Topics in Multi-User Information Theory

This survey reviews fundamental concepts of multi-user information theory. Starting with typical sequences, the survey builds up knowledge on random coding, binning, superposition coding, and capacity converses by introducing progressively more sophisticated tools for a selection of source and channel models. The problems addressed include: Source Coding; Rate-Distortion and Multiple Descriptions; Capacity-Cost; The Slepian–Wolf Problem; The Wyner-Ziv Problem; The Gelfand-Pinsker Problem; The Broadcast Channel; The Multiaccess Channel; The Relay Channel; The Multiple Relay Channel; and The Multiaccess Channel with Generalized Feedback. The survey also includes a review of basic probability and information theory. Notations and Acronyms We use standard notation for probabilities, random variables, entropy, mutual information, and so forth. Table 1 lists notation developed in the appendices of this survey, and we use this without further explanation in the main body of the survey. We introduce the remaining notation as we go along. The reader is referred to the appendices for a review of the relevant probability and information theory concepts. Table 1 Probability and information theory notation. Sequences, Vectors, Matrices xn the finite sequence x1,x2, . . . ,xn xnym sequence concatenation: x1,x2, . . . ,xn,y1,y2, . . . ,ym x the vector [x1,x2, . . . ,xn] H a matrix |Q| determinant of the matrix Q (Continued)