Publications (7)6.98 Total impact

Article: Index Coding With Side Information
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ABSTRACT: Motivated by a problem of transmitting supplemental data over broadcast channels (Birk and Kol, INFOCOM 1998), we study the following coding problem: a sender communicates with n receivers R<sub>1</sub>,..., R<sub>n</sub>. He holds an input x ∈ {0,01l}<sup>n</sup> and wishes to broadcast a single message so that each receiver Ri can recover the bit x<sub>i</sub>. Each R<sub>i</sub> has prior side information about x, induced by a directed graph Grain nodes; Ri knows the bits of a; in the positions {j  (i,j) is an edge of G}.G is known to the sender and to the receivers. We call encoding schemes that achieve this goal INDEXcodes for {0,1}<sup>n</sup> with side information graph G. In this paper we identify a measure on graphs, the minrank, which exactly characterizes the minimum length of linear and certain types of nonlinear INDEX codes. We show that for natural classes of side information graphs, including directed acyclic graphs, perfect graphs, odd holes, and odd antiholes, minrank is the optimal length of arbitrary INDEX codes. For arbitrary INDEX codes and arbitrary graphs, we obtain a lower bound in terms of the size of the maximum acyclic induced subgraph. This bound holds even for randomized codes, but has been shown not to be tight. 
Article: Index Coding With Side Information.
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ABSTRACT: Peertopeer storage and in particular backupsystem architectures have recently attracted much interest due to their use of "free " resources, with disk spindles and communication bandwidth being at least as important as storage space. This paper complements most of the works on this topic, whose focus was on metadata, security, locating the stored data, etc., by focusing on the data itself. It offers important design considerations and insights pertaining to the composition of erasurecorrection code (ECC) groups, their size and the level of redundancy. Dynamic issues such as the coscheduling of the concurrent reconstruction of multiple ECC groups are also explored. Finally, we identify an interesting natural match between asymmetric communication bandwidth (e.g., ADSL) and a hierarchical reconstruction architecture aimed at alleviating bottlenecks at the reconstructing node. 
Conference Paper: Index Coding with Side Information
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ABSTRACT: Motivated by a problem of transmitting data over broadcast channels (BirkandKol, INFOCOM1998), we study the following coding problem: a sender communicates with n receivers R<sub>l</sub>,.., R<sub>n</sub>. He holds an input x isin {0, 1}<sub>n</sub> and wishes to broadcast a single message so that each receiver R<sub>i</sub> can recover the bit x<sub>i</sub>. Each R<sub>i</sub> has prior side information about x, induced by a directed graph G on n nodes; R<sub>i </sub> knows the bits of x in the positions {j  (i, j) is anedge of G}. We call encoding schemes that achieve this goal INDEX codes for {0, 1} <sup>n</sup> with side information graph G. In this paper we identify a measure on graphs, the minrank, which we conjecture to exactly characterize the minimum length of INDEX codes. We resolve the conjecture for certain natural classes of graphs. For arbitrary graphs, we show that the minrank bound is tight for both linear codes and certain classes of nonlinear codes. For the general problem, we obtain a (weaker) lower bound that the length of an INDEX code for any graph G is at least the size of the maximum acyclic induced subgraph of G  [Show abstract] [Hide abstract]
ABSTRACT: The InformedSource Coding On Demand (ISCOD) approach for efficiently supplying nonidentical data from a central server to multiple caching clients over a broadcast channel is presented. The key idea underlying ISCOD is the joint exploitation of the data blocks already cached by each client, the server's full knowledge of clientcache contents and client requests, and the fact that each client only needs to be able to derive the blocks requested by it rather than all the blocks ever transmitted or even the union of the blocks requested by the different clients. We present twophase ISCOD algorithms: the server first creates adhoc errorcorrection sets based on its knowledge of client states; next, it uses erasurecorrection codes to construct the data for transmission. Each client uses its cached data and the received supplemental data to derive its requested blocks. The result is up to a severalfold reduction in the amount of transmitted supplemental data. Also, we define kpartial cliques in a directed graph and cast ISCOD in terms of partialclique covers. 

Conference Paper: Informedsource codingondemand (ISCOD) over broadcast channels
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ABSTRACT: We present the informed source coding ondemand (ISCOD) approach for efficiently supplying nonidentical data from a central server to multiple caching clients through a broadcast channel. The key idea underlying ISCOD is the joint exploitation of the data already cached by each client, the server's full awareness of client cache contents and client requests, and the fact that each client only needs to be able to derive the items requested by it rather than all the items ever transmitted or even the union of the items requested by the different clients. We present a set of twophase ISCOD algorithms. The server uses these algorithms to assemble adhoc error correction sets based its knowledge of every client's cache content and of the items requested by it; next, it uses errorcorrection codes to construct the data that is actually transmitted. Each client uses its cached data and the received supplemental data to derive the items that it has requested. This technique achieves a reduction of up to tens of percents in the amount of data that must be transmitted in order for every client to be able to derive the data requested by it. Finally, we define kpartial cliques in a directed graph, and cast the two phase approach in terms of partial clique covers. As a byproduct of this work, bounds and a close approximation for the expected cardinality of the maximum matching in a random graph have been derived and are outlined
Publication Stats
482  Citations  
6.98  Total Impact Points  
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Institutions

19982011

Technion  Israel Institute of Technology
 Electrical Engineering Group
H̱efa, Haifa, Israel
