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lattice quantization with side information: Codes, asymptotics, and applications in sensor networks

IEEE TRANSACTIONS ON INFORMATION THEORY 2007年第2期53卷 714-731页

作者： Servetto, Sergio D. Cornell Univ Sch Elect & Comp Engn Ithaca NY 14853 USA

In this paper, we consider the problem of rate/distortion with side information available only at the decoder. For the case of jointly Gaussian source X and side information Y, and mean-squared error distortion, Wyner proved in 1976 that the rate/distortion function for this problem is identical to the conditional rate/distortion function R-X\Y, assuming the side information Y is available at the encoder. In this paper we construct a structured class of asymptotically optimal quantizers for this problem: under the assumption of high correlation between source X and side information Y, we show there exist quantizers within our class whose performance comes arbitrarily close to Wyner's bound. As an application illustrating the relevance of the high-correlation asymptotics, we also explore the use of these quantizers in the context of a problem of data compression for sensor networks, in a setup involving a large number of devices collecting highly correlated measurements within a confined area. An important feature of our formulation is that, although the per-node throughput of the network tends to zero as network size increases, so does the amount of information generated by each transmitter. This is a situation likely to be encountered often in practice, which allows us to cast under new-and more "optimistic"-light some negative results on the transport capacity of large-scale wireless networks.

关键词： ad hoc networks capacity hexagonal lattice lattice codes lattice quantization multihop radio networks network information theory quantization rate/distortion rate/distortion with side information sensor networks source coding throughput vector quantization wireless networks

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lattice quantization error for redundant representations

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APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS 2009年第3期27卷 334-341页

作者： Borodachov, Sergiy Wang, Yang Towson Univ Dept Math Baltimore MD 21252 USA Michigan State Univ Dept Math E Lansing MI 48824 USA

Redundant systems such as frames are often used to represent a signal for error correction, denoising and general robustness. In the digital domain quantization needs to be performed. Given the redundancy, the distribution of quantization errors can be rather complex. In this paper we study quantization error for a signal X in R-d represented by a frame using a lattice quantizer. We completely characterize the asymptotic distribution of the quantization error as the cell size of the lattice goes to zero. We apply these results to get the necessary and sufficient conditions for the asymptotic form of the White Noise Hypothesis in the case of the pulse-code modulation scheme. Published by Elsevier Inc.

关键词： White Noise Hypothesis Finite frame Voronoi cell Vector quantization Linear independence over the rationals lattice quantization Asymptotically uniformly distributed PCM

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Some new lattice quantization algorithms for video compression coding

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY 2002年第1期12卷 53-60页

作者： Postoll, MS Natl Secur Agcy Ft George G Meade MD 20755 USA

We describe some improvements to a proposed algorithm which encodes the error due to motion compensation in a videoconferencing codec. The algorithm involves lattice quantization using the 8-dimensional E8 lattice. We show that by using a different but equivalent form of E8 based on the extended Hamming code, we can significantly reduce storage requirements and computational complexity at the receiver. We also show that it is easy to perform lattice quantization using the well known 24-dimensional Leech lattice, which is an even better quantizer than E8.

关键词： lattice quantization Leech lattice motion compensation vector quantization video compression videoconferencing

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RATE-DISTORTION MODELS FOR ENTROPY CONSTRAINED lattice quantization

RATE-DISTORTION MODELS FOR ENTROPY CONSTRAINED LATTICE QUANT...

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2010 IEEE International Conference on Acoustics, Speech, and Signal Processing

作者： Vasilache, Adriana Nokia Res Ctr Tampere 33720 Finland

ISBN: (纸本)9781424442966

In this paper we present new models for rate-distortion curves for entropy coded lattice codevectors. Exact models for both the rate and the distortion are proposed for the lattice Z(n) for generalized Gaussian sources. The resulting precision with respect to experimental values is improved by 50% over previously proposed models. In addition an approximate model for general lattices is proposed for Gaussian sources, its precision being verified against experimental values and shown to improve the estimation precision from 10% to 4%.

关键词： lattice quantization entropy coding rate-distortion models

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Privacy-preserving federated learning on lattice quantization

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INTERNATIONAL JOURNAL OF WAVELETS MULTIRESOLUTION AND INFORMATION PROCESSING 2023年第6期21卷

作者： Zhang, Lingjie Zhang, Hai Northwest Univ Xian Sch Math Xian 710127 Peoples R China Informat Sci Baoji Univ Arts & Sci Sch Math Baoji 721000 Peoples R China

Federated learning (FL) is an important approach to cooperate with multiple devices for learning without exchanging data between devices and central server. However, due to bandwidth and other reasons, the communication efficiency should be considered when the volume of information transmitted is limited. In this paper, we utilize the tool of lattice quantization form quantization theory and the variable intercommunication interval to improve communication efficiency. Meanwhile, to make strong privacy guarantee, we incorporate the notion of differential privacy (DP) to the FL framework with local SGD algorithm. By adding calibrated noises, we propose a universal lattice quantization for differentially private federated averaging algorithm (ULQ-DP-FedAvg). We provide tight privacy bound by using some privacy techniques. We also analyze the convergence bound of ULQ-DP-FedAvg based on bits rate constraints and the growing inter-communication interval as well as the data are non-independent identically distribution (Non-IID). It turns out that the algorithm converges and preserves that the privacy has scarcely influenced on the convergence rate. The effectiveness of our algorithm is demonstrated by synthetic and real datasets.

关键词： Differential privacy federated learning privacy amplification lattice quantization

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UNIFORM AND PIECEWISE UNIFORM lattice VECTOR quantization FOR MEMORYLESS GAUSSIAN AND LAPLACIAN SOURCES

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IEEE TRANSACTIONS ON INFORMATION THEORY 1993年第3期39卷 786-804页

作者： JEONG, DG GIBSON, JD TEXAS A&M UNIV SYST DEPT ELECT ENGNCOLL STNTX 77843

New lattice vector quantizer design procedures for nonuniform sources are developed that yield lattice vector quantizers with excellent performance while retaining the structure required for fast quantization. Analytical methods for truncating and scaling lattices to be used in vector quantizations are given, and their utility is demonstrated for i.i.d. Gaussian and Laplacian sources. An analytical technique for piecewise linear multidimensional companding is derived and the effectiveness of the multidimensional compandor designs is evaluated for i.i.d. Gaussian and Laplacian sources by performance comparisons to other vector quantizers.

关键词： VECTOR quantization lattice quantization MULTIDIMENSIONAL COMPANDING

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n-Channel entropy-constrained multiple-description lattice vector quantization

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IEEE TRANSACTIONS ON INFORMATION THEORY 2006年第5期52卷 1956-1973页

作者： Ostergaard, J Jensen, J Heusdens, R Delft Univ Technol Dept Informat & Commun Theory NL-2628 CD Delft Netherlands

In this paper, we derive analytical expressions for the central and side quantizers which, under high-resolution assumptions, minimize the expected distortion of a symmetric multiple-description lattice vector quantization (MD-LVQ) system subject to entropy constraints on the side descriptions for given packet-loss probabilities. We consider a special case of the general n-channel symmetric multiple-description problem where only a single parameter controls the redundancy tradeoffs between the central and the side distortions. Previous work on two-channel MD-LVQ showed that the distortions of the side quantizers can be expressed through the normalized second moment of a sphere. We show here that this is also the case for three-channel MD-LVQ. Furthermore, we conjecture that this is true for the general n-channel MD-LVQ. For given source, target rate, and packet-loss probabilities we find the optimal number of descriptions and construct the MD-LVQ system that minimizes the expected distortion. We verify theoretical expressions by numerical simulations and show in a practical setup that significant performance improvements can be achieved over state-of-the-art two-channel MD-LVQ by using three-channel MD-LVQ.

关键词： high-rate quantization lattice quantization multiple-description coding (NMC) vector quantization

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lattice AND TRELLIS quantization WITH lattice-BOUNDED AND TRELLIS-BOUNDED CODEBOOKS - HIGH-RATE THEORY FOR MEMORYLESS SOURCES

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IEEE TRANSACTIONS ON INFORMATION THEORY 1993年第1期39卷 46-59页

作者： EYUBOGLU, MV FORNEY, GD NORTHEASTERN UNIV BOSTONMA 02115

High-rate lattice and trellis quantizers for nonuniform sources are introduced and analyzed. The performance of these quantizers is determined by two separable quantities, the granular gain and the boundary gain, which are determined by the shapes of the granular cells and of the support region, respectively. The granular gain and boundary gain are the duals of shaping and coding gain in data transmission applications. Using this duality, it is shown for Gaussian sources that the ultimate achievable boundary gain with high-rate lattice-bounded lattice codebooks is the same as the ultimate gain that can be obtained from variable-rate entropy coding. It is observed that if lattice codebooks can achieve the ultimate granular gain of 0.255 bit per dimension, then lattice-bounded lattice codebooks can approach the rate-distortion limit. Finally, the performance of lattice quantizers is compared to that of optimum vector quantizers.

关键词： SOURCE CODING VECTOR quantization lattice quantization TRELLIS-CODED quantization TRELLIS-CODED MODULATION SHAPING

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n-Channel Asymmetric Entropy-Constrained Multiple-Description lattice Vector quantization

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IEEE TRANSACTIONS ON INFORMATION THEORY 2010年第12期56卷 6354-6375页

作者： Ostergaard, Jan Heusdens, Richard Jensen, Jesper Aalborg Univ Aalborg Denmark Delft Univ Technol Delft Netherlands Oticon Copenhagen Denmark

This paper is about the design and analysis of an index-assignment (IA)-based multiple-description coding scheme for the n-channel asymmetric case. We use entropy constrained lattice vector quantization and restrict attention to simple reconstruction functions, which are given by the inverse IA function when all descriptions are received or otherwise by a weighted average of the received descriptions. We consider smooth sources with finite differential entropy rate and MSE fidelity criterion. As in previous designs, our construction is based on nested lattices which are combined through a single IA function. The results are exact under high-resolution conditions and asymptotically as the nesting ratios of the lattices approach infinity. For any n, the design is asymptotically optimal within the class of IA-based schemes. Moreover, in the case of two descriptions and finite lattice vector dimensions greater than one, the performance is strictly better than that of existing designs. In the case of three descriptions, we show that in the limit of large lattice vector dimensions, points on the inner bound of Pradhan et al. can be achieved. Furthermore, for three descriptions and finite lattice vector dimensions, we show that the IA-based approach yields, in the symmetric case, a smaller rate loss than the recently proposed source-splitting approach.

关键词： High-rate quantization index assignments lattice quantization multiple description coding

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RATE-DISTORTION MODELS FOR ENTROPY CONSTRAINED lattice quantization

RATE-DISTORTION MODELS FOR ENTROPY CONSTRAINED LATTICE QUANT...

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IEEE International Conference on Acoustics, Speech, and Signal Processing

作者： Adriana Vasilache Nokia Research Center Visiokatu 1 33720 Tampere FINLAND

ISBN: (纸本)9781424442959

In this paper we present new models for rate-distortion curves for entropy coded lattice codevectors. Exact models for both the rate and the distortion are proposed for the lattice Z_(n) for generalized Gaussian sources. The resulting precision with respect to experimental values is improved by 50percent over previously proposed models. In addition an approximate model for general lattices is proposed for Gaussian sources, its precision being verified against experimental values and shown to improve the estimation precision from 10percent to 4percent.

关键词： lattice quantization entropy coding ratedistortion models Entropy coding entropy Precision quantization Rate distortion crystal lattices Gauss experimental value

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