Multiple Description Vector Quantization Research Articles

Self-organizing maps for the design of multiple description vector quantizers

Multiple description coding is an appealing tool to guarantee graceful signal degradation in the presence of unreliable channels. While the principles of multiple description scalar quantization are well-understood and solid guidelines exist to design effective systems, the same does not hold for vector quantization, especially at low bit-rates, where burdensome and unsatisfactory design techniques discourage its use altogether in applications.In this work we use the self-organizing maps to design multiple description VQ codebooks. The proposed algorithm is flexible, fast and effective: it deals easily with a large variety of situations, including the case of more than two descriptions, with a computational complexity that remains fully affordable even for large codebooks, and a performance comparable to that of reference techniques.A thorough experimental analysis, conducted in a wide range of operating conditions, proves the proposed technique to perform on par with well-known reference methods based on greedy optimization, but with a much lower computational burden. In addition, the resulting codebook can be itself optimized, thus providing even better performance. All experiments are fully reproducible, with all software and data available online for the interested researchers.

Channel Optimized Distributed Multiple Description Coding

In this paper, channel optimized distributed multiple description vector quantization (CDMD) schemes are presented for distributed source coding in symmetric and asymmetric settings. The CDMD encoder is designed using a deterministic annealing approach over noisy channels with packet loss. A minimum mean squared error asymmetric CDMD decoder is proposed for effective reconstruction of a source, utilizing the side information (SI) and its corresponding received descriptions. The proposed iterative symmetric CDMD decoder jointly reconstructs the symbols of multiple correlated sources. Two types of symmetric CDMD decoders, namely the estimated-SI and the soft-SI decoders, are presented which respectively exploit the reconstructed symbols and a posteriori probabilities of other sources as SI in iterations. In a multiple source CDMD setting, for reconstruction of a source, three methods are proposed to select another source as its SI during the decoding. The methods operate based on minimum physical distance (in a wireless sensor network setting), maximum mutual information and minimum end-to-end distortion. The performance of the proposed systems and algorithms are evaluated and compared in detail.

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.

Multiple Descriptions With Symbol Based Turbo Codes Over Noisy Channels With Packet Loss: Design and Performance Analysis

Channel optimized multiple description (MD) vector quantization with symbol-based turbo codes are proposed, where the decoder exploits both nonuniformity of descriptions and their dependencies. The joint source channel coding strategy is devised by setting an entropy constraint for quantizer design, which together with the MD index assignment (IA), control the level of redundancy at the MD source coder output. This is in turn exploited by the source and channel decoders for robust transmission in presence of noise and packet loss. At the source coder, the IA is designed for an M-description vector quantizer using an efficient simulated annealing algorithm. Various numerical results and comparisons are provided to investigate the effect of different system and design parameters on the performance. The results specifically indicate improved performance in comparison to the prior art, and also in multiple input multiple output communications.

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.

Index assignment for MDVQ over memoryless binary symmetric channel with packet erasure

Genetic algorithm is applied to index assignment for multiple description vector quantization (MDVQ) over memoryless binary symmetric channel (BSC) with packet erasure. The cost evaluation function is presented based on this hybrid model. Simulation results based on the bit error rate for binary symmetric channel and the packet erasure rate demonstrate the usefulness of the proposed optimization scheme.

Robust low-delay audio coding using multiple descriptions

This paper proposes an encoding method for high-quality, low-delay audio communication that is robust to losses in packetized transmission. Robustness is provided by a multiple description vector quantization (MDVQ) technique that is designed to minimize the mean-squared error (MSE). The key to applying this technique effectively is the use of psycho-acoustically controlled preand post-filters that make the mean-squared quantization error perceptually relevant. Experiments show that the MDVQ-based encoder yields better results-in both MSE and subjective audio quality-than simple alternative coders with the same low delay.

Optimality and Suboptimality of Multiple-Description Vector Quantization With a Lattice Codebook

The asymptotic analysis of multiple-description vector quantization (MDVQ) with a lattice codebook for sources with smooth probability density functions (pdfs) is considered in this correspondence. Goyal et al. (2002) observed that as the side distortion decreases and the central distortion correspondingly increases, the quantizer cells farther away from the coarse lattice points shrink in a spatially periodic pattern. In this correspondence, two special classes of index assignments are used along strategic groupings of central quantizer cells to derive a straightforward asymptotic analysis, which provides an analytical explanation for the aforementioned observation. MDVQ with a lattice codebook was shown earlier to be asymptotically optimal in high dimensions, with a curious converging property, that the side quantizers achieve the space filling advantage of an n-dimensional sphere instead of an n-dimensional optimal polytope. The analysis presented here explains this behavior readily. While central quantizer cells on a uniform lattice are asymptotically optimal in high dimensions, the present authors have shown that by using nonuniform rather than uniform central quantizer cells, the central-side distortion product in an MDSQ can be reduced by 0.4 dB at asymptotically high rate. The asymptotic analysis derived here partially unifies these previous results in the same framework, though a complete characterization is still beyond reach.

Optimization of the index assignments for multiple description vector quantizers

The optimization criterion and a practically feasible new algorithm is stated for the optimization of the index assignments of a multiple-description unconstrained vector quantizer with an arbitrary number of descriptions. In the simulations, the index-optimized multiple-description vector quantizer achieves significant gains in source signal-to-noise ratio over scalar multiple description schemes.

Multiple description vector quantization with a coarse lattice

A multiple description (MD) lattice vector quantization technique for two descriptions was previously introduced in which fine and coarse codebooks are both lattices. The encoding begins with quantization to the nearest point in the fine lattice. This encoding is an inherent optimization for the decoder that receives both descriptions; performance can be improved with little increase in complexity by considering all decoders in the initial encoding step. The altered encoding relies only on the symmetries of the coarse lattice. This allows us to further improve performance without a significant increase in complexity by replacing the fine lattice codebook with a nonlattice codebook that respects many of the symmetries of the coarse lattice. Examples constructed with the two-dimensional (2-D) hexagonal lattice demonstrate large improvement over time sharing between previously known quantizers.

Multiple-description vector quantization with lattice codebooks: design and analysis

The problem of designing a multiple description vector quantizer with lattice codebook Lambda is considered. A general solution is given to a labeling problem which plays a crucial role in the design of such quantizers. Numerical performance results are obtained for quantizers based on the lattices A_2 and Z^i, i=1,2,4,8, that make use of this labeling algorithm. The high-rate squared-error distortions for this family of L-dimensional vector quantizers are then analyzed for a memoryless source with probability density function p and differential entropy h(p) < infty. For any a in (0,1) and rate pair (R,R), it is shown that the two-channel distortion d_0 and the channel 1 (or channel 2) distortions d_s satisfy lim_{R -> infty} d_0 2^(2R(1+a)) = (1/4) G(Lambda) 2^{2h(p)} and lim_{R -> infty} d_s 2^(2R(1-a)) = G(S_L) 2^2h(p), where G(Lambda) is the normalized second moment of a Voronoi cell of the lattice Lambda and G(S_L) is the normalized second moment of a sphere in L dimensions.