The history of the theory and practice of quantization dates to 1948, although similar ideas had appeared in the literature as long ago as 1898. The fundamental role of quantization in modulation and analog-to-digital conversion was first recognized during the early development of pulsecode modulation systems, especially in the 1948 paper of Oliver, Pierce, and Shannon. Also in 1948, Bennett published the first high-resolution analysis of quantization and an exact analysis of quantization noise for Gaussian processes, and Shannon published the beginnings of rate distortion theory, which would provide a theory for quantization as analog-to-digital conversion and as data compression. Beginning with these three papers of fifty years ago, we trace the history of quantization from its origins through this decade, and we survey the fundamentals of the theory and many of the popular and promising techniques for quantization.

The problem of error control and concealment in video communication is becoming increasingly important because of the growing interest in video delivery over unreliable channels such as wireless networks and the Internet. This paper reviews the techniques that have been developed for error control and concealment in the past ten to fifteen years. These techniques are described in three categories according to the roles that the encoder and decoder play in the underlying approaches. Forward error concealment includes methods that add redundancy at the source end to enhance error resilience of the coded bit streams. Error concealment by postprocessing refers to operations at the decoder to recover the damaged areas based on characteristics of image and video signals. Finally, interactive error concealment covers techniques that are dependent on a dialog between the source and destination. Both current research activities and practice in international standards are covered.

This thesis proposes two constructive methods of approaching the Shannon limit very closely. Interestingly, these two methods operate in opposite regions, one has a block length of one and the other has a block length approaching infinity. The first approach is based on novel memoryless joint source-channel coding schemes. We first show some examples of sources and channels where no coding is optimal for all values of the signal-to-noise ratio (SNR). When the source bandwidth is greater than the channel bandwidth, joint coding schemes based on space-filling curves and other families of curves are proposed. For uniform sources and modulo channels, our coding scheme based on space-filling curves operates within 1.1 dB of Shannon’s rate-distortion bound. For Gaussian sources and additive white Gaussian noise (AWGN) channels, we can achieve within 0.9 dB of the rate-distortion bound. The second scheme is based on low-density parity-check (LDPC) codes. We first demonstrate that we can translate threshold values of an LDPC code between channels accurately using a simple mapping. We develop some models for density evolution

We explore joint source-channel coding (JSCC) for time-varying channels using a multiresolution framework for both source coding and transmission via novel multiresolution modulation constellations. We consider the problem of still image transmission over time-varying channels with the channel state information (CSI) available at 1) receiver only and 2) both transmitter and receiver being informed about the state of the channel, and we quantify the effect of CSI availability on the performance. Our source model is based on the wavelet image decomposition, which generates a collection of subbands modeled by the family of generalized Gaussian distributions. We describe an algorithm that jointly optimizes the design of the multiresolution source codebook, the multiresolution constellation, and the decoding strategy of optimally matching the source resolution and signal constellation resolution “trees” in

Asymptotically optimal zero-delay vector quantization in the presence of channel noise is studied using random coding techniques. First, an upper bound is derived for the average r th - power distortion of channel optimized k-dimensional vector quantization at transmission rate R on a binary symmetric channel with bit error probability ffl. The upper bound asymptotically equals 2 \GammarRg(ffl;k;r) , where k k+r h 1 \Gamma log 2 i 1 + 2 p ffl(1 \Gamma ffl) ji g(ffl; k; r) 1 for all ffl 0, lim ffl!0 g(ffl; k; r) = 1, and lim k!1 g(ffl; k; r) = 1. Numerical computations of g(ffl; k; r) are also given. This result is analogous to Zador's asymptotic distortion rate of 2 \GammarR for quantization on noiseless channels. Next, using a random coding argument on nonredundant index assignments, a useful upper bound is derived in terms of point density functions, on the minimum mean squared error of high resolution, regular, vector quantizers in the presence of channel noise. T...

Abstract — We study hybrid error control for real-time video transmission. The study is carried out using a proposed integrated joint source-channel coding framework, which jointly considers error resilient source coding, channel coding, and error concealment, in order to achieve the best video quality. We focus on the performance comparison of several error correction scenarios, such as forward error correction (FEC), retransmission, and the combination of both. Simulation results show that either FEC or retransmission can be optimal depending on the packet loss rates and network round trip time. The proposed hybrid FEC/retransmission scheme outperforms both. I.

We determine analytic expressions for the performance of some low-complexity combined source-channel coding systems. The main tool used is the Hadamard transform. In particular, we obtain formulas for the average distortion of binary lattice vector quantization with affine index assignments, linear block channel coding, and a binary-symmetric channel. The distortion formulas are specialized to nonredundant channel codes for a binary-symmetric channel, and then extended to affine index assignments on a binary-asymmetric channel. Various structured index assignments are compared. Our analytic formulas provide a computationally efficient method for determining the performance of various coding schemes. One interesting result shown is that for a uniform source and uniform quantizer, the Natural Binary Code is never optimal for a nonsymmetric channel, even though it is known to be optimal for a symmetric channel. Index Terms--- Index assignment, lattices, linear error-correcting codes, sou...

We propose three new design algorithms for jointly optimizing source and channel codes. Our optimality criterion is to minimize the average end-to-end distortion. For a given channel SNR and transmission rate, our joint source and channel code designs achieve an optimal allocation of bits between the source and channel coders. Our three techniques include a sourceoptimized channel code, a channel-optimized source code, and an iterative descent technique combining the design strategies of the other two codes. The joint designs use channel-optimized vector quantization (COVQ) for the source code and rate-compatible punctured convolutional (RCPC) coding for the channel code. The optimal bit allocation reduces distortion by up to 6 dB over suboptimal allocations and by up to 4 dB relative to standard COVQ for the source data set considered. We find that all three code designs have roughly the same performance when their bit allocations are optimized. This result follows from the fact that at the optimal bit allocation the channel code removes most of the channel errors, in which case the three design techniques are roughly equivalent. We also compare the robustness of the three techniques to channel mismatch. We conclude the paper by relaxing the fixed transmission rate constraint and jointly optimizing the transmission rate, source code, and channel code. Index Terms---Joint source/channel coding, optimal bit allocation, RCPC channel code, vector quantization. I.

In digital transmission of speech, audio, images and video signals residual redundancy is often left after source coding due to the complexity and delay constraints. This redundancy remains both inside one block or frame but also in a time correlation of subsequent frames. We describe an approach to improve channel and source decoding by using both kinds of correlation. Further on we consider the bit-mapping and the multiplexing in coding and its effect on decoding. The mutual information as measurement for the gain in decoding through a priori information is explained. In this work on combined source and channel decoding, we try to answer the following question: Can a priori information that models the source parameters be used twice; first at the channel decoder and then at the source decoden The channel decoder uses the a priori informarion that models the bit stream generated by the source coden This doesn't capture all the details of the source parameter level statistics. By exploiting the a priori knowledge of parameters (once more) at the source decoder, we show that it is possible to achieve better reconstruction than if this information was used at either of the decoders.

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