Dynamic Information and Constraints in Source and Channel Coding

Abstract

This thesis explore dynamics in source coding and channel coding. We begin by introducing the idea of distortion side information, which does not directly depend on the source but instead affects the distortion measure. Such distortion side information is not only useful at the encoder but under certain conditions knowing it at the encoder is optimal and knowing it at the decoder is useless. Thus distortion side information is a natural complement to Wyner-Ziv side information and may be useful in exploiting properties of the human perceptual system as well as in sensor or control applications. In addition to developing the theoretical limits of source coding with distortion side information, we also construct practical quantizers based on lattices and codes on graphs. Our use of codes on graphs is also of independent interest since it highlights some issues in translating the success of turbo and LDPC codes into the realm of source coding. Finally, to explore the dynamics of side information correlated with the source, we consider fixed lag side information at the decoder. We focus on the special case of perfect side information with unit lag corresponding to source coding with feedforward (the dual of channel coding with feedback). Using duality, we develop a linear complexity algorithm which exploits the feedforward information to achieve the rate-distortion bound. The second part of the thesis focuses on channel dynamics in communication by introducing a new system model to study delay in streaming applications. We first consider an adversarial channel model where at any time the channel may suffer a burst of degraded performance (e.g., due to signal fading, interference, or congestion) and prove a coding theorem for the minimum decoding delay required to recover from such a burst. Our coding theorem illustrates the relationship between the structure of a code, the dynamics of the channel, and the resulting decoding delay. We also consider more general channel dynamics. Specifically, we prove a coding theorem establishing that, for certain collections of channel ensembles, delay-universal codes exist that simultaneously achieve the best delay for any channel in the collection. Practical constructions with low encoding and decoding complexity are described for both cases. Finally, we also consider architectures consisting of both source and channel coding which deal with channel dynamics by spreading information over space, frequency, multiple antennas, or alternate transmission paths in a network to avoid coding delays. Specifically, we explore whether the inherent diversity in such parallel channels should be exploited at the application layer via multiple description source coding, at the physical layer via parallel channel coding, or through some combination of joint source-channel coding. For on-off channel models application layer diversity architectures achieve better performance while for channels with a continuous range of reception quality (e.g., additive Gaussian noise channels with Rayleigh fading), the reverse is true. Joint source-channel coding achieves the best of both by performing as well as application layer diversity for on-off channels and as well as physical layer diversity for continuous channels.