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The second-order coding rate of the MIMO Quasi-Static Rayleigh Fading Channel

IEEE TRANSACTIONS ON INFORMATION THEORY 2015年第12期61卷 6591-6622页

作者： Hoydis, Jakob Couillet, Romain Piantanida, Pablo Alcatel Lucent Bell Labs F-91620 Nozay France Cent Supelec Univ Paris Sud Lab Signaux & Syst Ctr Natl Rech Sci F-91192 Gif Sur Yvette France

The second-order coding rate of the multiple-input multiple-output (MIMO) quasi-static Rayleigh fading channel is studied. We tackle this problem via an information-spectrum approach and statistical bounds based on recent random matrix theory techniques. We derive a central limit theorem (CLT) to analyze the information density in the regime where the block length n and the number of transmit and receive antennas K and N, respectively, grow simultaneously large. This result leads to the characterization of closed-form upper and lower bounds on the optimal average error probability when the coding rate is within Omicron(1/root nK) of the asymptotic capacity.

关键词： Finite block-length second-order coding rate error probability quasi-static fading channel block-fading channel MIMO information spectrum random matrix theory

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Channel coding With Mean and Variance Cost Constraints

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IEEE TRANSACTIONS ON INFORMATION THEORY 2025年第3期71卷 1504-1532页

作者： Mahmood, Adeel Wagner, Aaron B. Cornell Univ Sch Elect & Comp Engn Ithaca NY 14853 USA

We consider channel coding for discrete memoryless channels (DMCs) with a novel cost constraint that constrains both the mean and the variance of the cost of the codewords. We show that the maximum (asymptotically) achievable rate under the new cost formulation is equal to the capacity-cost function;in particular, the strong converse holds. We further characterize the optimal second-order coding rate of these cost-constrained codes;in particular, the optimal second-order coding rate is finite. We then show that the second-order coding performance is strictly improved with feedback using a new variation of timid/bold coding, significantly broadening the applicability of timid/bold coding schemes from unconstrained compound-dispersion channels to all cost-constrained channels. Equivalent results on the minimum average probability of error are also given.

关键词： Costs Encoding Reactive power Random variables Error probability Channel coding Standards Power demand Noise Memoryless systems feedback communications second-order coding rate stochastic control

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A New Method for Employing Feedback to Improve coding Performance

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IEEE TRANSACTIONS ON INFORMATION THEORY 2020年第11期66卷 6660-6681页

作者： Wagner, Aaron B. Shende, Nirmal V. Altug, Yucel Cornell Univ Sch Elect & Comp Engn Ithaca NY 14853 USA Marvell Semicond Santa Clara CA 95054 USA Natera Inc San Carlos CA 94070 USA

We introduce a novel mechanism, called timid/bold coding, by which feedback can be used to improve coding performance. For a certain class of DMCs, called compound-dispersion channels, we show that timid/bold coding allows for an improved second-order coding rate compared with coding without feedback. For DMCs that are not compound dispersion, we show that feedback does not improve the second-order coding rate. Thus we completely determine the class of DMCs for which feedback improves the second-order coding rate. An upper bound on the second-order coding rate is provided for compound-dispersion DMCs. We also show that feedback does not improve the second-order coding rate for very noisy DMCs. The main results are obtained by relating feedback codes to certain controlled diffusions.

关键词： Encoding Monte Carlo methods Standards Compounds Dispersion Decoding Noise measurement Channel coding diffusions feedback communications second-order coding rate stochastic control

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MmWave-MIMO Based 5G Wireless Ad-Hoc Networks in the Finite Blocklength Regime

MmWave-MIMO Based 5G Wireless Ad-Hoc Networks in the Finite ...

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IEEE Global Communications Conference (GLOBECOM)

作者： Zhang, Xi Wang, Jingqing Poor, H. Vincent Texas A&M Univ Dept Elect & Comp Engn Networking & Informat Syst Lab College Stn TX 77843 USA Princeton Univ Dept Elect Engn Princeton NJ 08544 USA

ISBN: (纸本)9781728109626

The integration of millimeter wave (mmWave) and multiple-input and multiple-output (MIMO) techniques has been designed to provide reliable communications with large degrees of freedom while supporting the explosively growing number of mobile users. Under stringent requirements in terms of latency and reliability, due to the infinite blocklength assumption of the Shannon's capacity result, researchers have investigated new methods to characterize wireless data transmissions considering the block error probability. The finite blocklength coding (FBC) technique has been developed to model the finite blocklength coding rate in the non-asymptotic regime while supporting short-packet communications over 5G wireless ad-hoc networks. However, because of the design complexity when characterizing the second-order coding rate over mmWave MIMO based wireless channels while being integrated with FBC, how to accurately derive the finite blocklength coding rate over mmWave MIMO wireless fading channels is still an open problem over 5G wireless ad-hoc networks. To tackle the above-mentioned challenges, we propose and develop a system model that can efficiently integrate mmWave-MIMO techniques with finite blocklength coding over 5G wireless ad-hoc networks. In particular, we derive system equations that characterize the foundational information-theoretic relationship between the finite blocklength channel capacity and the coding rate over our proposed mmWave MIMO based 5G wireless ad-hoc networks in the finite blocklength regime. Also conducted is a MATLAB-based performance evaluation, which validates and analyzes our proposed schemes over mmWave MIMO based 5G wireless ad-hoc networks in the finite blocklength regime.

关键词： Finite blocklength coding mmWave MIMO second-order coding rate error probability information density 5G wireless ad-hoc networks

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Position-based coding and convex splitting for private communication over quantum channels

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QUANTUM INFORMATION PROCESSING 2017年第10期16卷 1-35页

作者： Wilde, Mark M. Louisiana State Univ Hearne Inst Theoret Phys Ctr Computat & Technol Dept Phys & Astron Baton Rouge LA 70803 USA

The classical-input quantum-output (cq) wiretap channel is a communication model involving a classical sender X, a legitimate quantum receiver B, and a quantum eavesdropper E. The goal of a private communication protocol that uses such a channel is for the sender X to transmit a message in such a way that the legitimate receiver B can decode it reliably, while the eavesdropper E learns essentially nothing about which message was transmitted. The epsilon-one-shot private capacity of a cq wiretap channel is equal to the maximum number of bits that can be transmitted over the channel, such that the privacy error is no larger than epsilon is an element of (0, 1). The present paper provides a lower bound on the epsilon-one-shot private classical capacity, by exploiting the recently developed techniques of Anshu, Devabathini, Jain, and Warsi, called position-based coding and convex splitting. The lower bound is equal to a difference of the hypothesis testing mutual information between X and B and the "alternate" smooth max-information between X and E. The one-shot lower bound then leads to a non-trivial lower bound on the second-order coding rate for private classical communication over a memoryless cq wiretap channel.

关键词： Private classical communication Quantum wiretap channel second-order coding rate Hypothesis testing mutual information Smooth max-mutual information

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On Gaussian Channels With Feedback Under Expected Power Constraints and With Non-Vanishing Error Probabilities

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IEEE TRANSACTIONS ON INFORMATION THEORY 2017年第3期63卷 1746-1765页

作者： Truong, Lan V. Fong, Silas L. Tan, Vincent Y. F. Natl Univ Singapore Dept Elect & Comp Engn Singapore 117583 Singapore NUS Dept Math Singapore 117583 Singapore

In this paper, we consider single-and multi-user Gaussian channels with feedback under expected power constraints and with non-vanishing error probabilities. In the first of two contributions, we study asymptotic expansions for the additive white Gaussian noise (AWGN) channel with feedback under the average error probability formalism. By drawing ideas from Gallager and Nakiboglu's work for the direct part and the meta-converse for the converse part, we establish the e-capacity and show that it depends on epsilon in general and so the strong converse fails to hold. Furthermore, we provide bounds on the second-order term in the asymptotic expansion. We show that for any positive integer L, the second-order term is bounded between a term proportional to -ln(L)n (where ln(L)(center dot) is the L-fold nested logarithm function) and a term proportional to +(n ln n)(1/2), where n is the blocklength. The lower bound on the second-order term shows that feedback does provide an improvement in the maximal achievable rate over the case where no feedback is available. In our second contribution, we establish the e-capacity region for the AWGN multiple access channel with feedback under the expected power constraint by combining ideas from hypothesis testing, information spectrum analysis, Ozarow's coding scheme, and power control.

关键词： Feedback AWGN channel multiple access channel expected power constraint strong converse second-order coding rate finite blocklength regime

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On Gaussian Channels With Feedback Under Expected Power Constraints and With Non-Vanishing Error Probabilities

On Gaussian Channels With Feedback Under Expected Power Cons...

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IEEE International Symposium on Information Theory (ISIT)

作者： Truong, Lan V. Fong, Silas L. Tan, Vincent Y. F. Natl Univ Singapore Dept Elect & Comp Engn Singapore 117583 Singapore NUS Dept Math Singapore 117583 Singapore

关键词： Feedback AWGN channel multiple access channel expected power constraint strong converse second-order coding rate finite blocklength regime

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Applications of position-based coding to classical communication over quantum channels

Applications of position-based coding to classical communica...

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2017 IEEE Information Theory Workshop (ITW)

作者： Qi, Haoyu Wang, Qingle Wilde, Mark M. Louisiana State Univ Dept Phys & Astron Hearne Inst Theoret Phys Baton Rouge LA 70803 USA Beijing Univ Posts & Telecommun State Key Lab Networking & Switching Technol Beijing Peoples R China Louisiana State Univ Ctr Computat & Technol Baton Rouge LA 70803 USA

ISBN: (纸本)9781509030972

We exploit a coding technique called position-based coding in the entanglement-assisted setting to establish lower bounds for error exponents, lower bounds on the second-order coding rate, and one-shot lower bounds, and we also demonstrate that position-based coding can be a powerful tool for analyzing other communication settings. In particular, we reduce the quantum simultaneous decoding conjecture for entanglement-assisted or unassisted communication over a quantum multiple access channel to open questions in multiple quantum hypothesis testing. We then determine an achievable rate region for entanglement-assisted or unassisted classical communication over a quantum multiple-access channel, when using a particular quantum simultaneous decoder. The achievable rate regions given in this latter case are generally suboptimal, involving differences of Renyi-two entropies and conditional quantum entropies.

关键词： position-based coding error exponents second-order coding rate one-shot lower bounds achievable rate

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First- and second-order coding Theorems for Mixed Memoryless Channels With General Mixture

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IEEE TRANSACTIONS ON INFORMATION THEORY 2016年第8期62卷 4395-4412页

作者： Yagi, Hideki Han, Te Sun Nomura, Ryo Univ Electrocommun Dept Commun Engn & Informat Tokyo 1828585 Japan Natl Inst Informat & Commun Technol Tokyo 1848795 Japan Senshu Univ Sch Network & Informat Kawasaki Kanagawa 2148580 Japan

This paper investigates the first-and second-order maximum achievable rates of codes with/without cost constraints for mixed channels whose channel law is characterized by a general mixture of (at most) uncountably many stationary and memoryless discrete channels. These channels are referred to as mixed memoryless channels with general mixture and include the class of mixed memoryless channels of finitely or countably memoryless channels as a special case. For the mixed memoryless channels with general mixture, the first-order coding theorem which gives a formula for the e-capacity is established, and then a direct part of the second-order coding theorem is provided. A subclass of mixed memoryless channels whose component channels can be ordered according to their capacity is introduced, and the first-and second-order coding theorems are established. It is shown that the established formulas reduce to several known formulas for restricted scenarios.

关键词： Channel coding cost constraint epsilon-capacity second-order coding rate mixed channel information spectrum

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On second-order Asymptotics of AWGN Channels with Feedback under the Expected Power Constraint

On Second-Order Asymptotics of AWGN Channels with Feedback u...

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IEEE International Symposium on Information Theory (ISIT)

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

ISBN: (纸本)9781509018062

In this paper, we analyze the asymptotic expansion for additive white Gaussian noise (AWGN) channels with feedback under an expected power constraint and the average error probability formalism. We show that the epsilon-capacity depends on epsilon in general and so the strong converse fails to hold. Furthermore, we provide bounds on the second-order term in the asymptotic expansion. We show that the second-order term is bounded between - ln ln n and a term that is proportional to + root n ln n. The lower bound on the second-order term shows that feedback does provide an improvement in the maximal achievable rate over the case where no feedback is available.

关键词： Feedback AWGN channel Strong converse second-order coding rate Finite blocklength regime

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