In this correspondence, we consider rate-distortion examples in the presence of side information. For a system with some side information known at both the encoder and decoder, and some known only at the decoder, we evaluate the rate distortion function for both Gaussian and binary sources. While the Gaussian example is a straightforward generalization of the corresponding result by Wyner, the binary example proves more difficult and is solved using a multidimensional optimization approach. Leveraging the insights gained from the binary example, we then solve the more complicated binary Heegard and Berger problem of decoding when side information may be present. The results demonstrate the existence of a new type of successive refinement in which the refinement information is decoded together with side information that is not available for the initial description.

We present an algorithm for designing locally optimal vector quantizers for general networks. We discuss the algorithm's implementation and compare the performance of the resulting "network vector quantizers" to traditional vector quantizers (VQs) and to rate-distortion (R-D) bounds where available. While some special cases of network codes (e.g., multiresolution (MR) and multiple description (MD) codes) have been studied in the literature, we here present a unifying approach that both includes these existing solutions as special cases and provides solutions to previously unsolved examples.

A network source code is an optimal source code for a network. To design network source codes, we require each node to have a single encoder, which jointly encodes all messages transmitted by that node, and a single decoder, which jointly decodes all messages arriving at that node. Given a distribution over the sources, the design of the network source code jointly optimizes all encoders and decoders to obtain the best performance with respect to a user-defined priority schedule over the rates and distortions of the system. In this paper we focus on fixed-rate codes and address the implementation of an existing design algorithm for optimal network vector quantizers. Implementing the design algorithm is not straightforward since each encoder must choose its reproduction based on the expected behavior of sources that are unknown to it. We describe a new implementation approach and demonstrate its performance on a three-node network. In addition, we extend the design algorithm to allow the decoder at each node to use side information (specifically, the messages that are to be encoded by the encoder at the same node).

Multiple description codes are data compression algorithms designed with the goal of minimizing the distortion caused by data loss in packet-based or diversity communications systems. Recently, techniques that achieve multiple description coding by combining embedded source codes with unequal error protection channel codes have become popular in the literature. These codes allow for data reconstruction with any subset of the transmitted packets and achieve progressively better source reconstructions as more and more packets are decoded. The given methods may be applied to any embedded source description. While applicability to all embedded source codes provides great flexibility, this separation approach begs the question of whether better performance could be achieved by taking advantage of the internal structure of a particular embedded code. In this paper, we investigate an extremely simple method for using an embedded source code's internal state information in the construction of a multiple description code. In particular, we protect an embedded SPIHT bitstream by adding to that bitstream periodic descriptions of state information from the encoder, and we demonstrate how the state information can be used to recover lost bits. For low probabilities of network packet loss, the proposed algorithm achieves performance within 0.35 dB of the performance of a more sophisticated channel coding algorithm when both algorithms are applied to same SPIHT embedded source code.

Packet-based data communication systems suffer from packet loss under high network traffic conditions. As a result, the receiver is often left with an incomplete description of the requested data. Multiple description source coding addresses the problem of minimizing the expected distortion caused by packet loss. An equivalent problem is that of source coding for data transmission over multiple channels where each channel has some probability of breaking down. Recent work in practical multiple description coding explores the design of multiple description scalar and vector quantizers for the case of two channels or packets. This paper presents a new practical algorithm, based on a ternary tree structure, for the design of both fixed- and variable-rate multiple description vector quantizers for an arbitrary number of channels. Experimental results achieved by codes designed with this algorithm show that they perform well under a wide range of packet loss scenarios.