We investigate distributed source coding of two correlated sources X and Y where messages are passed to a decoder in a cascade fashion. The encoder of X sends a message at rate R_1 to the encoder of Y. The encoder of Y then sends a message to the decoder at rate R_2 based both on Y and on the message it received about X. The decoder's task is to estimate a function of X and Y. For example, we consider the minimum mean squared-error distortion when encoding the sum of jointly Gaussian random variables under these constraints. We also characterize the rates needed to reconstruct a function of X and Y losslessly.
Our general contribution toward understanding the limits of the cascade multiterminal source coding network is in the form of inner and outer bounds on the achievable rate region for satisfying a distortion constraint for an arbitrary distortion function d(x,y,z). The inner bound makes use of a balance between two encoding tactics--relaying the information about X and recompressing the information about X jointly with Y. In the Gaussian case, a threshold is discovered for identifying which of the two extreme strategies optimizes the inner bound. Relaying outperforms recompressing the sum at the relay for some rate pairs if the variance of X is greater than the variance of Y.
A conjectural expression of the asymptotic gap between the rate-distortion function of an arbitrary generalized Gaussian multiterminal source coding system and that of its centralized counterpart in the high-resolution regime is proposed. The validity of this expression is verified when the number of sources is no more than 3.
In this paper, we present iterative algorithms that numerically compute the rate-distortion regions of two problems: the two-encoder multiterminal source coding problem and the Chief Executive Officer (CEO) problem, both under logarithmic loss distortion measure.With the clear connection of these models with the distributed information bottleneck method, the proposed algorithms may find usefulness in a variety of applications, such as clustering, pattern recognition and learning. We illustrate the efficiency of our algorithms through some numerical examples.
We study the problem of receive beamforming in uplink cascade multiple-input multiple-output (MIMO) systems as an instance of that of cascade multiterminal source coding for lossy function computation. Using this connection, we develop two coding schemes for the second and show that their application leads to beamforming schemes for the first. In the first coding scheme, each terminal in the cascade sends a description of the source that it observes; the decoder reconstructs all sources, lossily, and then computes an estimate of the desired function. This scheme improves upon standard routing …
Unified Theory of Source Coding: Part II -- Multiterminal Problems
在这两部分通信的第一篇论文中，我们在一个统一的框架中解决了各种非合作编码器的两终端信源编码问题，从而巩固了Shannon，Slepian-Wolf，Wyner，Ahlswede-Körner，Wyner-Ziv，Berger { \em et al.}的工作。还有杨柏格为了实现这样的统一，我们利用了一个基本原则，将大量的分析与手头的失真标准（如果有的话）分离开来，并扩展了香农和Wyner-Ziv的典型性论点。在这第二篇论文中，我们推广的基本原则，为任何数量的来源，并在其基础上详尽地解决所有的多端信源编码问题与非合作的编码器和一个解码器。失真标准（如适用）要求适用于单个字母并有界。我们的分析包括边信息的情况下，分别是部分可用，完全可用和完全不可用的解码器。正如我们的第一篇论文中所看到的，可实现的区域允许无限阶信息论描述。我们还表明，熵约束的多端估计问题可以解决作为我们的理论的一个特例。
Consider a generalized multiterminal source coding system, where $\ell\choose m$ encoders, each observing a distinct size-$m$ subset of $\ell$ ($\ell\geq 2$) zero-mean unit-variance symmetrically correlated Gaussian sources with correlation coefficient $ρ$, compress their observations in such a way that a joint decoder can reconstruct the sources within a prescribed mean squared error distortion based on the compressed data. The optimal rate-distortion performance of this system was previously known only for the two extreme cases $m=\ell$ (the centralized case) and $m=1$ (the distributed case)…
We consider a multiterminal source coding problem in which a source is estimated at a central processing unit from lossy-compressed remote observations. Each lossy-encoded observation is produced by a remote sensor which obtains a noisy version of the source and compresses this observation minimizing a local distortion measure which depends only on the marginal distribution of its observation. The central node, on the other hand, has knowledge of the joint distribution of the source and all the observations and produces the source estimate which minimizes a different distortion measure between…
We consider the problem of how to determine a fair source coding rate allocation method for the lossless data compression problem in multiterminal networks, e.g, the wireless sensor network where there are a large number of sources to be encoded. We model this problem by a game-theoretic approach and present a decomposition method for obtaining the Shapley value, a fair source coding rate vector in the Slepian-Wolf achievable region. We formulate a coalitional game model where the entropy function quantifies the cost incurred due to the source coding rates in each coalition. In the typical cas…
The three-node multiterminal lossy source coding problem is investigated. We derive an inner bound to the general rate-distortion region of this problem which is a natural extension of the seminal work by Kaspi'85 on the interactive two-terminal source coding problem. It is shown that this (rather involved) inner bound contains several rate-distortion regions of some relevant source coding settings. In this way, besides the non-trivial extension of the interactive two terminal problem, our results can be seen as a generalization and hence unification of several previous works in the field. Spe…
One of the main focus in federated learning (FL) is the communication efficiency since a large number of participating edge devices send their updates to the edge server at each round of the model training. Existing works reconstruct each model update from edge devices and implicitly assume that the local model updates are independent over edge devices. In FL, however, the model update is an indirect multi-terminal source coding problem, also called as the CEO problem where each edge device cannot observe directly the gradient that is to be reconstructed at the decoder, but is rather provided …
In this article, we study the problem of secret key generation in the multiterminal source model, where the terminals have access to correlated Gaussian sources. We assume that the sources form a Markov chain on a tree. We give a nested lattice-based key generation scheme whose computational complexity is polynomial in the number, N , of independent and identically distributed samples observed by each source. We also compute the achievable secret key rate and give a class of examples where our scheme is optimal in the fine quantization limit. However, we also give examples that show that our s…
In this paper, we consider the information-theoretic characterization of the set of achievable rates and distortions in a broad class of multiterminal communication scenarios with general continuous-valued sources and channels. A framework is presented which involves fine discretization of the source and channel variables followed by communication over the resulting discretized network. In order to evaluate fundamental performance limits, convergence results for information measures are provided under the proposed discretization process. Using this framework, we consider point-to-point source …
Practical implementations of secret-key generation are often based on sequential strategies, which handle reliability and secrecy in two successive steps, called reconciliation and privacy amplification. In this paper, we propose an alternative approach based on polar codes that jointly deals with reliability and secrecy. Specifically, we propose secret-key capacity-achieving polar coding schemes for the following models: (i) the degraded binary memoryless source (DBMS) model with rate-unlimited public communication, (ii) the DBMS model with one-way rate-limited public communication, (iii) the…
Index coding studies multiterminal source-coding problems where a set of receivers are required to decode multiple (possibly different) messages from a common broadcast, and they each know some messages a priori. In this paper, at the receiver end, we consider a special setting where each receiver knows only one message a priori, and each message is known to only one receiver. At the broadcasting end, we consider a generalized setting where there could be multiple senders, and each sender knows a subset of the messages. The senders collaborate to transmit an index code. This work looks at mini…
This work investigates functional source coding problems with maximal distortion, motivated by approximate function computation in many modern applications. The maximal distortion treats imprecise reconstruction of a function value as good as perfect computation if it deviates less than a tolerance level, while treating reconstruction that differs by more than that level as a failure. Using a geometric understanding of the maximal distortion, we propose a hypergraph-based source coding scheme for function computation that is constructive in the sense that it gives an explicit procedure for fin…
Coding and testing schemes and the corresponding achievable type-II error exponents are presented for binary hypothesis testing over two-hop relay networks. The schemes are based on cascade source coding techniques and {unanimous decision-forwarding}, the latter meaning that a terminal decides on the null hypothesis only if all previous terminals have decided on the null hypothesis. If the observations at the transmitter, the relay, and the receiver form a Markov chain in this order, then, without loss in performance, the proposed cascade source code can be replaced by two independent point-to…
This work considers the problem of multiterminal secret key agreement by limited total public discussion under the hypergraphical source model. The secrecy capacity as a function of the total discussion rate is completely characterized by a polynomial-time computable linear program. Compared to the existing solution for a particular hypergraphical source model called the pairwise independent network (PIN) model, the current result is a non-trivial extension as it applies to a strictly larger class of sources and a more general scenario involving helpers and wiretapper's side information. In pa…
This paper establishes the rate region for a class of source coding function computation setups where sources of information are available at the nodes of a tree and where a function of these sources must be computed at the root. The rate region holds for any function as long as the sources' joint distribution satisfies a certain Markov criterion. This criterion is met, in particular, when the sources are independent. This result recovers the rate regions of several function computation setups. These include the point-to-point communication setting with arbitrary sources, the noiseless multipl…
We consider the problem of distributed lossy linear function computation in a tree network. We examine two cases: (i) data aggregation (only one sink node computes) and (ii) consensus (all nodes compute the same function). By quantifying the accumulation of information loss in distributed computing, we obtain fundamental limits on network computation rate as a function of incremental distortions (and hence incremental loss of information) along the edges of the network. The above characterization, based on quantifying distortion accumulation, offers an improvement over classical cut-set type t…
