<p>Video coding schemes designed based on sequential or predictive coding models are vulnerable to the loss of encoded frames at the decoder end. Motivated by this observation, in this thesis we propose two new coding models: robust sequential coding and robust predictive coding. For the Gauss-Markov source with the mean squared error distortion measure, we characterize certain supporting hyperplanes of the rate region of these two coding problems. The proof is divided into three steps: 1) it is shown that each supporting hyperplane of the rate region of Gaussian robust sequential coding admits a max-min lower bound; 2) the corresponding min-max upper bound is shown to be achievable by a robust predictive coding scheme; 3) a saddle point analysis proves that the max-min lower bound coincides with the min-max upper bound. Furthermore, it is shown that the proposed robust predictive coding scheme can be implemented using a successive quantization system. Theoretical and experimental results indicate that this scheme has a desirable \self-recovery" property. Our investigation also reveals an information-theoretic minimax theorem and the associated extremal inequalities.</p> / Doctor of Philosophy (PhD)

Traditionally, source coding (data compression) and channel coding (error protection) are performed separately and sequentially, resulting in what we call a tandem (separate) coding system. In practical implementations, however, tandem coding might involve a large delay and a high coding/decoding complexity, since one needs to remove the redundancy in the source coding part and then insert certain redundancy in the channel coding part. On the other hand, joint source-channel coding (JSCC), which coordinates source and channel coding or combines them into a single step, may offer substantial improvements over the tandem coding approach. This thesis deals with the fundamental Shannon-theoretic limits for a variety of communication systems via JSCC. More specifically, we investigate the reliability function (which is the largest rate at which the coding probability of error vanishes exponentially with increasing blocklength) for JSCC for the following discrete-time communication systems: (i) discrete memoryless systems; (ii) discrete memoryless systems with perfect channel feedback; (iii) discrete memoryless systems with source side information; (iv) discrete systems with Markovian memory; (v) continuous-valued (particularly Gaussian) memoryless systems; (vi) discrete asymmetric 2-user source-channel systems. For the above systems, we establish upper and lower bounds for the JSCC reliability function and we analytically compute these bounds. The conditions for which the upper and lower bounds coincide are also provided. We show that the conditions are satisfied for a large class of source-channel systems, and hence exactly determine the reliability function. We next provide a systematic comparison between the JSCC reliability function and the tandem coding reliability function (the reliability function resulting from separate source and channel coding). We show that the JSCC reliability function is substantially larger than the tandem coding reliability function for most cases. In particular, the JSCC reliability function is close to twice as large as the tandem coding reliability function for many source-channel pairs. This exponent gain provides a theoretical underpinning and justification for JSCC design as opposed to the widely used tandem coding method, since JSCC will yield a faster exponential rate of decay for the system error probability and thus provides substantial reductions in complexity and coding/decoding delay for real-world communication systems. / Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2008-05-13 22:31:56.425