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The efficiency of investment information

IEEE TRANSACTIONS ON information THEORY 1998年第3期44卷 1026-1040页

作者： Erkip, E Cover, TM Rice Univ Dept Elect & Comp Engn Houston TX 77005 USA Stanford Univ Dept Stat Stanford CA 94305 USA Stanford Univ Dept Elect Engn Stanford CA 94305 USA

We investigate how the description of a correlated information V improves the investment in the stock market X. The objective is to maximize the growth rate of wealth in repeated investments. We find a single-letter characterization of the incremental growth rate Delta(R), the maximum increase in growth rate when V is described to the investor at rate R. The incremental growth rate specialized to the horse race market is related to source coding with side information of Wyner and Ahlswede-Korner. We provide two horse race examples: jointly binary and jointly Gaussian. The initial efficiency Delta'(0) is the maximum possible increase in the growth rate per bit of description. We show that the initial efficiency is related to the dependency between V and the market. In particular, for the horse race market, the initial efficiency is the square of the Hirschfeld-Gebelein-Renyi maximal correlation between V and X. This provides a connection with the hypercontraction of the Markov operator of Ahlswede and Gacs. For the general market the initial efficiency is 1 when the side information V is equal to the stock market outcome X.

关键词： investment maximal correlation portfolio source coding with side information

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Density Evolution for the Design of Non-Binary Low Density Parity Check Codes for Slepian-Wolf coding

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IEEE TRANSACTIONS ON COMMUNICATIONS 2015年第1期63卷 25-36页

作者： Dupraz, Elsa Savin, Valentin Kieffer, Michel Univ Cergy Pontoise CNRS ETIS ENSEA Cergy Pontoise France CEA LETI Digital Commun Lab Grenoble France Univ Paris 11 L2S CNRS SUPELEC Gif Sur Yvette France Inst Univ France Paris France

In this paper, we investigate the problem of designing good non-binary LDPC codes for Slepian-Wolf coding. The design method is based on Density Evolution which gives the asymptotic error probability of the decoder for given code degree distributions. Density Evolution was originally introduced for channel coding under the assumption that the channel is symmetric. In Slepian-Wolf coding, the correlation channel is not necessarily symmetric and the source distribution has to be taken into account. In this paper, we express the non-binary Density Evolution recursion for Slepian-Wolf coding. From Density Evolution, we then perform code degree distribution optimization using an optimization algorithm called differential evolution. Both asymptotic performance evaluation and finite-length simulations show the gain at considering optimized degree distributions for SW coding.

关键词： source coding with side information LDPC codes density evolution degree distribution optimization

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Precoding and decoding paradigms for distributed vector data compression

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2007年第4期55卷 1445-1460页

作者： Vosoughi, Azadeh Scaglione, Anna Univ Rochester Dept Elect & Comp Engn Rochester NY 14627 USA Cornell Univ Sch Elect & Comp Engn Ithaca NY 14853 USA

In this paper, we consider the problem of lossy coding of correlated vector sources with uncoded side information available at the decoder. In particular, we consider lossy coding of vector source x is an element of R-N which is correlated with vector source y is an element of R-N, known at the decoder. We propose two compression schemes, namely, distributed adaptive compression (DAC) and distributed universal compression (DUC) schemes. The DAC algorithm is inspired by the optimal solution for Gaussian sources and requires computation of the conditional Karhunen-Love transform (CKLT) of the data at the encoder. The DUC algorithm, however, does not require knowledge of the CKLT at the encoder. The DUC algorithms are based on the approximation of the correlation model between the sources V and x through a linear model y = Hx + n in which H is a matrix and n is a random vector and independent of x. This model can be viewed as a fictitious communication channel with input x and output V. Utilizing channel equalization at the receiver, we convert the original vector source coding problem into a set of manageable scalar source coding problems. Furthermore, inspired by bit loading strategies employed in wireless communication systems, we propose for both compression schemes a rate allocation policy which minimizes the decoding error rate under a total rate constraint. Equalization and bit loading are paired with a quantization scheme for each vector source entry (a slightly simplified version of the so called DISCUS scheme). The merits of our work are as follows: 1) it provides a simple, yet optimized, implementation of Wyner-Ziv quantizers for correlated vector sources, by using the insight gained in the design of communication systems;2) it provides encoding schemes that, with or without the knowledge of the correlation model at the encoder, enjoy distributed compression gains.

关键词： binnig Conditional Karhunen-Loeve transform (CKLT) correlated vector sources coset construction distributed source coding equalization Gaussian sources lossy coding pre-coding quantization rate allocation source coding with side information transform coding Wyner-Ziv encoders

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CHANNEL SIMULATION AND coding WITH side information

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IEEE TRANSACTIONS ON information THEORY 1994年第3期40卷 634-646页

作者： STEINBERG, Y VERDU, S Princeton University

We study the minimum random bit rate required to simulate a random system (channel), where the simulator operates with a given external input. As measures of simulation accuracy we use both the variational distance and the dBAR distance between joint input-output distributions. We find the asymptotic number of random bits per input sample required for accurate simulation, as a function of the distribution of the input process. These results hold for arbitrary channels and input processes, including nonstationary and nonergodic processes and do not hinge on a specific simulation scheme. A by-product of our analysis is a general formula for the minimal achievable source coding rate with side information.

关键词： CHANNEL SIMULATION CHANNEL SUP-ENTROPY CONDITIONAL SUP-ENTROPY RATE CONDITIONAL RESOLVABILITY source coding with side information

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Colored Gaussian source-channel broadcast for heterogeneous (analog/digital) receivers

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IEEE TRANSACTIONS ON information THEORY 2008年第4期54卷 1807-1814页

作者： Prabhakaran, Vinod M. Puri, Rohit Ramchandran, Karman Univ Illinois Coordinated Sci Lab Urbana IL 61801 USA NVIDIA Corp Santa Clara CA 95051 USA Univ Calif Berkeley Dept Elect Engn & Comp Sci Berkeley CA 94720 USA

The problem of transmitting a Gaussian source with memory to a digital and a linear-analog receiver, over an arbitrarily colored, non-degraded Gaussian broadcast channel is studied. The main result of this work is a complete characterization of the set of achievable distortion pairs at the two receivers given a power constraint at the transmitter. Further, a constructive hybrid uncoded-coded scheme consisting of the cascade of source coding with side information and channel coding with side information systems is shown to achieve the entire power-mean squared error (MSE) distortion region associated with the problem. An interesting operating point in this region is one where the digital receiver obtains the classical point-to-point optimal quality and the analog receiver attains the best possible simultaneously achievable distortion. This problem is motivated by the practical application of the seamless "in-band" digital upgrade of legacy analog transmission systems.

关键词： channel coding with side information colored Gaussian source-channel broadcast digital simulcast in-band digital overlay non-degraded broadcast source coding with side information source-channel broadcast

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A Note on the Broadcast Channel With Stale State information at the Transmitter

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IEEE TRANSACTIONS ON information THEORY 2015年第7期61卷 3622-3631页

作者： Kim, Hyeji Chia, Yeow-Khiang El Gamal, Abbas Stanford Univ Dept Elect Engn Stanford CA 94305 USA Inst Infocomm Res Singapore 138632 Singapore

This paper shows that the Maddah-Ali-Tse (MAT) scheme, which achieves the symmetric capacity of two example broadcast channels with strictly causal state information at the transmitter, is a simple special case of the Shayevitz-Wigger (SW) scheme for the broadcast channel with generalized feedback, which involves block Markov coding, Gray-Wyner compression, superposition coding, and Marton coding. Focusing on the class of symmetric broadcast channels with state, we derive an expression for the maximum achievable symmetric rate using the SW scheme. We show that the MAT results for the two-receiver case can be recovered by evaluating this expression for the special case in which superposition coding and Marton coding are not used. We then introduce a new broadcast channel example that shares many features of the MAT examples. We show that another special case of our maximum symmetric rate expression in which superposition coding is also used attains a higher symmetric rate than the MAT scheme. The symmetric capacity of this new example is not known, however.

关键词： Broadcast channel channel with state feedback source coding with side information

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information-Theoretic Caching: Sequential coding for Computing

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IEEE TRANSACTIONS ON information THEORY 2016年第11期62卷 6393-6406页

作者： Wang, Chien-Yi Lim, Sung Hoon Gastpar, Michael Univ Paris Saclay Telecom ParisTech Commun & Elect Dept F-75013 Paris France Ecole Polytech Fed Lausanne Sch Comp & Commun Sci CH-1015 Lausanne Switzerland

Under the paradigm of caching, partial data are delivered before the actual requests of users are known. In this paper, this problem is modeled as a canonical distributed source coding problem with side information, where the side information represents the users' requests. For the single-user case, a single-letter characterization of the optimal rate region is established, and for several important special cases, closed-form solutions are given, including the scenario of uniformly distributed user requests. In this case, it is shown that the optimal caching strategy is closely related to total correlation and Wyner's common information. Using the insight gained from the single-user case, three two-user scenarios admitting single-letter characterization are considered, which draw connections to existing source coding problems in the literature: the Gray-Wyner system and distributed successive refinement. Finally, the model studied by Maddah-Ali and Niesen is rephrased to make a comparison with the considered information-theoretic model. Although the two caching models have a similar behavior for the single-user case, it is shown through a two-user example that the two caching models behave differently in general.

关键词： Coded caching function computation Gray-Wyner system information bottleneck multi-terminal source coding source coding with side information successive refinement

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Heegard-Berger and Cascade source coding Problems With Common Reconstruction Constraints

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IEEE TRANSACTIONS ON information THEORY 2013年第3期59卷 1458-1474页

作者： Ahmadi, Behzad Tandon, Ravi Simeone, Osvaldo Poor, H. Vincent New Jersey Inst Technol Ctr Wireless Commun & Signal Proc Res Newark NJ 07102 USA Princeton Univ Princeton NJ 08544 USA

In lossy source coding with side information at the decoder (i.e., the Wyner-Ziv problem), the estimate of the source obtained at the decoder cannot be generally reproduced at the encoder, due to its dependence on the side information. In some applications, this may be undesirable, and a common reconstruction (CR) requirement, whereby one imposes that the encoder and decoder be able to agree on the decoder's estimate, may be instead in order. The rate-distortion function under the CR constraint has been derived recently for a point-to-point (Wyner-Ziv) problem. In this paper, this result is extended to three multiterminal settings with three nodes, namely the Heegard-Berger (HB) problem, its variant with cooperating decoders, and the cascade source coding problem. The HB problem consists of an encoder broadcasting to two decoders with respective side information. The cascade source coding problem is characterized by a two-hop system with side information available at the intermediate and final nodes. For the HB problem with the CR constraint, the rate-distortion function is derived under the assumption that the side information sequences are (stochastically) degraded. The rate-distortion function is also calculated explicitly for three examples, namely Gaussian source and side information with quadratic distortion metric, and binary source and side information with erasure and Hamming distortion metrics. The rate-distortion function is then characterized for the HB problem with cooperating decoders and (physically) degraded side information. For the cascade problem with the CR constraint, the rate-distortion region is obtained under the assumption that side information at the final node is physically degraded with respect to that at the intermediate node. For the latter two cases, it is worth emphasizing that the corresponding problem without the CR constraint is still open. Outer and inner bounds on the rate-distortion region are also obtained for the cascade probl

关键词： Cascade source coding common reconstruction (CR) Heegard-Berger (HB) problem source coding with side information

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information-Theoretic Caching: The Multi-User Case

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IEEE TRANSACTIONS ON information THEORY 2017年第11期63卷 7018-7037页

作者： Lim, Sung Hoon Wang, Chien-Yi Gastpar, Michael Korea Institute of Ocean Science and Technology Ansan South Korea MediaTek Inc. Hsinchu Taiwan School of Computer and Communication Sciences EPFL Lausanne Switzerland

In this paper, we consider a cache aided network in which each user is assumed to have individual caches, while upon users' requests, an update message is sent through a common link to all users. First, we formulate a general information theoretic setting that represents the database as a discrete memoryless source, and the users' requests as side information that is available everywhere except at the cache encoder. The decoders' objective is to recover a function of the source and the side information. By viewing cache aided networks in terms of a general distributed source coding problem and through information theoretic arguments, we present inner and outer bounds on the fundamental tradeoff of cache memory size and update rate. Then, we specialize our general inner and outer bounds to a specific model of content delivery networks: file selection networks, in which the database is a collection of independent equal-size files and each user requests one of the files independently. For file selection networks, we provide an outer bound and two inner bounds (for centralized and decentralized caching strategies). For the case when the user request information is uniformly distributed, we characterize the rate versus cache size tradeoff to within a multiplicative gap of 4. By further extending our arguments to the framework of Maddah-Ali and Niesen, we also establish a new outer bound and two new inner bounds in which it is shown to recover the centralized and decentralized strategies, previously established by Maddah-Ali and Niesen. Finally, in terms of rate versus cache size tradeoff, we improve the previous multiplicative gap of 72 to 4.7 for the average case with unitbrm requests.

关键词： Coded caching function computation multi terminal source coding source coding with side information

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Bit-Plane coding in Extractable source coding: Optimality, Modeling, and Application to 360° Data

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IEEE COMMUNICATIONS LETTERS 2021年第5期25卷 1412-1416页

作者： Ye, Fangping Bidgoli, Navid Mahmoudian Dupraz, Elsa Roumy, Aline Amis, Karine Maugey, Thomas UBL Lab STICC IMT Atlantique F-29238 Brest France Inria Rennes F-35042 Rennes France

In extractable source coding, multiple correlated sources are jointly compressed but can be individually accessed in the compressed domain. Performance is measured in terms of storage and transmission rates. This problem has multiple applications in interactive video compression such as Free Viewpoint Television or navigation in 360 degrees videos. In this letter, we analyze and improve a practical coding scheme. We consider a binarized coding scheme, which insures a low decoding complexity. First, we show that binarization does not impact the transmission rate but only slightly the storage with respect to a symbol based approach. Second, we propose a Q-ary symmetric model to represent the pairwise joint distribution of the sources instead of the widely used Laplacian model. Third, we introduce a novel pre-estimation strategy, which allows to infer the symbols of some bit planes without any additional data and therefore permits to reduce the storage and transmission rates. In the context of 360 degrees images, the proposed scheme allows to save 14% and 34% bitrate in storage and transmission rates respectively.

关键词： Decoding Parity check codes source coding Laplace equations Image coding Data models Video compression source coding with side information source modeling bit plane coding LDPC

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