Multivariate Time Series (MTS) forecasting plays a vital role in various real-world applications, such as traffic management and predictive maintenance. Existing approaches typically model MTS data in either Euclidean or Riemannian space, limiting their ability to capture the diverse geometric structures and complex Spatio-Temporal (ST) dependencies inherent in real-world data. To overcome this limitation, we propose the Hybird Symmetric Positive-Definite Manifold Graph Neural Network (HSMGNN), a novel graph neural network-based model that captures data geometry within a hybrid Euclidean–Riemannian framework. To the best of our knowledge, this is the first work to leverage hybrid geometric representations for MTS forecasting, enabling expressive and comprehensive modeling of geometric properties. Specifically, we introduce a Submanifold-Cross-Segment (SCS) embedding to project input MTS into both Euclidean and Riemannian spaces, thereby capturing ST variations across distinct geometric domains. To alleviate the high computational cost of Riemannian distance, we further design an Adaptive-Distance-Bank (ADB) layer with a trainable memory mechanism. Finally, a Fusion Graph Convolutional Network (FGCN) is devised to integrate features from the dual spaces via a learnable fusion operator for accurate prediction. Experiments on three benchmark datasets demonstrate that HSMGNN achieves up to 13.8% improvement over state-of-the-art baselines in forecasting accuracy.

This survey article focuses on the emerging connections between machine learning and data compression. While the fundamental limits of classical (lossy) data compression are well-established through rate-distortion theory, recent advancements have uncovered new theoretical analyses and application areas inspired by machine learning. We review recent works on task-based and goal-oriented compression, rate-distortion-perception theory, and compression for estimation and inference. Deep learning-based approaches have provided natural, data-driven methods for compression. Accordingly, we survey recent efforts in applying deep learning techniques to task-based or goal-oriented compression, as well as image/video compression and transmission. Additionally, we discuss the potential use of large language models for text compression. Finally, we outline future research directions in this promising field.

Distributed Source Coding (DSC), a scheme that encodes multiple correlated sources separately while decoding their bitstreams jointly, is an important branch of network information theory. Due to the advantages of shifting complexity burden from the encoder to the decoder and canceling the flow of data across terminals, DSC has potential applications in many scenarios, e.g., wireless sensor network, distributed genome data compression, etc. There are two forms (lossless and lossy) of DSC. Overlapped arithmetic codes, featured by overlapped intervals, are a variant of arithmetic codes that can implement distributed lossless compression, or the so-called Slepian-Wolf coding. For uniform binary sources, an overlapped arithmetic code is essentially a nonlinear many-to-one mapping that partitions source space into unequal-sized cosets. To analyze overlapped arithmetic codes, two theoretical tools have been proposed, i.e., Coset Cardinality Spectrum (CCS) and Hamming Distance Spectrum (HDS). The former describes how source space is partitioned into cosets (equally or unequally), and the latter describes how codewords are structured within each coset (densely or sparsely). However, until now, these two tools are almost parallel to each other, and it seems that there is no intersection between them. The main contribution of this paper is tightly bridging HDS with CCS. Specifically, HDS can be quickly and accurately calculated with CCS in some cases. In addition, the paper also proves the necessary and sufficient condition for the convergence of HDS and reveals the close relation between divergent HDS and polynomial division. All theoretical analyses are verified by experimental results.

Laplacian distribution is widely used to model the differences between correlated continuous or nonbinary signals, e.g., the predictive residues of videos. Usually, distributed coding of correlated nonbinary sources, e.g., distributed video coding, is implemented by binary or nonbinary Low-Density Parity-Check (LDPC) codes. In this paper, as an alternative, we attempt using nonbinary Distributed Arithmetic Coding (DAC) to implement distributed coding of uniform nonbinary sources with Laplace-distributed correlation. To analyze$Q$-ary DAC for uniform$Q$-ary sources, following the methodology developed in our prior work for binary DAC, we define and deduce Coset Cardinality Spectrum (CCS) from both fixed-length and variable-length perspectives, whose physical meanings are explained in detail; while for binary DAC, our prior work totally ignored the subtle difference between these two perspectives. Compared with binary DAC, an important advantage of nonbinary DAC is that, the mapping from source symbols to coding intervals is so flexible that there are many parameters that can be tuned to achieve better performance; while for binary DAC, there are very few tunable parameters, making it very hard to achieve better performance. This paper proposes a simple method to map source symbols onto coding intervals, which results in a very lightweight codec, while possessing a good Manhattan distance distribution. Then this paper deduces the formula of path metrics for decoder design by making use of CCS. All theoretical analyses are perfectly verified by simulation results. Most important, experimental results show that$Q$-ary DAC achieves significantly better performance than LDPC codes for distributed coding of uniform$Q$-ary sources with Laplace-distributed correlation.

Convolutional neural networks (CNNs)-based video quality enhancement generally employs optical flow for pixelwise motion estimation and compensation, followed by utilizing motion-compensated frames and jointly exploring the spatiotemporal correlation across frames to facilitate the enhancement. This method, called the optical-flow-based method (OPT), usually achieves high accuracy at the expense of high computational complexity. In this article, we develop a new framework, referred to as biprediction-based multiframe video enhancement (PMVE), to achieve a one-pass enhancement procedure. PMVE designs two networks, that is, the prediction network (Pred-net) and the frame-fusion network (FF-net), to implement the two steps of synthesization and fusion, respectively. Specifically, the Pred-net leverages frame pairs to synthesize the so-called virtual frames (VFs) for those low-quality frames (LFs) through biprediction. Afterward, the slowly fused FF-net takes the VFs as the input to extract the correlation across the VFs and the related LFs, to obtain an enhanced version of those LFs. Such a framework allows PMVE to leverage the cross-correlation between successive frames for enhancement, hence capable of achieving high accuracy performance. Meanwhile, PMVE effectively avoids the explicit operations of motion estimation and compensation, hence greatly reducing the complexity compared to OPT. The experimental results demonstrate that the peak signal-to-noise ratio (PSNR) performance of PMVE is fully on par with that of OPT while its computational complexity is only 1% of OPT. Compared with other state-of-the-art methods in the literature, PMVE is also confirmed to achieve superior performance in both objective quality and visual quality at a reasonable complexity level. For instance, PMVE can surpass its best counterpart method by up to 0.42 dB in PSNR.

Decoding of polar codes, a class of capacity-achieving channel codes, typically requires the perfect knowledge of channel parameter in advance. This paper aims to investigate how to decode polar codes when channel parameter is unknown. Specifically, we study a generalized Gilbert-Elliott channel model, which assumes that the channel switches between a finite number of states. On the platform of Soft CANcellation (SCAN), which is a low-complexity iterative decoding algorithm of polar codes superior to the widely-used Successive Cancellation (SC) decoder, we propose three adaptive algorithms,i.e., Sliding-Window SCAN (SWSCAN), Weighted-Window SCAN (W2SCAN), and Linear-Weighting SCAN (LWSCAN). These adaptive SCAN decoders are seeded with a coarse estimate of channel state, and after each SCAN iteration, the decoders progressively refine the estimate of channel state. Experimental results demonstrate that the proposed adaptive SCAN decoders outperform the original SCAN decoder and other competitors.

Distributed Arithmetic Coding (DAC) is a practical realization of Slepian-Wolf coding that partitions source space into cosets. Coset Cardinality Spectrum (CCS) is an important property of DAC that was defined in our previous work. In this paper, we give two applications of CCS. First, we find that DAC bitstream is not compact. The rate loss of DAC bitstream is caused by two factors:unequal coset partitioningandbit indivisibility. It is proved that as code length goes to infinity, the expected value ofbit-indivisibilityrate loss will tend to 0.5 for any irrational Rate Change Step (RCS), where the RCS refers to the rate change when one source bit is flipped. With the help of CCS, thebit-indivisibilityrate loss can be compensated to some extend. Especially, for any irrational RCS, as code length goes to infinity, the expected value of the remainingbit-indivisibilityrate loss after compensation will tend to about 0.47. The second application of CCS is DAC decoder design. We derive the formula of path metric and find that in the original paper on DAC, the intuitive formula of path metric is not correct. Thebackward-replacingalgorithm is proposed to make full use of memory. Experimental results confirm the correctness of theoretical analyses.

This paper designs a Distributed Arithmetic Coding (DAC) decoder using the depth-first search method. In addition, a method is proposed to control the decoder complexity. Simulation results compare the DFD with the traditional Breadth-First Decoder (BFD) showing that under the same complexity constraints, the DFD outperforms the BFD when the code length is not too long and the quality of side information is not too poor.

Deep learning provides a great potential for in-loop filtering to improve both coding efficiency and subjective quality in video coding. State-of-the-art work focuses on network structure design and employs a single powerful network to solve all problems. In contrast, this paper proposes a deep learning based systematic approach that includes an effective Convolutional Neural Network (CNN) structure, a hierarchical training strategy, and a video codec oriented switchable mechanism. First, we propose a novel CNN structure, i.e., Squeeze-and-Excitation Filtering CNN (SEFCNN), as an optional in-loop filter. To capture the non-linear interaction between channels, the SEFCNN is comprised of two subnets, i.e., Feature EXtracting (FEX) subnet and Feature ENhancing (FEN) subnet. Then, we develop a hierarchical model training strategy to adapt the two subnets to different coding scenarios. For high-rate videos with small artifacts, we train a single global model using the FEX for all types of frames, whereas for low-rate videos with large artifacts, different models are trained using both FEX and FEN for different types of frames. Finally, we propose an adaptive enhancing mechanism which is switchable between the CNN-based and the conventional methods. We selectively apply the CNN model to some frames or some regions in a frame. Experimental results show that the proposed scheme outperforms state-of-the-art work in coding efficiency, while the computational complexity is acceptable after GPU acceleration.

It was demonstrated that, as a nonlinear implementation of Slepian-Wolf Coding, Distributed Arithmetic Coding (DAC) outperforms traditional Low-Density Parity-Check (LPDC) codes for short code length and biased sources. This fact triggers research efforts into theoretical analysis of DAC. In our previous work, we proposed two analytical tools, Codebook Cardinality Spectrum (CCS) and Hamming Distance Spectrum, to analyze DAC for independent and identically-distributed (i.i.d.) binary sources with uniform distribution. This article extends our work on CCS from uniform i.i.d. binary sources to biased i.i.d. binary sources. We begin with the final CCS and then deduce each level of CCS backwards by recursion. The main finding of this article is that the final CCS of biased i.i.d. binary sources is not uniformly distributed over [0, 1). This article derives the final CCS of biased i.i.d. binary sources and proposes a numerical algorithm for calculating CCS effectively in practice. All theoretical analyses are well verified by experimental results.

Distributed arithmetic coding (DAC) is an effective technique for implementing Slepian-Wolf coding (SWC). It has been shown that a DAC code partitions source space into unequal-size codebooks, so that the overall performance of DAC codes depends on the cardinality and structure of these codebooks. The problem of DAC codebook cardinality has been solved by the so-called codebook cardinality spectrum (CCS). This paper extends the previous work on CCS by studying the problem of DAC codebook structure. We define Hamming distance spectrum (HDS) to describe DAC codebook structure and propose a mathematical method to calculate the HDS of DAC codes. The theoretical analyses are verified by experimental results.

Distributed arithmetic coding (DAC) is a variant of AC that can realize Slepian-Wolf coding in a nonlinear way. In our previous work, we defined codebook cardinality spectrum (CCS) and Hamming distance spectrum (HDS) for DAC. In this paper, we make use of CCS and HDS to analyze tailed DAC, which is a form of DAC that, as traditional AC, maps the last few symbols of each source block onto non-overlapped intervals. First, we derive the exact HDS formula for tailless DAC, a form of DAC that maps all the symbols of each source block onto overlapped intervals, and show that the HDS formula previously given is in fact approximation. Then, the HDS formula is extended to tailed DAC. Using CCS, we also deduce the average codebook cardinality, which is closely related to decoding complexity, and rate loss of tailed DAC. The effects of tail length are extensively analyzed. It is revealed that by increasing tail length to a value not close to the bitstream length, closely spaced codewords within the same codebook can be removed at the cost of a higher decoding complexity and a larger rate loss. Finally, theoretical analyses are verified by experiments.

Slepian-Wolf coding (SWC) can be effectively implemented by distributed arithmetic coding (DAC) codes. A theoretical tool named spectrum has been developed to analyze the complexity of the full-search binary DAC (BDAC) decoder for equiprobable sources. Following this work, this paper aims at improving the coding efficiency of BDAC codes. To achieve this goal, this paper analyzes how BDAC codes partition source space into codebooks and links codebook cardinalities with the initial spectrum. Further, by exploiting the final spectrum, this paper proves that the decoding error probability of BDAC codes will not tend to zero as code length goes to infinity, even at rates greater than the Slepian-Wolf limit. On the basis of theoretical analyses, two techniques are proposed to reduce the decoding error probability of BDAC codes, i.e., the permutation technique, which removes "near" (in the sense of Hamming distance) codewords in each codebook, and the weighted branching technique, which reduces the mis-pruning risk of proper paths during the decoding. The effectiveness of both techniques is well verified by experimental results.

Though distributed arithmetic coding (DAC) is an effective implementation of Slepian-Wolf coding, its performance, which is closely linked with its decoding complexity, has not received a thorough analysis. With binary sources with equally-likely symbols as the research object, this paper develops the DAC spectrum and makes use of it as a tool to answer the complexity problem of the ideal DAC decoder. Based on an in-depth analysis on DAC decoding process, we define the DAC spectrum and propose to find it by a recursive formulation. Firstly, the initial DAC spectrum is constrained by a functional equation and the Fourier transform is utilized to obtain its general explicit form. Secondly, an equation is given through which stage-(i+1) DAC spectrum can be deduced from stage-i DAC spectrum. A numerical method is also proposed for calculating DAC spectrum, whose convergency is proved. To measure the complexity of the ideal DAC decoder, we define the expansion factor and relate it to DAC spectrum. It is proved that if binary symbols 0 and 1 are mapped onto partially overlapped intervals [0, q) and [1-q, 1) respectively, the expansion factor will converge to 2q, i.e., the complexity of the ideal rate-α DAC decoder is approximately O(2^{n(1-α)}).

Asymmetric Slepian-Wolf coding (ASWC) of M-ary sources with nonstationary correlation is a very useful model for many practical problems. An effective implementation of this coding scheme is to binarize each M-ary source into multiple bitplanes which are then compressed by a single binary low-density parity-check (LDPC) code. Though the inter-bitplane correlation of M-ary sources can be exploited at the decoder by the joint-bitplane belief propagation (JBBP) algorithm, accurate online estimation of varying local source correlation still remains a major challenge. To tackle this problem, this paper proposes an M-ary counterpart of the sliding-window belief propagation (SWBP) algorithm to realize simultaneous source recovery and correlation estimation. To search for the optimal sliding-window size, the expected rate is raised as a new criterion. Moreover, an adaptive method is proposed to decide whether correlation reestimation is necessary. The M-ary SWBP (MSWBP) algorithm is then generalized to obtain its 2D form, which can be used to tackle the ASWC of 2D M-ary sources with nonstationary correlation. The developed 1D/2D-MSWBP algorithm inherits all merits of the original binary SWBP algorithm, e.g., near-optimal coding efficiency, low complexity, insensitivity to initial settings, etc., making it a very attractive technique in practice.

Low-density parity-check (LDPC) codes have been used to implement lossless distributed or conventional source coding. However, block-wise LDPC codes are difficult to adapt to varying source statistics as traditional symbol-wise entropy coding techniques. In this paper, we propose the sliding-window belief propagation (SWBP) algorithm which is able to simultaneously recover the source and refine the estimate of varying source statistics. The SWBP is easy to implement and performs well in simulations.

Recovery algorithms play a key role in compressive sampling (CS). Currently, a popular recovery algorithm for CS is the orthogonal matching pursuit (OMP), which possesses the merits of low complexity and good recovery quality. Considering that the OMP involves massive matrix/vector operations, it is very suited to being implemented in parallel on graphics processing unit (GPU). In this paper, we first analyze the complexity of each module in the OMP and point out the bottlenecks of the OMP lie in the projection module and the least-squares module. To speedup the projection module, Fujimoto's matrix-vector multiplication algorithm is adopted. To speedup the least-squares module, the matrix-inverse-update algorithm is adopted. Experimental results show that +40x speedup is achieved by our implementation of OMP on GTX480 GPU over on Intel(R) Core(TM) i7 CPU. Since the projection module occupies more than 2/3 of the total run time, we are looking for a faster matrix-vector multiplication algorithm.

This paper considers the LDPC-based Slepian-Wolf coding with decoder side information. The paper analyzes the statistical properties of LDPC syndromes and shows that there are residual redundancies in LDPC syndromes, especially at low rates. Furthermore, this paper proposes a rate-adaptive way to compress LDPC syndromes.

This paper proposes an improved algorithm of the error-resilient entropy coding (EREC). The idea is to record and transmit the states of variable-length data blocks (VLBs) and fixed-length data slots (FLSs) during EREC encoding process. The state information (SI) of VLBs and FLSs is used at the receiver to resynchronize VLBs during EREC decoding process. It is proved that the cost of SI is fewer than 3 bits per VLB. To combat errors in SI bits, we propose to code SI bits into EREC structure. Experimental results show that our proposed method improves recovery quality of VLC bitstream significantly.

The variable-length coding (VLC) is widely used in video coding to improve compression efficiency. However, suffering from the loss of synchronization, VLC bit stream is much more sensitive to random errors than fixed-length coding (FLC) bit stream. The EREC is a valid tool combating random errors in VLC bit stream. Due to its intrinsic property of error propagation, when the EREC is applied to video bit stream, those blocks placed later become much more likely to be lost. This paper proposes a simple method to further improve the error robustness of video bit stream by interleaving transform coefficients of blocks so that low-frequency information is always placed ahead of high-frequency information. Thus, low-frequency information of greater significance is less likely to be lost. Experimental results prove the superiority of the proposed method. In addition, block interleaving can also be used in data-partitioned video bit stream with ease.

H.264/AVC encoder complexity is remarkable due to mainly variable block size ME and exhaustive RDO mode decision. This makes application of H.264/AVC in network especially wireless environments very difficult. To reduce encoder complexity, statistical characteristics of modes among adjacent macroblocks (MBs) spatially and temporally are first studied using H.264 reference software. Then a fast algorithm is presented to reduce jointly the computational load of mode decision and ME. The main ideas are as follows: (1) candidate modes for current MB are first inferred from mode and motion information of defined reference MBs and then partial RDO approach is applied to make target selection; (2) ME is considered as a part of mode decision and no ME is required for particular modes that are eliminated in advance; (3) the exhaustive RDO method is invoked only if average distortion of the reference MBs goes beyond a predefined threshold. Simulation results demonstrate that our scheme can reduce encoder complexity significantly while coding efficiency is only slightly decreased.