Exponential Golomb and Rice Error Correction codes for generalized near-capacity joint source and channel coding

The recently proposed Unary Error Correction (UEC) and Elias Gamma Error Correction (EGEC) codes facilitate the near-capacity Joint Source and Channel Coding (JSCC) of symbol values selected from large alphabets at a low complexity. Despite their large alphabet, these codes were only designed for a limited range of symbol value probability distributions. In this paper, we generalize the family of UEC and EGEC codes to the class of Rice and Exponential Golomb (ExpG) Error Correction (RiceEC and ExpGEC) codes, which have a much wider applicability, including the symbols produced by the H.265 video codec, the letters of the English alphabet and in fact any arbitrary monotonic unbounded source distributions. Furthermore, the practicality of the proposed codes is enhanced to allow a continuous stream of symbol values to be encoded and decoded using only fixed-length system components. We explore the parameter space to offer beneficial trade-offs between error correction capability, decoding complexity, as well as transmission-energy, -duration and -bandwidth over a wide range of operating conditions. In each case, we show that our codes offer significant performance improvements over the best of several state-of-the-art benchmarkers. In particular, our codes achieve the same error correction capability, as well as transmissionenergy, -duration and -bandwidth as a Variable Length Error- Correction (VLEC) code benchmarker, while reducing the decoding complexity by an order of magnitude. In comparison with the best of the other JSCC and Separate Source and Channel Coding (SSCC) benchmarkers, our codes consistently offer E_b/N_0 gains of between 0.5 dB and 1.0 dB which only appear to be modest, because the system operates close to capacity. These improvements are achieved for free, since they are not achieved at the cost of increasing transmission-energy, -duration, -bandwidth or decoding complexity

Dynamic information and constraints in source and channel coding

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2004.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 237-251).This thesis explore dynamics in source coding and channel coding. We begin by introducing the idea of distortion side information, which does not directly depend on the source but instead affects the distortion measure. Such distortion side information is not only useful at the encoder but under certain conditions knowing it at the encoder is optimal and knowing it at the decoder is useless. Thus distortion side information is a natural complement to Wyner-Ziv side information and may be useful in exploiting properties of the human perceptual system as well as in sensor or control applications. In addition to developing the theoretical limits of source coding with distortion side information, we also construct practical quantizers based on lattices and codes on graphs. Our use of codes on graphs is also of independent interest since it highlights some issues in translating the success of turbo and LDPC codes into the realm of source coding. Finally, to explore the dynamics of side information correlated with the source, we consider fixed lag side information at the decoder. We focus on the special case of perfect side information with unit lag corresponding to source coding with feedforward (the dual of channel coding with feedback).(cont.) Using duality, we develop a linear complexity algorithm which exploits the feedforward information to achieve the rate-distortion bound. The second part of the thesis focuses on channel dynamics in communication by introducing a new system model to study delay in streaming applications. We first consider an adversarial channel model where at any time the channel may suffer a burst of degraded performance (e.g., due to signal fading, interference, or congestion) and prove a coding theorem for the minimum decoding delay required to recover from such a burst. Our coding theorem illustrates the relationship between the structure of a code, the dynamics of the channel, and the resulting decoding delay. We also consider more general channel dynamics. Specifically, we prove a coding theorem establishing that, for certain collections of channel ensembles, delay-universal codes exist that simultaneously achieve the best delay for any channel in the collection. Practical constructions with low encoding and decoding complexity are described for both cases.(cont.) Finally, we also consider architectures consisting of both source and channel coding which deal with channel dynamics by spreading information over space, frequency, multiple antennas, or alternate transmission paths in a network to avoid coding delays. Specifically, we explore whether the inherent diversity in such parallel channels should be exploited at the application layer via multiple description source coding, at the physical layer via parallel channel coding, or through some combination of joint source-channel coding. For on-off channel models application layer diversity architectures achieve better performance while for channels with a continuous range of reception quality (e.g., additive Gaussian noise channels with Rayleigh fading), the reverse is true. Joint source-channel coding achieves the best of both by performing as well as application layer diversity for on-off channels and as well as physical layer diversity for continuous channels.by Emin Martinian.Ph.D

Network vector quantization

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

On some new approaches to practical Slepian-Wolf compression inspired by channel coding

This paper considers the problem, first introduced by Ahlswede and Körner in 1975, of lossless source coding with coded side information. Specifically, let X and Y be two random variables such that X is desired losslessly at the decoder while Y serves as side information. The random variables are encoded independently, and both descriptions are used by the decoder to reconstruct X. Ahlswede and Körner describe the achievable rate region in terms of an auxiliary random variable. This paper gives a partial solution for the optimal auxiliary random variable, thereby describing part of the rate region explicitly in terms of the distribution of X and Y