Multiple Description Quantizer Research Articles

Symmetric Scalable Multiple Description Scalar Quantization

Real-time data delivery over best-effort error-prone packet networks has invigorated the study of robust coding schemes, such as scalable multiple description coding (SMDC). In this context, the paper introduces a novel generic symmetric scalable multiple description quantizer (SSMDSQ) which generates perfectly balanced source descriptions. Novel embedded index assignments are proposed which are used to realize high, as well as medium-to-low redundancy SSMDSQs. Compared to existing designs, it is shown that the proposed quantizer constructions exhibit superior distortion-rate (D-R) performance. Moreover, this paper describes an innovative extension of the Lloyd-Max algorithm in order to optimize symmetric and asymmetric scalable multiple description quantizers. For a family of Generalized Gaussian (GG) source distributions, the proposed optimization algorithm yields on average a significant D-R performance gain over unoptimized quantizers. Furthermore, anchored in the designed SSMDSQs, an SMDC framework is established to realize packet-based transmission over erasure channels. In this framework, transmission strategies are determined for scenarios wherein the average packet loss rate over the transmission link is (a) unknown and (b) can be estimated at the encoder. For both scenarios, SMDC packetized transmission is simulated for a family of GG distributions. Experimental results confirm that, compared to contemporary schemes, the designed quantizer constructions (with or without optimization) account for a significant average gain in signal-to-noise ratio (SNR) for a wide range of packet loss rates.

Multiple Description Distribution Preserving Quantization

The notion of a multiple description quantizer (MDQ) includes providing multiple distortion levels. If a human observer is involved, the design of MDQ requires a suitable distortion measure to achieve a graceful quality degradation in the case of description losses. While the mean squared error is a ubiquitous distortion measure for many classic MDQ schemes, it is known to be perceptually relevant only at low distortions. We propose a new MDQ designed according to an unconventional distortion criterion that combines the mean squared error with a constraint on the probability distribution of the reconstructed signal. The performance of the new MDQ is shown to approach that of the classic MDQ asymptotically as rate increases. However, once applied in the context of transform audio coding, the new MDQ significantly outperforms a classic MDQ in perceptual tests. The new scheme is suitable for a wide range of distortions and renders a seamless transition between coding that preserves signal features and coding of a waveform.

Multiple description quantizer design for multiple-antenna systems with MAP detection

We study the design of index assignment based multiple description quantizers for multiple-antenna systems with slow Rayleigh fading. A time-interleaver is employed at the transmitter to provide independent channel instances for the multiple descriptions, and a maximum a posteriori (MAP) detector is employed at the receiver to jointly decode the multiple descriptions. The concatenation of index assignment, binary phase-shift keying modulators, space-time orthogonal block coder, multiple-antenna channel, and MAP detector is modeled as a discrete memoryless channel. We optimize multiple description vector quantizers using an upper bound of the channel transition probability achieved by the MAP detector. The proposed scheme of combining multiple description coding and space-time orthogonal block coding is shown to be superior to each individual coding scheme.

Resource-Scalable Joint Source-Channel MAP and MMSE Estimation of Multiple Descriptions

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> A joint source-channel multiple description (JSC-MD) framework for signal estimation and communication in resource-constrained lossy networks is presented. To keep the encoder complexity at a minimum, a signal is coded by a multiple description quantizer (MDQ) with neither entropy nor channel coding. The code diversity of MDQ and the path diversity of the network are exploited by decoders to combat transmission errors. A key design objective is resource scalability: powerful nodes in the network can perform JSC-MD estimation under the criteria of maximum <emphasis emphasistype="boldital">a posteriori</emphasis> probability (MAP) or minimum mean-square error (MMSE), while primitive nodes resort to simpler MD decoding, all working with the same MDQ code. The application of JSC-MD to distributed estimation of hidden Markov models in a sensor network is demonstrated. The proposed JSC-MD MAP estimator is an algorithm of the longest path in a weighted directed acyclic graph, while the JSC-MD MMSE decoder is an extension of the well-known forward-backward algorithm to multiple descriptions. Both algorithms simultaneously exploit the source memory, the redundancy of the fixed-rate MDQ and the inter-description correlations. They outperform the existing hard-decision MDQ decoders by large margins (up to 8 dB). For Gaussian Markov sources, the complexity of JSC-MD distributed MAP sequence estimation can be made as low as that of typical single description Viterbi-type algorithms. </para>

Multiple description coding by successive quantization

Two structured multiple description (MD) vector quantization schemes with an iterative technique for designing the codebooks and partitions are proposed. The schemes are derived from the recent theoretical work by Chen et al. In the first scheme, the central decoder is formed by the weighted sum of the side codebooks, whereas the second scheme employs the optimum central decoder. The objective of the proposed iterative method is to minimize a Lagrangian cost function (defined as the weighted sum of the central and side distortions) to jointly design the side codebooks and find the associated partitions. The optimal parameters for minimizing the central distortion are also found. Simulations demonstrate that the proposed methods achieve performance close to that of the unstructured, full-search MD quantizer with considerably less complexity and with only a few iterations.

Sorting-based multiple description quantization

We introduce a new method for multiple description quantization (MDQ), based on sorting a frame of samples and transmitting, as side-information/redundancy, an index that describes the resulting permutation. The sorting-based approach has a similar performance to multiple description scalar quantization and a flexible structure, providing straightforward implementation of multidimensional MDQ

Multiple Description Quantization Via Gram–Schmidt Orthogonalization

The multiple description (MD) problem has received considerable attention as a model of information transmission over unreliable channels. A general framework for designing efficient multiple description quantization schemes is proposed in this paper. We provide a systematic treatment of the El Gamal-Cover (EGC) achievable MD rate-distortion region, and show that any point in the EGC region can be achieved via a successive quantization scheme along with quantization splitting. For the quadratic Gaussian case, the proposed scheme has an intrinsic connection with the Gram-Schmidt orthogonalization, which implies that the whole Gaussian MD rate-distortion region is achievable with a sequential dithered lattice-based quantization scheme as the dimension of the (optimal) lattice quantizers becomes large. Moreover, this scheme is shown to be universal for all i.i.d. smooth sources with performance no worse than that for an i.i.d. Gaussian source with the same variance and asymptotically optimal at high resolution. A class of low-complexity MD scalar quantizers in the proposed general framework also is constructed and is illustrated geometrically; the performance is analyzed in the high resolution regime, which exhibits a noticeable improvement over the existing MD scalar quantization schemes.

Optimal Two-Description Scalar Quantizer Design

Multiple description quantization is a signal compression technique for robust networked multimedia communication. In this paper we consider the problem of optimally quantizing a random variable into two descriptions, with each description being produced by a side quantizer of convex codecells. The optimization objective is to minimize the expected distortion given the probabilities of receiving either and both descriptions. The problem is formulated as one of shortest path in a weighted directed acyclic graph with constraints on the number and types of edges. An $O(K_1K_2N^3)$ time algorithm for designing the optimal two-description quantizer is presented, where $N$ is the cardinality of the source alphabet, and $K_1$, $K_2$ are the number of codewords of the two quantizers, respectively. This complexity is reduced to $O(K_1K_2N^2)$ by exploiting the Monge property of the objective function. Furthermore, if $K_1 = K_2 = K$ and the two descriptions are transmitted through two channels of the same statistics, then the optimal two-description quantizer design problem can be solved in $O(KN^2)$ time.

Monotonicity-Based Fast Algorithms for MAP Estimation of Markov Sequences Over Noisy Channels

In this correspondence, we study algorithmic approach to solving the problem of maximum a posteriori (MAP) estimation of Markov sequences transmitted over noisy channels, which is also known as the MAP decoding problem. For the class of memoryless binary channels that produce independent substitution and erasure errors, the MAP sequence estimation problem can be formulated and solved as one of the longest path in a weighted directed acyclic graph. But for algorithm efficiency, we transform the graph problem to one of matrix search. If the underlying matrix is totally monotone, then the complexity of MAP sequence estimation can be greatly reduced. We give a sufficient condition for the matrix induced by MAP sequence estimation to be totally monotone, which is indeed the case if the input sequence is Gaussian Markov. Under this condition, the complexity of MAP decoding can be reduced from O(N/sup 2/M) to O(NM), where N is the size of source alphabet and M is the length of input sequence. Furthermore, for Markov sequences of fixed-length code we propose a block parsing strategy to reduce the complexity of MAP sequence estimation to O(M+N/sup 2/M/logM) or to O(M+NM/logM), depending on if the total monotonicity holds. Another significance of this correspondence lies in the applicability of the presented algorithmic approach, which has been thoroughly studied in computer science literature, to many other discrete optimization problems encountered in both source and channel coding, ranging from optimal multiresolution and multiple-description quantizer design, to context quantization for minimum conditional entropy, and to optimal packetization with uneven error protection.

Entropy-Constrained Index Assignments for Multiple Description Quantizers

Multiple description coding has revealed itself highly useful for the transmission of digital signals over packet-switched networks or diversity systems. The index assignment problem is central in the theory and practice of multiple description quantizers. We propose a novel local optimization algorithm that produces index assignments for such quantizers. It locally minimizes the distortion due to description losses with constraints on the entropy of each description. It works in any vector dimension and is easily generalizable to various cases such as asymmetric descriptions or m-description systems. We present experimental comparisons with previously known index assignment methods in both scalar and vector cases and show that the proposed algorithm performs significantly better.

Multiple description quantization by deterministic annealing

The design of vector quantizers for diversity-based communication over two or more channels of possibly differing capacities and failure probabilities, is considered. The crucial dependence of current design techniques on initialization, especially of index assignment, is well recognized. Instead, we propose to pursue a deterministic annealing approach which is independent of initialization, does not assume any prior knowledge of the source density, and avoids many poor local minima of the cost surface. The approach consists of iterative optimization of a random encoder at gradually decreasing levels of randomness as measured by the Shannon entropy. At the limit of zero entropy, a hard multiple description (MD) quantizer is obtained. This process is directly analogous to annealing processes in statistical physics. Via an alternative derivation, we show that it may also be interpreted as approximating the minimum rate sums among points on the convex hull of the MD achievable rate-distortion region of El Gamal and Cover, subject to constraints on the sizes of the reproduction alphabets. To illustrate the potential of our approach, we present simulation results that show substantial performance gains over existing design techniques.

Asymptotic analysis of multiple description quantizers

A high-rate analysis of multiple description quantizers is presented for rth-power distortions and general source densities. Both, fixed-length and variable-length encoding of the quantizer indices are considered. Optimal companding functions are shown to be the same as for single-channel quantizers. As compared to the bound of Ozarow (1980), a gap of 8.69 dB and 3.07 dB exists between the entropy-constrained and level-constrained cases, respectively, for a memoryless Gaussian source and r=2.

Low-delay communication for Rayleigh fading channels: an application of the multiple description quantizer

We show the multiple description scalar quantizer (MDSQ), when used over a slow fading Rayleigh channel, results in a smaller interleaving delay than traditional channel code-based approaches and substantially outperforms a system using a maximum ratio combiner. We consider a continuous alphabet source without memory over a slow Rayleigh fading channel. Specifically, it is initially assumed that the Rayleigh parameter remains constant over a specific time interval and the demodulator has available perfect estimates of the Rayleigh parameter. An analysis of the problem is presented and theoretical justification is provided for using the MDSQ. For a Gaussian source without memory, performance comparisons are presented against a traditional maximum ratio combiner (MRC)-based system as well as against channel code-based systems. It is shown that the performance of the MDSQ-based system dominates the MRC-based system at all channel signal-to-noise ratios and is superior to channel code-based systems when the interleaving delay is constrained. Simulation results for a mobile radio channel model at 15 m.p.h. indicate a reduction in the interleaving delay by at least a factor of three.