Strategies for Delay-Limited Source-Channel Coding

Abstract

In point-to-point source-channel communication with a fidelity criterion and a transmission cost constraint, the region of achievable cost and fidelity pairs is completely characterized by Shannon's separation theorem. However, this is in general only true if coding of arbitrary complexity and delay is admitted. If the delay is constrained, the separation theorem only provides an outer bound to the achievable cost/distortion region, and the exact shape of this region is in general not known. The first part of this thesis studies source-channel communication when neither a required average fidelity nor a cost constraint are specified, but when the goal is to maximize the ratio of fidelity to cost. It is shown how the maximal ratio relates to existing quantities such as the capacity per unit cost. Finally, necessary and sufficient conditions are derived to test whether a given system operates at this maximal ratio and when this is possible using a single-letter code. The second part of the thesis studies communication of continuous-valued sources over the additive white Gaussian noise channel when only a single source symbol is to be encoded at a time. In particular, the case is considered where several uses of the channel can be made for each source symbol. Inspired by communication with feedback, a simple communication strategy combining quantization and uncoded transmission is derived and analyzed. It is shown that this strategy achieves a mean squared error that performs as well as any known communication strategy that encodes a single source symbol at a time. On the other hand, it is strictly suboptimal in the sense that the gap (in dB) between the achievable signal-to-distortion ratio (SDR) and the best SDR achievable without a delay limit grows with increasing signal-to-noise ratio. The thesis turns to a more practical subject in its last part. The case is made why object-oriented programming is particularly suited to implementing simulations. As a proof of concept, a complete implementation of an object-oriented simulator for source-channel coding is presented that allows for rapid development and analysis of arbitrary communication strategies.