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...
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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.
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, individua...
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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.
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 decode...
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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.
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 mi...
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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.
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 minimi...
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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.
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 s...
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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.
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 p...
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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.
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 ...
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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.
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 ...
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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.
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 a...
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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.
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