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sequential coding of correlated sources

IEEE TRANSACTIONS ON INFORMATION THEORY 2000年第1期46卷 236-246页

作者： Viswanathan, H Berger, T Cornell Univ Sch Elect Engn Ithaca NY 14850 USA

We study a generalization of the successive refinement coding problem called the sequential coding of correlated sources. In successive refinement source coding one first describes the given source using a few bits of information, and then subsequently improves the description of the same source when more information is supplied. sequential coding differs from successive refinement in that the second-stage encoding involves describing a correlated source as opposed to improving the description of the same source. We introduce the notion of a coupled fidelity criterion to quantify perceived distortion in certain applications of sequential coding. We characterize the achievable rate region far this source coding problem and show that the rate region reduces to the successive refinement rate region when the two sources are the same. Then we consider the specific case of a pair of correlated Gaussian sources as an example. We give an explicit characterization that reveals an interesting generalization of a property of successive refinement of a single Gaussian source.

关键词： Gaussian source coding multiterminal source coding perceptual distortion sequential coding successive refinement

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On Delayed sequential coding of Correlated Sources

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IEEE TRANSACTIONS ON INFORMATION THEORY 2011年第6期57卷 3763-3782页

作者： Ma, Nan Ishwar, Prakash Boston Univ Dept Elect & Comp Engn Boston MA 02215 USA

Motivated by video coding applications, the problem of sequential coding of correlated sources with encoding and/or decoding frame-delays is studied. The fundamental tradeoffs between individual frame rates, individual frame distortions, and encoding/decoding frame-delays are derived in terms of a single-letter information-theoretic characterization of the rate-distortion region for general interframe source correlations and certain types of potentially frame specific and coupled single-letter fidelity criteria. The sum-rate-distortion region is characterized in terms of generalized directed information measures highlighting their role in delayed sequential source coding problems. For video sources which are spatially stationary memoryless and temporally Gauss-Markov, MSE frame distortions, and a sum-rate constraint, our results expose the optimality of idealized differential predictive coding among all causal sequential coders, when the encoder uses a positive rate to describe each frame. Somewhat surprisingly, causal sequential encoding with one-frame-delayed noncausal sequential decoding can exactly match the sum-rate-MSE performance of joint coding for all nontrivial MSE-tuples satisfying certain positive semidefiniteness conditions. Thus, even a single frame-delay holds potential for yielding significant performance improvements. Generalizations to higher order Markov sources are also presented and discussed. A rate-distortion performance equivalence between, causal sequential encoding with delayed noncausal sequential decoding, and delayed noncausal sequential encoding with causal sequential decoding, is also established.

关键词： Differential predictive coded modulation directed information Gauss-Markov sources mean squared error rate-distortion theory sequential coding source coding successive refinement coding sum-rate video coding

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On Two-Stage sequential coding of Correlated Sources

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IEEE TRANSACTIONS ON INFORMATION THEORY 2014年第12期60卷 7490-7505页

作者： Wang, Jia Wu, Xiaolin Sun, Jun Yu, Songyu Shanghai Jiao Tong Univ Inst Image Commun & Network Engn Dept Elect Engn Shanghai 200030 Peoples R China Shanghai Key Lab Digital Media Proc & Transmiss Shanghai 200240 Peoples R China McMaster Univ Dept Elect & Comp Engn Hamilton ON L8S 4L8 Canada

We study the problem of two-stage sequential coding (TSSC), which is an extension of sequential coding of correlated sources. Let X and Y be dependent random variables. The network contains two encoders and two decoders: 1) a Y encoder with input Y;2) an X encoder with inputs X and Y;3) a Y decoder that reconstructs Y;and 4) an X decoder that reconstructs X. The first stage is traditional sequential coding, where the Y encoder describes Y to both the X decoder and Y decoder, and the X encoder describes X and Y to the X decoder. At the second stage, the Y encoder refines the description of Y, and the X encoder refines the description of X. The TSSC model is a theoretical abstraction of scalable video coding;here, Y and X represent successive frames of a video sequence, and the two stages together give an embedded description that allows the video to be decoded at two distinct rates. We give an inner bound on the rate distortion region for this TSSC model. The tight bound on the rate distortion region is derived when Y must be reconstructed losslessly (in the usual Shannon sense) in the second stage. We also study the minimum total rate of the TSSC model and show that the minimum total rate of one-stage sequential coding cannot be achieved at both stages for jointly Gaussian sources. This theoretical result can shed light on the rate-distortion performance behavior of scalable video coding widely noted by practitioners.

关键词： sequential coding minimum total rate sequentially successive refinability cardinality bound

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Design of Optimal Scalar Quantizer for sequential coding of Correlated Sources

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IEEE TRANSACTIONS ON COMMUNICATIONS 2019年第1期67卷 693-707页

作者： Wu, Huihui Dumitrescu, Sorina McMaster Univ Dept Elect & Comp Engn Hamilton ON L8S 4L8 Canada

This paper addresses the design of a sequential scalar quantizer (SSQ) for finite-alphabet correlated sources in the fixed-rate (FR) and entropy-constrained (EC) cases. The optimization problem is formulated as the minimization of a weighted sum of distortions and rates. The proposed solution is globally optimal for the class of SSQs with convex cells and is based on solving the minimum-weight path (MWP) problem in the EC case, respectively, a length-constrained MWP problem in the FR case, in a series of weighted directed acyclic graphs. The asymptotic time complexity is O((K1K22)-K-2), where K-1 and K-2 are the respective sizes of the alphabets of the two sources. Additionally, it is proved that, by applying the proposed algorithms to discretizations of correlated sources with continuous joint probability density function, the performance approaches that of the optimal EC-SSQ, respectively, FR-SSQ, with convex cells for the original sources as the accuracy of the discretization increases. Extensive experiments performed with correlated Gaussian sources validate the effectiveness in practice of the proposed approach in approximating the optimal SSQ for the case of continuous-alphabet sources.

关键词： sequential coding scalar quantization globally optimal algorithm minimum-weight path problem

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Design of Optimal Entropy-constrained Scalar Quantizer for sequential coding of Correlated Sources

Design of Optimal Entropy-constrained Scalar Quantizer for S...

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2017 IEEE Information Theory Workshop (ITW)

作者： Wu, Huihui Dumitrescu, Sorina McMaster Univ Dept Elect & Comp Engn Hamilton ON Canada

ISBN: (纸本)9781509030972

This work addresses the design of a sequential code for correlated sources using entropy-constrained scalar quantization at each encoder. We consider discrete sources and propose a globally optimal algorithm to minimize a weighted sum of distortions and rates. Our algorithm is based on solving the minimum weight path problem in a series of appropriately constructed weighted directed acyclic graphs. Its asymptotical time complexity is O((N1N22)-N-2), where N-1 and N-2 denote the alphabet sizes of the two sources, respectively.

关键词： sequential coding scalar quantization entropy-constrained globally optimal algorithm minimum weight path problem

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Achievability of Maximum Decoding Rate on sequential coding

Achievability of Maximum Decoding Rate on Sequential Coding

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IEEE Information Theory Workshop (ITW)

作者： Nishiara, Mikihiko Shinshu Univ Dept Elect & Elect Engn Nagano Japan

ISBN: (纸本)9781457704376

A sequential code such as an arithmetic code is a code that determines a prefix of the codeword from a prefix of the source sequence. The reciprocal of the time period in which the transmitter can send a single code symbol is called the transmission velocity. Since, at every moment, the restored length cannot be longer than the source length, the decoding rate is one at most. In this manuscript, we derive a transmission velocity at which the decoding rate is one almost surely with sequential codes.

关键词： Block codes Decoding Delay Transmitters arithmetic code arithmetic codes decoding maximum decoding rate sequential coding single code symbol transmission velocity

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Signal analysis and classification of a novel active brain-computer interface based on four-category sequential coding

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BIOMEDICAL SIGNAL PROCESSING AND CONTROL 2022年第0期78卷 000-000页

作者： Wang, Li Huang, Xuewen Ren, Lingling Zhan, Qianqian Guangzhou Univ Sch Elect & Commun Engn Guangzhou 510006 Peoples R China

In order to increase the number of instruction sets for the active brain-computer interface (BCI), a novel experimental paradigm based on the sequential coding of motor imagery and speech imagery is proposed in this paper. By dividing one motor imagery and one speech imagery into time series, four imagination tasks are obtained: 1) motor imagery;2) speech imagery;3) motor imagery first and then speech imagery;4) speech imagery first and then motor imagery. After analyzing the temporal, frequency and spatial features of electroencephalography (EEG) signals, four types of signals are classified by a multi-classification model based on time sequence. In this model, feature extraction and classification are accomplished by common spatial pattern (CSP) and support vector machine (SVM), respectively. 12 subjects participate in this experimental paradigm, and their average classification accuracy is 68.94%. The classification results are much higher than random probability, so the proposed experimental paradigm is feasible and valuable. The experimental paradigm based on sequential coding can effectively increase the number of instruction sets of active BCIs, so the practicability of BCIs is also improved.

关键词： Brain-computer interface (BCI) sequential coding Motor imagery Speech imagery Electroencephalogram (EEG)

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Low-complexity sequential lossless coding for piecewise-stationary memoryless sources

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IEEE TRANSACTIONS ON INFORMATION THEORY 1999年第5期45卷 1498-1519页

作者： Shamir, GI Merhav, N Univ Notre Dame Dept Elect Engn Notre Dame IN 46556 USA Technion Israel Inst Technol Dept Elect Engn IL-32000 Haifa Israel

Three strongly sequential, lossless compression schemes, one with linearly growing per-letter computational complexity, and two with fixed per-letter complexity, are presented and analyzed for memoryless sources with abruptly changing statistics. The first method, which improves on Willems' weighting approach, asymptotically achieves a lower bound on the redundancy, and hence is optimal, The second scheme achieves redundancy of O(log N/N) when the transitions in the statistics are large, and O (log log N/ log N) otherwise. The third approach always achieves redundancy of O(root log N/N). Obviously, the two fixed complexity approaches can be easily combined to achieve the better redundancy between the two. Simulation results support the analytical bounds derived for all the coding schemes.

关键词： change detection ideal code length minimum description length piecewise-stationary memoryless source redundancy segmentation sequential coding source block code strongly sequential coding transition path universal coding weighting

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Gaussian Robust sequential and Predictive coding

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IEEE TRANSACTIONS ON INFORMATION THEORY 2013年第6期59卷 3635-3652页

作者： Song, Lin Chen, Jun Wang, Jia Liu, Tie McMaster Univ Dept Elect & Comp Engn Hamilton ON L8S 4K1 Canada Shanghai Jiao Tong Univ Dept Elect Engn Shanghai 200240 Peoples R China Shanghai Jiao Tong Univ Inst Image Commun & Network Engn Shanghai 200240 Peoples R China Texas A&M Univ Dept Elect & Comp Engn College Stn TX 77843 USA

We introduce two new source coding problems: robust sequential coding and robust predictive coding. For the Gauss-Markov source model with the mean squared error distortion measure, we characterize certain supporting hyperplanes of the rate region of these two coding problems. Our investigation also reveals an information-theoretic minimax theorem and the associated extremal inequalities.

关键词： Extremal inequality Gauss-Markov source minimax theorem predictive coding saddle point sequential coding

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Faster sequential universal coding via block partitioning

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IEEE TRANSACTIONS ON INFORMATION THEORY 2006年第4期52卷 1708-1710页

作者： Baron, D Baraniuk, RG Rice Univ Dept Elect & Comp Engn Houston TX 77005 USA

Rissanen provided a sequential universal coding algorithm based on a block partitioning scheme, where the source model is estimated at the beginning of each block. This approach asymptotically approaches the entropy at the fastest possible rate of 1/2 log (n) bits per unknown parameter. We show that the complexity of this algorithm is ohm(n log(n)), which is comparable to existing sequential universal algorithms. We provide a sequential O(n log (log (n))) algorithm by modifying Rissanen's block partitioning scheme. The redundancy with our approach is greater than with Rissanen's block partitioning scheme by a multiplicative factor 1 + O(1/log(log(n))), hence it asymptotically approaches the entropy at the fastest possible rate.

关键词： lossless source coding redundancy sequential coding universal coding

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