Jonathan Scarlett

Mismatched decoding has long been studied and used when considering practical considerations such as channel uncertainty and implementation constraints that rule out the use of an optimal decoder in reliably transmitting over a communication channel. 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, the authors survey both classical literature and recent developments on the mismatched decoding problem, with an emphasis on achievable random-coding rates for memoryless channels. In doing so they present two widely-considered achievable rates known as the generalized mutual information (GMI) and the LM rate, and overview their derivations and properties. The authors bring the reader up to date by including discussion of 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. This monograph is aimed at students, researchers and practitioners in information theory and communications. It provides a thorough and clear survey of the topic and highlights a variety of applications and connections with other prominent information theory problems.

Group testing emerged as an area for research from the need for the US Government to screen recruits in the second world war for syphilis. Obviously rather than testing each recruit, a more efficient method involving the minimal number of tests was required. The central problem of group testing is thus: Given a number of items and a number of defectives, how many tests are required to accurately discover the defective items, and how can this be achieved? Group testing has since found applications in medical testing, biology, telecommunications, information technology, data science, and more. The focus of this survey is on the non-adaptive setting of group testing. In this setting, the test pools are designed in advance enabling them to be implemented in parallel. The survey gives a comprehensive and thorough treatment of the subject from an information theoretic perspective. It covers several related developments: efficient algorithms with practical storage and computation requirements, achievability bounds for optimal decoding methods, and algorithm-independent converse bounds. It assesses the theoretical guarantees not only in terms of scaling laws, but also in terms of the constant factors, leading to the notion of the rate of group testing, indicating the amount of information learned per test. Considering both noiseless and noisy settings, it identifies several regimes where existing algorithms are provably optimal or near-optimal, as well as regimes where there remains greater potential for improvement. This monograph is an accessible treatment of an important topic for researchers and students in Information Theory.