Multiple-symbol detection of space-time differential codes (MS-STDC) decodes N consecutive space-time symbols using maximum likelihood (ML) sequence detection to gain in performance over the conventional differential detection scheme. However its computational complexity is exponential in N . A fast algorithm for implementing the MD-STDC in block-fading channels with complexity O(N 4) is developed. Its performance in both block-fading and symbol-by-symbol fading channels is demonstrated through simulations. Set partitioning in hierarchical trees (SPIHT) coupled with rate compatible punctured convolution code (RCPC) and cyclic redundancy check (CRC) is employed as a generalized multiple description source coder with robustness to channel errors. We propose a serial concatenation of the above with a differential space-time code (STDC) and invoke an iterative joint source channel decoding procedure for decoding differentially space-time coded multiple descriptions. Experiments show a gain of up to 5 dB in PSNR with four iterations for image transmission in the absence of channel state information (CSI) at the receiver. A serial concatenation of SPIHT + RCPC/CRC is also considered with space-time codes (STC) instead of STDC. Experiments show a gain of up to 7 dB with four iterations in the absence of CSI

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.