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Equivocations, Exponents, and second-order coding rates Under Various Renyi Information Measures ( vol 63, pg 975, 2016)

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IEEE TRANSACTIONS ON INFORMATION THEORY 2024年第4期70卷 3046-3048页

作者： Hayashi, Masahito Tan, Vincent Y. F. Chinese Univ Hong Kong Shenzhen Sch Data Sci Shenzhen 518172 Peoples R China Int Quantum Acad SIQA Shenzhen 518048 Peoples R China Nagoya Univ Grad Sch Math Chikusa Ku Nagoya 4648602 Japan Natl Univ Singapore Dept Math Singapore 119077 Singapore Natl Univ Singapore Dept Elect & Comp Engn Singapore 119077 Singapore

There exists a gap for the proofs of the converse parts of (49) and (50) in Theorem 1 and (74) of Theorem 3. These converse parts use Lemma 4, whose proofs contain a gap. We fix these errors when the rate is larger than the critical rate. A special case of (50) does not coincide the recent result (Li and Yao, 2022, arXiv:2209.00554v1) when the rate is smaller than the critical rate.

关键词： Encoding Hash functions Mathematics Security Quantum mechanics Mutual information Indexes Information-theoretic security equivocation conditional Renyi entropies Renyi divergence Sibson's mutual information Arimoto's mutual information error exponents secrecy exponents second-order coding rates

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Equivocations, Exponents, and second-order coding rates Under Various Renyi Information Measures

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IEEE TRANSACTIONS ON INFORMATION THEORY 2017年第2期63卷 975-1005页

作者： Hayashi, Masahito Tan, Vincent Y. F. Nagoya Univ Grad Sch Math Nagoya Aichi 4648601 Japan Natl Univ Singapore Ctr Quantum Technol Singapore 119077 Singapore Natl Univ Singapore Dept Elect & Comp Engn Singapore 119077 Singapore Natl Univ Singapore Dept Math Singapore 119077 Singapore

We evaluate the asymptotics of equivocations, their exponents as well as their second-order coding rates under various Renyi information measures. Specifically, we consider the effect of applying a hash function on a source and we quantify the level of non-uniformity and dependence of the compressed source from another correlated source when the number of copies of the sources is large. Unlike previous works that use Shannon information measures to quantify randomness, information, or uniformity, we define our security measures in terms of a more general class of information measures-the Renyi information measures and their Gallager-type counterparts. A special case of these Renyi information measure is the class of Shannon information measures. We prove tight asymptotic results for the security measures and their exponential rates of decay. We also prove bounds on the second-order asymptotics and show that these bounds match when the magnitudes of the second-order coding rates are large. We do so by establishing new classes non-asymptotic bounds on the equivocation and evaluating these bounds using various probabilistic limit theoremsxxx asymptotically.

关键词： Information-theoretic security equivocation conditional Renyi entropies Renyi divergence Sibson's mutual information Arimoto's mutual information error exponents secrecy exponents second-order coding rates

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second-order coding rates for pure-loss bosonic channels

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QUANTUM INFORMATION PROCESSING 2016年第3期15卷 1289-1308页

作者： Wilde, Mark M. Renes, Joseph M. Guha, Saikat Louisiana State Univ Dept Phys & Astron Hearne Inst Theoret Phys Ctr Computat & Technol Baton Rouge LA 70803 USA ETH Inst Theoret Phys CH-8093 Zurich Switzerland Raytheon BBN Technol Quantum Informat Proc Grp Cambridge MA 02138 USA

A pure-loss bosonic channel is a simple model for communication over free-space or fiber-optic links. More generally, phase-insensitive bosonic channels model other kinds of noise, such as thermalizing or amplifying processes. Recent work has established the classical capacity of all of these channels, and furthermore, it is now known that a strong converse theorem holds for the classical capacity of these channels under a particular photon-number constraint. The goal of the present paper is to initiate the study of second-order coding rates for these channels, by beginning with the simplest one, the pure-loss bosonic channel. In a second-order analysis of communication, one fixes the tolerable error probability and seeks to understand the back-off from capacity for a sufficiently large yet finite number of channel uses. We find a lower bound on the maximum achievable code size for the pure-loss bosonic channel, in terms of the known expression for its capacity and a quantity called channel dispersion. We accomplish this by proving a general "one-shot" coding theorem for channels with classical inputs and pure-state quantum outputs which reside in a separable Hilbert space. The theorem leads to an optimal second-order characterization when the channel output is finite-dimensional, and it remains an open question to determine whether the characterization is optimal for the pure-loss bosonic channel.

关键词： second-order coding rates Pure-loss bosonic channel Optical communication Spectral entropy

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second- and Third-order Asymptotics of the Continuous-Time Poisson Channel

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IEEE TRANSACTIONS ON INFORMATION THEORY 2020年第8期66卷 4742-4760页

作者： Sakai, Yuta Tan, Vincent Y. F. Kovacevic, Mladen Natl Univ Singapore Dept Elect & Comp Engn Singapore 119077 Singapore Natl Univ Singapore Dept Math Singapore 119077 Singapore Univ Novi Sad Fac Tech Sci Novi Sad 21000 Serbia

The paper derives the optimal second-order coding rate for the continuous-time Poisson channel. We also obtain bounds on the third-order coding rate. This is the first instance of a second-order result for a continuous-time channel. The converse proof hinges on a novel construction of an output distribution induced by Wyner's discretized channel and the construction of an appropriate epsilon-net of the input probability simplex. While the achievability proof follows the general program to prove the third-order term for non-singular discrete memoryless channels put forth by Polyanskiy, several non-standard techniques-such as new definitions and bounds on the probabilities of typical sets using logarithmic Sobolev inequalities-are employed to handle the continuous nature of the channel.

关键词： second-order coding rates continuous-time channels Poisson channel channel dispersion fixed-error probability regime

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Achievable second-order coding rates for the Wiretap Channel

Achievable Second-Order Coding Rates for the Wiretap Channel

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IEEE International Conference on Communication Systems (ICCS)

作者： Tan, Vincent Y. F. ASTAR Inst Infocomm Res I2R Singapore Singapore

ISBN: (纸本)9781467320542

We derive lower bounds to the second-order coding rates for the wiretap channel. The decoding error probability and the information leakage measured in terms of the variational distance secrecy metric are fixed at some constants epsilon(r) and epsilon(s) respectively. We leverage on the connection between wiretap channel coding and channel resolvability to derive tighter secrecy bounds than those available in the literature. We then use central limit theorem-style analysis to evaluate these bounds for the discrete memoryless wiretap channel with cost constraints and the Gaussian wiretap channel.

关键词： second-order coding rates Dispersion analysis Wiretap channel Information-theoretic secrecy

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Streaming Data Transmission in the Moderate Deviations and Central Limit Regimes

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IEEE TRANSACTIONS ON INFORMATION THEORY 2016年第12期62卷 6816-6830页

作者： Lee, Si-Hyeon Tan, Vincent Y. F. Khisti, Ashish Univ Toronto Dept Elect & Comp Engn Toronto ON M5S Canada Natl Univ Singapore Dept Elect & Comp Engn Singapore 119077 Singapore Natl Univ Singapore Dept Math Singapore 119077 Singapore

We consider streaming data transmission over a discrete memoryless channel. A new message is given to the encoder at the beginning of each block and the decoder decodes each message sequentially, after a delay of T blocks. In this streaming setup, we study the fundamental interplay between the rate and error probability in the central limit and moderate deviations regimes and show that: 1) in the moderate deviations regime, the moderate deviations constant improves over the block coding or non-streaming setup by a factor of T and 2) in the central limit regime, the second-order coding rate improves by a factor of approximately root T for a wide range of channel parameters. For both the regimes, we propose coding techniques that incorporate a joint encoding of fresh and previous messages. In particular, for the central limit regime, we propose a coding technique with truncated memory to ensure that a summation of constants, which arises as a result of applications of the central limit theorem, does not diverge in the error analysis. Furthermore, we explore interesting variants of the basic streaming setup in the moderate deviations regime. We first consider a scenario with an erasure option at the decoder, i.e., the decoder can output an erasure symbol instead of a message estimate, and show that both the exponents of the total error and the undetected error probabilities improve by factors of T. Next, by utilizing the erasure option, we show that the exponent of the total error probability can be improved to that of the undetected error probability (in the order sense) at the expense of a variable decoding delay.

关键词： Streaming communication moderate deviations central limit regime second-order coding rates channel dispersion

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Streaming Data Transmission in the Moderate Deviations and Central Limit Regimes

Streaming Data Transmission in the Moderate Deviations and C...

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IEEE International Symposium on Information Theory (ISIT)

ISBN: (纸本)9781509018062

关键词： Streaming communication moderate deviations central limit regime second-order coding rates channel dispersion

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The ε-Capacity Region of AWGN Multiple Access Channels with Feedback 11

The ε-Capacity Region of AWGN Multiple Access Channels with...

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11th International Conference on Signal Processing and Communications (SPCOM)

作者： Truong, Lan V. Fong, Silas L. Tan, Vincent Y. F. Natl Univ Singapore Dept Elect & Comp Engn Singapore 117548 Singapore

In this paper, we establish the epsilon-capacity region for the AWGN multiple access channel (MAC) with feedback under an expected power constraint by combining ideas from binary hypothesis testing, information spectr... 详细信息

ISBN: (纸本)9781509017461

关键词： Feedback AWGN channel Multiple access channel Expected power constraint Strong converse second-order coding rates Finite blocklength regime

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The Third-order Term in the Normal Approximation for the AWGN Channel

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IEEE TRANSACTIONS ON INFORMATION THEORY 2015年第5期61卷 2430-2438页

作者： Tan, Vincent Yan Fu Tomamichel, Marco Natl Univ Singapore Dept Elect & Comp Engn Singapore 119077 Singapore Natl Univ Singapore Dept Math Singapore 119077 Singapore Natl Univ Singapore Ctr Quantum Technol Singapore 119077 Singapore Univ Sydney Sch Phys Sydney NSW 2006 Australia

This paper shows that, under the average error probability formalism, the third-order term in the normal approximation for the additive white Gaussian noise channel with a maximal or equal power constraint is at least (1/2) log n + O(1). This improves on the lower bound by Polyanskiy-Poor-Verdu (2010) and matches the upper bound proved by the same authors.

关键词： Additive white Gaussian noise channel third-order asymptotics finite blocklength minimum-distance decoding Shannon capacity dispersion second-order coding rates

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second-order Asymptotics for the Gaussian MAC With Degraded Message Sets

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IEEE TRANSACTIONS ON INFORMATION THEORY 2015年第12期61卷 6700-6718页

作者： Scarlett, Jonathan Tan, Vincent Y. F. Univ Cambridge Dept Engn Cambridge CB2 1PZ England Agcy Sci Technol & Res Inst Infocomm Res Singapore 138632 Singapore

This paper studies the second-order asymptotics of the Gaussian multiple-access channel with degraded message sets. For a fixed average error probability epsilon is an element of (0, 1) and an arbitrary point on the boundary of the capacity region, we characterize the speed of convergence of rate pairs that converge to that boundary point for codes that have asymptotic error probability no larger than e. As a stepping stone to this local notion of the second-order asymptotics, we study a global notion, and establish relationships between the two. We provide a numerical example to illustrate how the angle of approach to a boundary point affects the second-order coding rate. This is the first conclusive characterization of the second-order asymptotics of a network information theory problem in which the capacity region is not a polygon.

关键词： Gaussian multiple-access channel degraded message sets superposition coding strong converse finite block-lengths second-order coding rates dispersion

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