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Register a new userImproved Communication Efficiency for Distributed Mean Estimation with Side Information
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Added by
Kai Liang
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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In this paper, we consider the distributed mean estimation problem where the server has access to some side information, e.g., its local computed mean estimation or the received information sent by the distributed clients at the previous iterations. We propose a practical and efficient estimator based on an r-bit Wynzer-Ziv estimator proposed by Mayekar et al., which requires no probabilistic assumption on the data. Unlike Mayekars work which only utilizes side information at the server, our scheme jointly exploits the correlation between clients data and server s side information, and also between data of different clients. We derive an upper bound of the estimation error of the proposed estimator. Based on this upper bound, we provide two algorithms on how to choose input parameters for the estimator. Finally, parameter regions in which our estimator is better than the previous one are characterized.
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We consider the problem of Private Information Retrieval with Private Side Information (PIR-PSI), wherein a user wants to retrieve a file from replication based non-colluding databases by using the prior knowledge of a subset of the files stored on the databases. The PIR-PSI framework ensures that the privacy of the demand and the side information are jointly preserved, thereby finding potential applications when multiple files have to be downloaded spread across different time-instants. Although the capacity of the PIR-PSI setting is known, we observe that the underlying capacity achieving code construction uses Maximum Distance Separable (MDS) codes thereby contributing to high computational complexity when retrieving the demand. Pointing at this drawback of MDS-based PIR-PSI codes, we propose XOR-based PIR-PSI codes for a simple yet non-trivial setting of two non-colluding databases and two side information files at the user. While our codes offer substantial reduction in complexity when compared to MDS based codes, the code-rate marginally falls short of the capacity of the PIR-PSI setting. Nevertheless, we show that our code-rate is strictly higher than that of XOR-based codes for PIR with no side information, thereby implying that our codes can be useful when downloading multiple files in a sequential manner, instead of applying XOR-based PIR codes on each file.
This letter investigates a new class of index coding problems. One sender broadcasts packets to multiple users, each desiring a subset, by exploiting prior knowledge of linear combinations of packets. We refer to this class of problems as index coding with coded side-information. Our aim is to characterize the minimum index code length that the sender needs to transmit to simultaneously satisfy all user requests. We show that the optimal binary vector index code length is equal to the minimum rank (minrank) of a matrix whose elements consist of the sets of desired packet indices and side- information encoding matrices. This is the natural extension of matrix minrank in the presence of coded side information. Using the derived expression, we propose a greedy randomized algorithm to minimize the rank of the derived matrix.
Index coding is a source coding problem in which a broadcaster seeks to meet the different demands of several users, each of whom is assumed to have some prior information on the data held by the sender. If the sender knows its clients requests and their side-information sets, then the number of packet transmissions required to satisfy all users demands can be greatly reduced if the data is encoded before sending. The collection of side-information indices as well as the indices of the requested data is described as an instance of the index coding with side-information (ICSI) problem. The encoding function is called the index code of the instance, and the number of transmissions employed by the code is referred to as its length. The main ICSI problem is to determine the optimal length of an index code for and instance. As this number is hard to compute, bounds approximating it are sought, as are algorithms to compute efficient index codes. Two interesting generalizations of the problem that have appeared in the literature are the subject of this work. The first of these is the case of index coding with coded side information, in which linear combinations of the source data are both requested by and held as users side-information. The second is the introduction of error-correction in the problem, in which the broadcast channel is subject to noise. In this paper we characterize the optimal length of a scalar or vector linear index code with coded side information (ICCSI) over a finite field in terms of a generalized min-rank and give bounds on this number based on constructions of random codes for an arbitrary instance. We furthermore consider the length of an optimal error correcting code for an instance of the ICCSI problem and obtain bounds on this number, both for the Hamming metric and for rank-metric errors. We describe decoding algorithms for both categories of errors.
This paper focuses on the structural properties of test channels, of Wyners operational information rate distortion function (RDF), $overline{R}(Delta_X)$, of a tuple of multivariate correlated, jointly independent and identically distributed Gaussian random variables (RVs), ${X_t, Y_t}_{t=1}^infty$, $X_t: Omega rightarrow {mathbb R}^{n_x}$, $Y_t: Omega rightarrow {mathbb R}^{n_y}$, with average mean-square error at the decoder, $frac{1}{n} {bf E}sum_{t=1}^n||X_t - widehat{X}_t||^2leq Delta_X$, when ${Y_t}_{t=1}^infty$ is the side information available to the decoder only. We construct optimal test channel realizations, which achieve the informational RDF, $overline{R}(Delta_X) triangleqinf_{{cal M}(Delta_X)} I(X;Z|Y)$, where ${cal M}(Delta_X)$ is the set of auxiliary RVs $Z$ such that, ${bf P}_{Z|X,Y}={bf P}_{Z|X}$, $widehat{X}=f(Y,Z)$, and ${bf E}{||X-widehat{X}||^2}leq Delta_X$. We show the fundamental structural properties: (1) Optimal test channel realizations that achieve the RDF, $overline{R}(Delta_X)$, satisfy conditional independence, $ {bf P}_{X|widehat{X}, Y, Z}={bf P}_{X|widehat{X},Y}={bf P}_{X|widehat{X}}, hspace{.2in} {bf E}Big{XBig|widehat{X}, Y, ZBig}={bf E}Big{XBig|widehat{X}Big}=widehat{X} $ and (2) similarly for the conditional RDF, ${R}_{X|Y}(Delta_X) triangleq inf_{{bf P}_{widehat{X}|X,Y}:{bf E}{||X-widehat{X}||^2} leq Delta_X} I(X; widehat{X}|Y)$, when ${Y_t}_{t=1}^infty$ is available to both the encoder and decoder, and the equality $overline{R}(Delta_X)={R}_{X|Y}(Delta_X)$.
The problem of joint source-channel coding in transmitting independent sources over interference channels with correlated receiver side information is studied. When each receiver has side information correlated with its own desired source, it is shown that source-channel code separation is optimal. When each receiver has side information correlated with the interfering source, sufficient conditions for reliable transmission are provided based on a joint source-channel coding scheme using the superposition encoding and partial decoding idea of Han and Kobayashi. When the receiver side information is a deterministic function of the interfering source, source-channel code separation is again shown to be optimal. As a special case, for a class of Z-interference channels, when the side information of the receiver facing interference is a deterministic function of the interfering source, necessary and sufficient conditions for reliable transmission are provided in the form of single letter expressions. As a byproduct of these joint source-channel coding results, the capacity region of a class of Z-channels with degraded message sets is also provided.
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