Network Distributed Quantization

Abstract

Abstract-We investigate the design of rate-distortion optimal quantizers for distributed compression in a network with multiple senders and receivers. In such network, several noisy observations of one or more unseen sources are separately encoded by each sender and the quantization indices transmitted to a number of receivers, which jointly decode all available transmissions with the help of side information locally available. The joint statistics of the source data, the noisy observations and the side information are known, and exploited in the quantizer design. A variety of lossless coders for the quantization indices, including ideal multiple-source Slepian-Wolf coders, are allowed.We present the optimality conditions such quantizers must satisfy, together with an extension of the Lloyd algorithm for a locally optimal design. Experimental results for distributed quantization of Gaussian sources confirm the high-rate quantization theory established in our previous work.

Distributed Distortion-Rate Optimized Compressed Sensing in Wireless Sensor Networks

“…The quantizer design is mostly related to [66], [67] which, differently from our work, 1) focus on channeloptimized VQs, 2) use fixed-rate VQs, and 3) involve complex encoders impeding the practical implementation. The entropy coding part utilizes the original ideas of [22], and those extended to multiple remote sources in, e.g., [39]. Apart from our initial works [71], [72], pre-quantization as a means to moderate encoding complexity, and the use of variable-rate coding in a QCS setup have not been addressed before.…”

“…Distributed compression of a remote source is addressed in [33], [34], the CEO problem in [35], and DSC of multiple remote Gaussian sources in [36]. Related quantizer based studies include distributed estimation of a remote source in [34], [37], [38], and its extension to multiple remote sources in [39].…”

Channel Optimized Distributed Multiple Description Coding

“…As evident in (10)- (12), the only depends on the CDMD source encoder and joint probability distribution of source and side information. Also, the channel distortion indicates the effect of channel disturbances reflected by the channel transition probability, ( | = , ).…”

“…The CDMD design procedure, with deterministic annealing algorithm, may now be summarized as follows. First a vector quantizer is selected, and the IA (24)-(25), and the distortion is computed using (9)- (12). Note that | obtained in the previous step is used for computing ( | , ).…”

“…Recently much effort has been devoted to designing source encoders for multi-terminal source coding over noiseless channels, e.g., [8] [11][12][13] and the references therein. In [14], two scalar quantizers are designed for two distributed correlated sources (symmetric setting) aiming at minimizing the overall reconstruction distortion at a single destination over noisy channels without PL.…”