Distributed lossy source coding using BCH-DFT codes

Distributed source coding, separate encoding (compression) and joint decoding of statistically dependent sources, arises in an increasing number of applications like sensor networks and multiview video coding.Many of those applications are highly interactive, requiring the development of low-delay, energy-limited communication and computing schemes.Currently, this compression is performed by using capacity-approaching binary channel codes.As a natural extension, distributed lossy source coding is realized by cascading a quantizer and Slepian-Wolf coding in the binary domain.Despite big strides in practical distributed source coding techniques, this problem is still demanding in terms of processing power, bandwidth, and delay.In this dissertation, we develop a new framework for distributed lossy source coding, in which we use real-number codes for binning.Specifically, we use a class of Bose-Chaudhuri-Hocquenghem (BCH) codes in the real/complex field known as the discrete Fourier transform (DFT) codes.Contrary to the conventional scheme, we first compress the continuousvalued sources and then quantize them.The new scheme exploits the correlation between continuous-valued sources, rather than quantized ones, which is more accurate.Also, by using short BCH-DFT codes, it reduces the complexity and delay and offers the potential to avoid the problems of the conventional quantization and binning approach, with relatively simple encoder/decoder.We propose both syndrome-and parity-based schemes, and we extend the parity-based scheme to distributed joint source-channel coding based on a single DFT code.Further, to adapt to uncertainty in the degree of statistical dependence between the sources, we construct rate-adaptive BCH-DFT codes.This allows the encoder to switch flexibly between encoding sample rates, if the degree of statistical dependence varies.The construction of rate-adaptive codes is based on transmission of additional syndrome samples and a simple extension of the subspace-based decoding.Another major contribution of this dissertation is to generalize the encoding/decoding of BCH-DFT codes.We prove that the parity frequencies of a BCH-DFT code, or equivalently the zeros of codewords in the frequency domain, are not required to be adjacent; we provide the decoding algorithm as well.This offers flexibility in constructing BCH-DFT codes and further improvement in the decoding which can be exploited in channel coding as well. Doctoral Award, NSERC and Hydro-Québec throughout my Ph.D. study.All my colleagues in the Telecommunications and Signal Processing group were sources of inspiration and friendship.I wish to give a special thanks to Sina for so many stimulating discussions, but also for his constant willingness to help, and Fabian for his meticulous translation of the abstract of this dissertation to French.It was a great pleasure to share, not just ideas and thoughts, but the daily ups and downs of research life with Hessam,

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