Abstract

This talk summarises my doctoral research over the last 3 years.

In real-time applications, data blocklength/delay is a design constraint of many point-to-point communication systems modeled by joint or separate source-channel coding blocks. Information theory traditionally studies such systems in the asymptotic regime and concludes that there is no loss in optimality by using separate instead of joint source-channel coding when the delay/blocklength goes to infinity. This is why due to the simplicity of a separation design source and channel coding are independently implemented in most applications.

However, this is no longer true when packets of hundreds of bits are sent over a noisy channel (e.g. wireless systems). In this situation joint coding schemes are expected to beat separation in terms of error probability but there is little knowledge on the actual gap. We characterize this gap by first providing new achievability and converse error bounds for both joint and separate source-channel coding and second by refining previous results on the error exponent. One could expect that the gap is optimized by fully exploiting the dependence of the channel input onto the source messages. However, our results show that this dependence is optimally weak in most of the cases.

Analysis and design of optimum (Bayes) detection of users’ (mobiles, tablettes, etc.) communicating with a base station is in general prohibitive. However, when we assume that the number of such users is large, there are statistical-physics techniques that fairly characterize the performance of finite systems (e.g., down to 8-10 users). That perfomance is typically specified by a fixed-point equation with multiple solutions, but only a subregion of those is of interest for practical purposes. We provide a formula for this subregion and derive conditions for near-optimal performance in terms of the number of users, their activity, and their power. We also study a scheme where both data and activity are encoded and propose an iterative algorithm to jointly detect users’ data and activity in the asymptotic regime.