n-Channel Asymmetric Multiple-Description Lattice Vector Quantization

We present analytical expressions for optimal entropy-constrained multiple-description lattice vector quantizers which, under high-resolutions assumptions, minimize the expected distortion for given packet-loss probabilities. We consider the asymmetric case where packet-loss probabilities and side entropies are allowed to be unequal and find optimal quantizers for any number of descriptions in any dimension. We show that the normalized second moments of the side-quantizers are given by that of an $L$-dimensional sphere independent of the choice of lattices. Furthermore, we show that the optimal bit-distribution among the descriptions is not unique. In fact, within certain limits, bits can be arbitrarily distributed.Comment: To appear in the proceedings of the 2005 IEEE International Symposium on Information Theory, Adelaide, Australia, September 4-9, 200

Multiple Description Coding Using A New Bitplane-LVQ Scheme.

In this paper, a novel Bitplane-LVQ technique to compress subbands bitplane coefficients is proposed for multiple description coding (MDC) system

Stabilizing Error Correction Codes for Controlling LTI Systems over Erasure Channels

We propose (k,k') stabilizing codes, which is a type of delayless error correction codes that are useful for control over networks with erasures. For each input symbol, k output symbols are generated by the stabilizing code. Receiving any k' of these outputs guarantees stability. Thus, the system to be stabilized is taken into account in the design of the erasure codes. Our focus is on LTI systems, and we construct codes based on independent encodings and multiple descriptions. The theoretical efficiency and performance of the codes are assessed, and their practical performances are demonstrated in a simulation study. There is a significant gain over other delayless codes such as repetition codes.Comment: Accepted and presented at the IEEE 60th Conference on Decision and Control (CDC). arXiv admin note: substantial text overlap with arXiv:2112.1171

Optimal Design of Multiple Description Lattice Vector Quantizers

In the design of multiple description lattice vector quantizers (MDLVQ), index assignment plays a critical role. In addition, one also needs to choose the Voronoi cell size of the central lattice v, the sublattice index N, and the number of side descriptions K to minimize the expected MDLVQ distortion, given the total entropy rate of all side descriptions Rt and description loss probability p. In this paper we propose a linear-time MDLVQ index assignment algorithm for any K >= 2 balanced descriptions in any dimensions, based on a new construction of so-called K-fraction lattice. The algorithm is greedy in nature but is proven to be asymptotically (N -> infinity) optimal for any K >= 2 balanced descriptions in any dimensions, given Rt and p. The result is stronger when K = 2: the optimality holds for finite N as well, under some mild conditions. For K > 2, a local adjustment algorithm is developed to augment the greedy index assignment, and conjectured to be optimal for finite N. Our algorithmic study also leads to better understanding of v, N and K in optimal MDLVQ design. For K = 2 we derive, for the first time, a non-asymptotical closed form expression of the expected distortion of optimal MDLVQ in p, Rt, N. For K > 2, we tighten the current asymptotic formula of the expected distortion, relating the optimal values of N and K to p and Rt more precisely.Comment: Submitted to IEEE Trans. on Information Theory, Sep 2006 (30 pages, 7 figures

Index assignment for multiple description repair in distributed storage systems

Distributed storage systems have been receiving increasing attention lately due to the developments in cloud and grid computing. Furthermore, a major part of the stored information comprises of multimedia, whose content can be communicated even with a lossy (non-perfect) reconstruction. In this context, Multiple Description Lattice Quantizers (MDLQ) can be employed to encode such sources for distributed storage and store them across distributed nodes. Their inherent properties yield that having access to all nodes gives perfect reconstruction of the source, while the reconstruction quality decreases gracefully with fewer available nodes. If a set of nodes fails, lossy repair techniques could be applied to reconstruct the failed nodes from the available ones. This problem has mostly been studied with the lossless (perfect) reconstruction assumption. In this work, a general model, Multiple Description Lattice Quantizer with Repairs (MDLQR), is introduced that encompasses the lossy repair problem for distributed storage applications. New performance measures and repair techniques are introduced for MDLQR, and a non-trivial identity is derived, which is related to other results in the literature. This enables us to find the optimal encoder for a certain repair technique used in the MDLQR. Furthermore, simulation results are used to evaluate the performance of the different repair techniques. © 2014 IEEE

Multiple-Description Coding by Dithered Delta-Sigma Quantization

We address the connection between the multiple-description (MD) problem and Delta-Sigma quantization. The inherent redundancy due to oversampling in Delta-Sigma quantization, and the simple linear-additive noise model resulting from dithered lattice quantization, allow us to construct a symmetric and time-invariant MD coding scheme. We show that the use of a noise shaping filter makes it possible to trade off central distortion for side distortion. Asymptotically as the dimension of the lattice vector quantizer and order of the noise shaping filter approach infinity, the entropy rate of the dithered Delta-Sigma quantization scheme approaches the symmetric two-channel MD rate-distortion function for a memoryless Gaussian source and MSE fidelity criterion, at any side-to-central distortion ratio and any resolution. In the optimal scheme, the infinite-order noise shaping filter must be minimum phase and have a piece-wise flat power spectrum with a single jump discontinuity. An important advantage of the proposed design is that it is symmetric in rate and distortion by construction, so the coding rates of the descriptions are identical and there is therefore no need for source splitting.Comment: Revised, restructured, significantly shortened and minor typos has been fixed. Accepted for publication in the IEEE Transactions on Information Theor