The Dispersion of Nearest-Neighbor Decoding for Additive Non-Gaussian Channels

We study the second-order asymptotics of information transmission using random Gaussian codebooks and nearest neighbor (NN) decoding over a power-limited stationary memoryless additive non-Gaussian noise channel. We show that the dispersion term depends on the non-Gaussian noise only through its second and fourth moments, thus complementing the capacity result (Lapidoth, 1996), which depends only on the second moment. Furthermore, we characterize the second-order asymptotics of point-to-point codes over $K$-sender interference networks with non-Gaussian additive noise. Specifically, we assume that each user's codebook is Gaussian and that NN decoding is employed, i.e., that interference from the $K-1$ unintended users (Gaussian interfering signals) is treated as noise at each decoder. We show that while the first-order term in the asymptotic expansion of the maximum number of messages depends on the power of the interferring codewords only through their sum, this does not hold for the second-order term.Comment: 12 pages, 3 figures, IEEE Transactions on Information Theor

Information-Theoretic Foundations of Mismatched Decoding

Shannon's channel coding theorem characterizes the maximal rate of information that can be reliably transmitted over a communication channel when optimal encoding and decoding strategies are used. In many scenarios, however, practical considerations such as channel uncertainty and implementation constraints rule out the use of an optimal decoder. The mismatched decoding problem addresses such scenarios by considering the case that the decoder cannot be optimized, but is instead fixed as part of the problem statement. This problem is not only of direct interest in its own right, but also has close connections with other long-standing theoretical problems in information theory. In this monograph, we survey both classical literature and recent developments on the mismatched decoding problem, with an emphasis on achievable random-coding rates for memoryless channels. We present two widely-considered achievable rates known as the generalized mutual information (GMI) and the LM rate, and overview their derivations and properties. In addition, we survey several improved rates via multi-user coding techniques, as well as recent developments and challenges in establishing upper bounds on the mismatch capacity, and an analogous mismatched encoding problem in rate-distortion theory. Throughout the monograph, we highlight a variety of applications and connections with other prominent information theory problems.Comment: Published in Foundations and Trends in Communications and Information Theory (Volume 17, Issue 2-3

Asymptotic Estimates in Information Theory with Non-Vanishing Error Probabilities

This monograph presents a unified treatment of single- and multi-user problems in Shannon's information theory where we depart from the requirement that the error probability decays asymptotically in the blocklength. Instead, the error probabilities for various problems are bounded above by a non-vanishing constant and the spotlight is shone on achievable coding rates as functions of the growing blocklengths. This represents the study of asymptotic estimates with non-vanishing error probabilities. In Part I, after reviewing the fundamentals of information theory, we discuss Strassen's seminal result for binary hypothesis testing where the type-I error probability is non-vanishing and the rate of decay of the type-II error probability with growing number of independent observations is characterized. In Part II, we use this basic hypothesis testing result to develop second- and sometimes, even third-order asymptotic expansions for point-to-point communication. Finally in Part III, we consider network information theory problems for which the second-order asymptotics are known. These problems include some classes of channels with random state, the multiple-encoder distributed lossless source coding (Slepian-Wolf) problem and special cases of the Gaussian interference and multiple-access channels. Finally, we discuss avenues for further research.Comment: Further comments welcom

Optimization in multi-relay wireless networks

The concept of cooperation in communications has drawn a lot of research attention in recent years due to its potential to improve the efficiency of wireless networks. This new form of communications allows some users to act as relays and assist the transmission of other users' information signals. The aim of this thesis is to apply optimization techniques in the design of multi-relay wireless networks employing cooperative communications. In general, the thesis is organized into two parts: ``Distributed space-time coding' (DSTC) and ``Distributed beamforming', which cover two main approaches in cooperative communications over multi-relay networks. In Part I of the thesis, various aspects of distributed implementation of space-time coding in a wireless relay network are treated. First, the thesis proposes a new fully-diverse distributed code which allows noncoherent reception at the destination. Second, the problem of coordinating the power allocation (PA) between source and relays to achieve the optimal performance of DSTC is studied and a novel PA scheme is developed. It is shown that the proposed PA scheme can obtain the maximum diversity order of DSTC and significantly outperform other suboptimal PA schemes. Third, the thesis presents the optimal PA scheme to minimize the mean-square error (MSE) in channel estimation during training phase of DSTC. The effect of imperfect channel estimation to the performance of DSTC is also thoroughly studied. In Part II of the thesis, optimal distributed beamforming designs are developed for a wireless multiuser multi-relay network. Two design criteria for the optimal distributed beamforming at the relays are considered: (i) minimizing the total relay power subject to a guaranteed Quality of Service (QoS) measured in terms of signal-to-noise-ratio (SNR) at the destinations, and (ii) jointly maximizing the SNR margin at the destinations subject to power constraints at the relays. Based on convex optimization techniques, it is shown that these problems can be formulated and solved via second-order conic programming (SOCP). In addition, this part also proposes simple and fast iterative algorithms to directly solve these optimization problems

Information-Theoretic Foundations of Mismatched Decoding

Shannon’s channel coding theorem characterizes the maximal rate of information that can be reliably transmitted over a communication channel when optimal encoding and decoding strategies are used. In many scenarios, however, practical considerations such as channel uncertainty and implementation constraints rule out the use of an optimal decoder. The mismatched decoding problem addresses such scenarios by considering the case that the decoder cannot be optimized, but is instead fixed as part of the problem statement. This problem is not only of direct interest in its own right, but also has close connections with other long-standing theoretical problems in information theory. In this monograph, we survey both classical literature and recent developments on the mismatched decoding problem, with an emphasis on achievable random-coding rates for memoryless channels. We present two widely-considered achievable rates known as the generalized mutual information (GMI) and the LM rate, and overview their derivations and properties. In addition, we survey several improved rates via multi-user coding techniques, as well as recent developments and challenges in establishing upper bounds on the mismatch capacity, and an analogous mismatched encoding problem in rate-distortion theory. Throughout the monograph, we highlight a variety of applications and connections with other prominent information theory problems

Short-Packet Communications: Fundamental Performance and Key Enablers

The paradigm shift from 4G to 5G communications, predicted to enable new use cases such as ultra-reliable low-latency communications (URLLC), will enforce a radical change in the design of communication systems. Unlike in 4G systems, where the main objective is to have a large transmission rate, in URLLC, as implied by its name, the objective is to enable transmissions with low latency and, simultaneously, very high reliability. Since low latency implies the use of short data packets, the tension between blocklength and reliability is studied in URLLC.\ua0Several key enablers for URLLC communications have been designated in the literature. A non-exhaustive list contains: multiple transmit and receive antennas (MIMO), short transmission-time intervals (TTI), increased bandwidth, and feedback protocols. Furthermore, it is not only important to introduce additional diversity by means of the above examples, one must also guarantee that the scarce number of channel uses are used in an optimal way. Therefore, protocols for how to convey meta-data such as control information and pilot symbols are needed as are efficient short-packet channel codes.\ua0This thesis focuses on the performance of reliable short-packet communications. Specifically, we provide converse (upper) bounds and achievability (lower) bounds on the maximum coding rate, based on finite-blocklength information theory, for systems that employ the key enablers outlined above. With focus on the Rician and Rayleigh block-fading channels, we are able to answer, e.g., how to optimally utilize spatial and frequency diversity, how far from optimal short-packet channel codes perform, and whether feedback-based schemes are preferable over non-feedback schemes.\ua0More specifically, in Paper A, we study the performance impact of MIMO and a shortened TTI in both uplink and downlink under maximum-likelihood decoding and Rayleigh block-fading. Based on our results, we are able to study the trade-off between bandwidth, latency, spatial diversity, and error probability. Furthermore, we give an example of a pragmatic design of a pilot-assisted channel code that comes within 2.7 dB of our achievability bounds. In Paper B, we partly extend our work in Paper A to the Rician block-fading channel and to practical schemes such as pilot-assisted transmission with nearest neighbor decoding. We derive achievability bounds for pilot-assisted transmission with several different decoders that allow us to quantify the impact, on the achievable performance, of pilots and mismatched decoding. Furthermore, we design short-packet channel codes that perform within 1 dB of our achievability bounds. Paper C contains an achievability bound for a system that employs a variable-length stop-feedback (VLSF) scheme with an error-free feedback link. Based on the results in Paper C and Paper B, we are able to compare non-feedback schemes to stop-feedback schemes and assess if, and when, one is superior to the other. Specifically, we show that, for some practical scenarios, stop-feedback does significantly outperform non-feedback schemes

Strategic Communication with Side Information at the Decoder

We investigate the problem of strategic point-to-point communication with side information at the decoder, in which the encoder and the decoder have mismatched distortion functions. The decoding process is not supervised, it returns the output sequence that minimizes the decoder's distortion function. The encoding process is designed beforehand and takes into account the decoder's distortion mismatch. When the communication channel is perfect and no side information is available at the decoder, this problem is referred to as the Bayesian persuasion game of Kamenica-Gentzkow in the Economics literature. We formulate the strategic communication scenario as a joint source-channel coding problem with side information at the decoder. The informational content of the source influences the design of the encoding since it impacts differently the two distinct distortion functions. The side information complexifies the analysis since the encoder is uncertain about the decoder's belief on the source statistics

Laser Frequency Combs for Coherent Optical Communications

Laser frequency combs with repetition rates on the order of 10 GHz and higher can he used as multi-carrier sources in wavelength-division multiplexing (WDM). They allow replacing tens of tunable continuous-wave lasers by a single laser source. In addition, the comb\u27s line spacing stability and broadband phase coherence enable signal processing beyond what is possible with an array of independent lasers. Modern WDM systems operate with advanced modulation formats and coherent receivers. This introduces stringent requirements in terms of signal-to-noise ratio, power per line, and optical linewidth which can be challenging to attain for frequency comb sources. Here, we set quantitative benchmarks for these characteristics and discuss tradeoffs in terms of transmission reach and achievable data rates. We also highlight recent achievements for comb-based superchannels, including >10 Tb/s transmission with extremely high spectral efficiency, and the possibility to significantly simplify the coherent receiver by realizing joint digital signal processing. We finally discuss advances with microresonator frequency combs and compare their performance in terms of flatness and conversion efficiency against state-of-the-art electro-optic frequency comb generators. This contribution provides guidelines for developing frequency comb sources in coherent fiber-optic communication systems