Multiple Description Coding (MDC) was fi rst formulated by A. Gersho and H. Witsenhausen as a way to improve the robustness of telephony links to outages. Lots of studies have been done in this area up to now. Another application of MDC is the transmission of an image in diff erent descriptions. If because of the link outage during transmission, any one of the descriptions fails, the image could still be reconstructed with some quality at the decoder side. In video coding, inter prediction is a way to reduce temporal redundancy. From an information theoretical point of view, one can model inter prediction with Causal Video Coding (CVC). If because of link outage, we lose any I-frame, how can we reconstruct the corresponding P- or B-frames at the decoder? In this thesis, we are interested in answering this question and we call this scenario as causal video coding with possible loss of the fi rst encoded frame and we denote it by CVC-PL as PL stands for possible loss. In this thesis for the fi rst time, CVC-PL is investigated. Although, due to lack of time, we mostly study two-frame CVC-PL, we extend the problem to M-frame CVC-PL as well. To provide more insight into two-frame CVC-PL, we derive an outer-bound to the achievable rate-distortion sets to show that CVC-PL is a subset of the region combining CVC and peer-to-peer coding. In addition, we propose and prove a new achievable region to highlight the fact that two-frame CVC-PL could be viewed as MDC followed by CVC. Afterwards, we present the main theorem of this thesis, which is the minimum total rate of CVC-PL with two jointly Gaussian distributed sources, i.e. X1 and X2 with normalized correlation coeffi cient r, for di fferent distortion pro files (D1,D2,D3). Defi ning Dr = r^2(D1 -1) + 1, we show that for small D3, i.e. D3 < Dr +D2 -1, CVC-PL could be treated as CVC with two jointly Gaussian distributed sources; for large D3, i.e. D3 > DrD2/(Dr+D2-DrD2), CVC-PL could be treated as two parallel peer-to-peer networks with distortion constraints D1 and D2; and for the other cases of D3, the minimum total rate is 0.5 log (1+ ??)(D3+??)/ (Dr+?? )(D2+?? ) + 0.5 log Dr/(D1D3) where ??=D3-DrD2+r[(1-D1)(1-D2)(D3-Dr)(D3-D2)]^0.5/[Dr+D2-(D3+1) ] We also determine the optimal coding scheme which achieves the minimum total rate. We conclude the thesis by comparing the scenario of CVC-PL with two frames with a coding scheme, in which both of the sources are available at the encoders, i.e. distributed source coding versus centralized source coding. We show that for small D2 or large D3, the distributed source coding can perform as good as the centralized source coding. Finally, we talk about future work and extend and formulate the problem for M sources.

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Quantization of multimodal vector data in Realtime Interactive Communication Networks (RICNs) associated with application areas such as speech, video, audio, and haptic signals introduces a set of unique challenges. In particular, achieving the necessary distortion performance with minimum rate while maintaining low end-to-end delay and handling packet losses is of paramount importance. This dissertation presents vector quantization schemes which aim to satisfy these important requirements based on two source coding paradigms; 1) Predictive coding 2) Distributed source coding. Gaussian Mixture Models (GMMs) can be used to model any probability density function (pdf) with an arbitrarily small error given a sufficient number of mixture components. Hence, Gaussian Mixture Models can be effectively used to model the underlying pdfs of a variety of data in RICN applications. In this dissertation, first we present Gaussian Mixture Models Kalman predictive coding, which uses transform domain predictive GMM quantization techniques with Kalman filtering principles. In particular, we show how suitable modeling of quantization noise leads to a signal-adaptive GMM Kalman predictive coder that provides improved coding performance. Moreover, we demonstrate how running a GMM Kalman predictive coder to convergence can be used to design a stationary GMM Kalman predictive coding system which provides improved coding of GMM vector data but now with only a modest increase in run-time complexity over the baseline. Next, we address the issues of packet loss in the networks using GMM Kalman predictive coding principles. In particular, we show how an initial GMM Kalman predictive coder can be utilized to obtain a robust GMM predictive coder specifically designed to operate in packet loss. We demonstrate how one can define sets of encoding and decoding modes, and design special Kalman encoding and decoding gains for each mode. With this framework, GMM predictive coding design can be viewed as determining the special Kalman gains that minimize the expected mean squared error at the decoder in packet loss conditions. Finally, we present analytical techniques for modeling, analyzing and designing Wyner-Ziv(WZ) quantizers for Distributed Source Coding for jointly Gaussian vector data with imperfect side information. In most of the DSC implementations, the side information is not explicitly available in the decoder. Thus, almost all of the practical implementations obtain the side information from the previously decoded frames. Due to model imperfections, packet losses, previous decoding errors, and quantization noise, the available side information is usually noisy. However, the design of Wyner-Ziv quantizers for imperfect side information has not been widely addressed in the DSC literature. The analytical techniques presented in this dissertation explicitly assume the existence of imperfect side information in the decoder. Furthermore, we demonstrate how the design problem for vector data can be decomposed into independent scalar design subproblems. Then, we present the analytical techniques to compute the optimum step size and bit allocation for each scalar quantizer such that the decoder's expected vector Mean Squared Error(MSE) is minimized. The simulation results verify that the predicted MSE based on the presented analytical techniques closely follow the simulation results.

This thesis present a new feature coding scheme for video-content matching tasks. The purpose of this feature coding scheme is to compress features under a strict bitrate budget. Features contain two parts of information: the descriptors and the feature locations. We propose a variable level scalar quantizer for descriptors and a variable block size location coding scheme for feature locations. For descriptor coding, the SIFT descriptors are transformed using Karhunen-Loéve Transform (KLT). This K-L transformation matrix is trained using the descriptors extracted from the 25K-MIRFLICKR image dataset. The quantization of descriptors is applied after descriptor transformation. Our proposed descriptor quantizer allocates different bitrates to the elements in the transformed descriptor according to the sequence order. We establish the correlation between the descriptor quantizer distortion and the video matching performance, given a strict bitrate budget. Our feature location coding scheme is built upon the location histogram coding method. Instead of using uniform block size, we use different sizes of blocks to quantize different areas of a video frame. We have achieved nearly 50% reduction in the bitrate allocated for location information compared to the bitrate allocated by the coding schemes that use uniform block size. With this location coding scheme, we achieve almost the same video matching performance as that of the uniform block size coding. By combining the descriptor and location coding schemes, experimental results have shown that the overall feature coding scheme achieves excellent video matching performance. / Thesis / Master of Applied Science (MASc)

In this thesis, robust transmission of 3D models represented by static or time consistent animated meshes is studied from the aspects of scalable coding, multiple description coding (MDC) and error resilient coding. First, three methods for MDC of static meshes are proposed which are based on multiple description scalar quantization, partitioning wavelet trees and optimal protection of scalable bitstream by forward error correction (FEC) respectively. For each method, optimizations and tools to decrease complexity are presented. The FEC based MDC method is also extended as a method for packet loss resilient transmission followed by in-depth analysis of performance comparison with state of the art techniques, which pointed significant improvement. Next, three methods for MDC of animated meshes are proposed which are based on layer duplication and partitioning of the set of vertices of a scalable coded animated mesh by spatial or temporal subsampling where each set is encoded separately to generate independently decodable bitstreams. The proposed MDC methods can achieve varying redundancy allocations by including a number of encoded spatial or temporal layers from the other description. The algorithms are evaluated with redundancy-rate-distortion curves and per-frame reconstruction analysis. Then for layered predictive compression of animated meshes, three novel prediction structures are proposed and integrated into a state of the art layered predictive coder. The proposed structures are based on weighted spatial/temporal prediction and angular relations of triangles between current and previous frames. The experimental results show that compared to state of the art scalable predictive coder, up to 30% bitrate reductions can be achieved with the combination of proposed prediction schemes depending on the content and quantization level. Finally, optimal quality scalability support is proposed for the state of the art scalable predictive animated mesh coding structure, which only supports resolution scalability. Two methods based on arranging the bitplane order with respect to encoding or decoding order are proposed together with a novel trellis based optimization framework. Possible simplifications are provided to achieve tradeoff between compression performance and complexity. Experimental results show that the optimization framework achieves quality scalability with significantly better compression performance than state of the art without optimization.