given covariance matrix and determine an analytic closed-form formula for its total rate distortion function subject to Mean Square Error (MSE) distortion constraints when all sources need a positive rate to be represented. It is first shown that the optimal reproduction random variables are jointly Gaussian with the sources. A novel causal coding scheme is then proposed to achieve the total rate distortion function, in which each source is first whitened with respect to all previous original sources and then encoded via encoding a proper linear combination of the residues of the previous sources with respect to all available encoded sources and the residue of the current source with respect to all previous original sources. The more-and-less coding theorem in causal coding of correlated sources-when sources do not form a Markov chain as X-1 -> X-2 -> X-3, under some conditions on sources and distortion, the more sources need to be encoded, the less total rate is required-is also investigated for Gaussian sources. For the underlying scenario in which all sources need a positive rate to be represented, it is proved that the more-and-less coding is always revealed for non-Markov chain Gaussian sources.

关键词： causal coding Gaussian sources more-and-less coding theorem rate-distortion theory

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causal coding of Multiple Jointly Gaussian Sources

Causal Coding of Multiple Jointly Gaussian Sources

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Annual Allerton Conference on Communication, Control, and Computing

作者： Mehdi Torbatian En-hui Yang Department of Electrical and Computer Engineering University of Waterloo

ISBN: (纸本)9781467345378

We consider causal coding of three jointly Gaussian correlated sources, X_1, X_2, X_3, with a given covariance matrix and determine an analytic closed-form formula for its total rate distortion function subject to Mean Square Error (MSE) distortion constraints when all sources need a positive rate to be represented. It is first shown that the optimal reproduction random variables are jointly Gaussian with the sources. A novel causal coding scheme is then proposed to achieve the total rate distortion function, in which each source is first whitened with respect to all previous original sources and then encoded via encoding a proper linear combination of the residues of the previous sources with respect to all available encoded sources and the residue of the current source with respect to all previous original sources. The more-and-less coding theorem in causal coding of correlated sources - when sources do not form a Markov chain as X_1 → X_2 → X_3, under some conditions on sources and distortion, the more sources need to be encoded, the less total rate is required - is also investigated for Gaussian sources. For the underlying scenario in which all sources need a positive rate to be represented, it is proved that the more-and-less coding is always revealed for non-Markov chain Gaussian sources.

关键词： causal coding Gaussian sources More-and-less coding theorem Rate-distortion theory

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coding for the degraded broadcast channel with random parameters, with causal and noncausal side information

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IEEE TRANSACTIONS ON INFORMATION THEORY 2005年第8期51卷 2867-2877页

作者： Steinberg, Y Technion Israel Inst Technol Dept Elect Engn IL-32000 Haifa Israel

In this work, coding for the degraded broadcast channel controlled by random parameters is studied. Two main paradigms are considered: where side information on the random parameters is provided to the transmitter in a noncausal manner (termed here noncausal coding), and where side information is provided in a causal manner (termed causal coding). Inner and outer bounds are derived on the capacity region with noncausal coding. For the special case where the nondegraded user is informed about the channel parameters, it is shown that the inner bound is tight, thus deriving the capacity region for that case. For causal coding, a single-letter characterization of the capacity region is derived. This characterization is expressed via auxiliary random variables (RVs), and can also be interpreted by means of Shannon strategies, as the formula for the capacity of the single-user channel with causal coding derived by Shannon. The capacity region of a class of binary broadcast channels with causal coding is computed, as an example. Applications to watermarking are suggested. In particular, the results on noncausal coding can be used to derive the capacity region of a watermarking system where the channel (attacker) is fixed, and the watermark is subject to several stages of attack, or a watermarking system where the encoder is required to encode watermarks for both private and public users.

关键词： broadcast channel causal coding degraded broadcast channel information hiding noncausal coding Shannon strategies side information watermarking

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

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IEEE TRANSACTIONS ON INFORMATION THEORY 2017年第9期63卷 5968-5980页

作者： Wood, Richard G. Linder, Tamas Yuksel, Serdar Queens Univ Dept Math & Stat Kingston ON K7L 3N6 Canada

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 block length (time horizon) performance of 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.

关键词： Zero delay source coding real time coding causal coding quantization stochastic control Markov sources Markov decision processes

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Optimality of Walrand-Varaiya Type Policies and Approximation Results for Zero Delay coding of Markov Sources

Optimality of Walrand-Varaiya Type Policies and Approximatio...

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IEEE International Symposium on Information Theory (ISIT)

作者： Wood, Richard G. Linder, Tamas Yuksel, Serdar Queens Univ Dept Math & Stat Kingston ON K7L 3N6 Canada

ISBN: (纸本)9781467377041

Optimal zero-delay coding (quantization) of a finite-state Markov source is considered. Building on our earlier work and previous literature, using a stochastic control problem formulation, the existence and structure of optimal quantization policies are studied. Our main result establishes, for infinite horizon problems, the optimality of deterministic and stationary (Walrand-Varaiya type) Markov coding policies. In addition, the epsilon-optimality of finite-memory quantizers is established and the dependence between the memory length and epsilon is quantified. Numerical results are also presented.

关键词： Zero-delay source coding causal coding quantization stochastic control

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Wiretap Channels With causal and Non-causal State Information: Revisited

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IEEE TRANSACTIONS ON INFORMATION THEORY 2021年第9期67卷 6122-6139页

作者： Han, Te Sun Sasaki, Masahide Natl Inst Informat & Commun Technol NICT Quantum ICT Collaborat Ctr Koganei Tokyo Japan

The coding problem for wiretap channels (WTCs) with causal and/or non-causal channel state information (CSI) available at the encoder (Alice) and/or the decoder (Bob) is studied, particularly focusing on achievable secret-message secret-key (SM-SK) rate pairs under the semantic security criterion. One of our main results is summarized as Theorem 3 on causal inner bounds for SM-SK rate pairs, which follows immediately by leveraging the unified seminal theorem for WTCs with non-causal CSI at Alice that has been recently established by Bunin et al.. The only thing to do here is just to re-interpret the latter non-causal scheme in a causal manner by restricting the range of auxiliary random variables appearing in non-causal encoding to a subclass of auxiliary random variables for the causal encoder. This technique is referred to as "plugging." Then, we are able to dispense with the block-Markov encoding scheme used in the previous works by Chia and El Gamal, Fujita, and Han and Sasaki and then extend all the known results on achievable rates. The other main results include the exact SM-SK capacity region for WTCs with non-causal CSI at "both" Alice and Bob (Theorem 2), a "tighter" causal SM-SK outer bound for state-reproducing coding schemes with CSI at Alice (Proposition 4), and the exact SM-SK capacity region for degraded WTCs with causal/non-causal CSI at both Alice and Bob (Theorem 4).

关键词： Probability distribution Random variables Decoding Channel coding Semantics Security Measurement Wiretap channel channel state information causal coding plugging secret-message capacity secret-key capacity semantic security

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Reliability Function for Streaming Over a DMC With Feedback

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IEEE TRANSACTIONS ON INFORMATION THEORY 2023年第4期69卷 2165-2192页

作者： Guo, Nian Kostina, Victoria CALTECH Dept Elect Engn Pasadena CA 91125 USA

Conventionally, posterior matching is investigated in channel coding and block encoding contexts - the source symbols are equiprobably distributed and are entirely known by the encoder before the transmission. In this paper, we consider a streaming source, whose symbols progressively arrive at the encoder at a sequence of deterministic times. We derive the joint source-channel coding (JSCC) reliability function for streaming over a discrete memoryless channel (DMC) with feedback. We propose a novel instantaneous encoding phase that operates during the symbol arriving period and achieves the JSCC reliability function for streaming when followed by a block encoding scheme that achieves the JSCC reliability function for a classical source whose symbols are fully accessible before the transmission. During the instantaneous encoding phase, the evolving message alphabet is partitioned into groups whose priors are close to the capacity-achieving distribution, and the encoder determines the group index of the actual sequence of symbols arrived so far and applies randomization to exactly match the distribution of the transmitted index to the capacity-achieving one. Surprisingly, the JSCC reliability function for streaming is equal to that for a fully accessible source, implying that the knowledge of the entire symbol sequence before the transmission offers no advantage in terms of the reliability function. For streaming over a symmetric binary-input DMC, we propose a one-phase instantaneous small-enough difference (SED) code that not only achieves the JSCC reliability function, but also, thanks to its single-phase time-invariant coding rule, can be used to stabilize an unstable linear system over a noisy channel. For equiprobably distributed source symbols, we design low complexity algorithms to implement both the instantaneous encoding phase and the instantaneous SED code. The algorithms group the source sequences into sets we call types, which enable the encoder and the de

关键词： Channels with feedback reliability function joint source-channel coding variable-length codes streaming causal coding posterior matching anytime codes control over noisy channels

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On State-Dependent Degraded Broadcast Channels With Cooperation

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IEEE TRANSACTIONS ON INFORMATION THEORY 2016年第5期62卷 2308-2323页

作者： Dikstein, Lior Permuter, Haim H. Steinberg, Yossef Ben Gurion Univ Negev Dept Elect & Comp Engn IL-84105 Beer Sheva Israel Technion Israel Inst Technol Dept Elect Engn IL-32000 Haifa Israel

In this paper, we investigate problems of communication over physically degraded, state-dependent broadcast channels (BCs) with cooperating decoders. Two different setups are considered, and their capacity regions are characterized. First, we study a setting in which one decoder can use a finite capacity link to send the other decoder information regarding the messages or the channel states. In this scenario, we analyze two cases: one, where noncausal state information, is available to the encoder and the strong decoder, and the other, where state information, is available only to the encoder in a causal manner. Second, we examine a setting in which the cooperation between the decoders is limited to taking place before the outputs of the channel are given. In this case, one decoder, which is informed of the state sequence noncausally, can cooperate only to send the other decoder rate-limited information about the state sequence. The proofs of the capacity regions introduce a new idea of coding for channels with cooperation between different users, where we exploit the link between the decoders for multiple binnings. Finally, we discuss the optimality of using rate-splitting techniques when coding for cooperative BCs. In particular, we show that rate splitting is not necessarily optimal when coding for cooperative BCs by solving an example in which our method of coding outperforms rate splitting.

关键词： Binning broadcast channels causal coding channel capacity cooperative broadcast degraded broadcast channel noncausal coding partial side information side information state-dependent channels

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Wiretap Channels With causal State Information: Strong Secrecy

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IEEE TRANSACTIONS ON INFORMATION THEORY 2019年第10期65卷 6750-6765页

作者： Han, Te Sun Sasaki, Masahide Natl Inst Informat & Commun Technol NICT Quantum ICT Adv Dev Ctr Tokyo 1848795 Japan Natl Inst Informat & Commun Technol Adv ICT Res Inst Tokyo 1848795 Japan

The coding problem for wiretap channels with causal channel state information available at the encoder and/ or the decoder is studied under the strong secrecy criterion. This problem consists of two aspects: one is due to wiretap channel coding and the other is due to one-time pad cipher based on the secret key agreement between Alice and Bob using the channel state information. These two aspects are closely related to each other and give rise to an intriguing tradeoff between exploiting the state to boost secret-message rates versus extracting cryptographic key to improve secrecy capabilities. This issue has yet to be understood how to optimally reconcile the two. We newly devised the "iterative" forward-backward coding scheme, combining wiretap channel coding and secretkey- agreement-based one-time pad cipher. We then established reasonable lower bounds of the secrecy capacity for wiretap channels with causal channel state information available only at the encoder (Theorem 1), which can be easily extended to general cases with various kinds of correlated channel state information at the encoder (Alice), decoder (Bob), and wiretapper (Eve). In particular, for degraded wiretap channels, we give the secret-message (secret-key) capacity bounds (Theorems 2, 4, and 5).

关键词： Wiretap channel channel state information causal coding secret key agreement secrecy capacity strong secrecy

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The State-Dependent Broadcast Channel with Cooperation

The State-Dependent Broadcast Channel with Cooperation

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51st IEEE Annual Allerton Conference on Communication, Control, and Computing

作者： Dikstein, Lior Permuter, Haim H. Steinberg, Yossef Ben Gurion Univ Negev IL-84105 Beer Sheva Israel Technion Israel Inst Technol IL-32000 Haifa Israel

ISBN: (纸本)9781479934096

In this paper, we investigate problems of communication over physically-degraded, state-dependent broadcast channels (BC) with cooperating decoders. Three different setups are considered and their capacity regions are characterized. First, we study a setting where noncausal state information is available to the encoder and the strong decoder. Furthermore, the strong decoder can use a finite capacity link to send the weak decoder information regarding the messages or the channel state. Second, we examine a setting where the encoder and the strong decoder both have access to noncausal state information, while the weak decoder has access to rate-limited state information. This scenario can be interpreted as a special case, where the strong decoder can only cooperate to send the weak decoder rate-limited information about the state sequence. A third case we consider, is a cooperative setting where state information is available only to the encoder in a causal manner. Finally, we discuss the optimality of using rate-splitting when coding for cooperative BC. In particular, we prove that rate-splitting is not necessarily optimal when coding for cooperative BC and solve an example where a multiple-binning coding scheme outperforms rate-splitting.

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