Conference Paper

Index Coding with Side Information

Dept. of Electr. Eng., Technion-Israel Inst. of Technol., Haifa
DOI: 10.1109/FOCS.2006.42 Conference: Foundations of Computer Science, 2006. FOCS '06. 47th Annual IEEE Symposium on
Source: IEEE Xplore


Motivated by a problem of transmitting data over broadcast channels (BirkandKol, INFOCOM1998), we study the following coding problem: a sender communicates with n receivers Rl,.., Rn. He holds an input x isin {0, 1}n and wishes to broadcast a single message so that each receiver Ri can recover the bit xi. Each Ri has prior side information about x, induced by a directed graph G on n nodes; Ri 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} n 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 non-linear 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

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    • "codewords, x (n) k , generated according to an independent normal distribution X k ∼ N (0, α k P ), where α k ≥0 and k α k = 1 to satisfy the transmission power constraint. Multiplexing coding [16] and index coding [17] are employed to construct the subcodebooks. In multiplexing coding, two or more messages are first bijectively mapped to a single message, and then, the codewords are generated for this message. "
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    ABSTRACT: This paper investigates the capacity region of the three-receiver AWGN broadcast channel where the receivers (i) have private-message requests, and (ii) may know some of the messages requested by other receivers as side information. We first classify all 64 possible side information configurations into eight groups, each consisting of eight members.We next construct transmission schemes, and derive new inner and outer bounds for the groups. This establishes the capacity region for 52 out of 64 possible side information configurations. For six groups (i.e., groups 1, 2, 3, 5, 6, and 8 in our terminology), we establish the capacity region for all their members, and show that it tightens both the best known inner and outer bounds. For group 4, our inner and outer bounds tighten the best known inner bound and/or outer bound for all the group members. Moreover, our bounds coincide at certain regions, which can be characterized by two thresholds. For group 7, our inner and outer bounds coincide for four members, thereby establishing the capacity region. For the remaining four members, our bounds tighten both the best known inner and outer bounds.
    IEEE Transactions on Information Theory 07/2015; DOI:10.1109/TIT.2015.2463277 · 2.33 Impact Factor
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    • "Giventhechromaticnumberoftheconflictgraph,the correspondingindexcodeisformedbythemodulosum ofthebitswiththesamecolor.DenotingbyXthe multicastcodewordoutputofthecodedmulticasting scheme,asshownin[7],[12] "
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    ABSTRACT: The capacity of caching networks has received considerable attention in the past few years. The problem consists of finding the minimum rate (or load) to deliver all users' requested messages from the sources and/or caches in the network. In particular, the capacity of two network models, shared link caching networks and device-to-device caching networks, is relatively well understood. To advance the understanding of the capacity of more general caching networks, in this paper, we study a class of networks of increasing practical interest, namely, the combination caching networks. These networks are formed by a single source connected to n = (rk) user nodes through a layer of k relay nodes, such that each user node is connected to a unique subset of r relay nodes, and caching takes place at the user nodes only. In this setting, particularly useful to model heterogeneous wireless and wireline networks, we show that, in most parameter regimes, by using a concatenated coded multicasting - combination network coding (CM-CNC) scheme, the achievable maximum link load is inversely proportional to the per-user storage capacity M and to the degree of each user r. In addition, we provide an information theoretic converse and show that the gap between achievability and converse bounds is within a logarithmic factor of the system parameters in most regimes of practical interest.
    Signal Processing Advances in Wireless Communications (SPAWC), 2015 IEEE 16th International Workshop on, Stockholm, Sweden; 06/2015
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    • "The CIC delivery scheme is based on a minimum vertex coloring of the corresponding index coding conflict graph [13], H C,W = (V, E), constructed as follows: • Each packet requested by each user is represented as a distinct vertex in V. Each vertex v ∈ V is hence uniquely identified by a pair {ρ(v), µ(v)} where ρ(v) indicates the packet identity and µ(v) the user requesting it. "
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    ABSTRACT: Coded multicasting has been shown to be a promising approach to significantly improve the caching performance of content delivery networks with multiple caches downstream of a common multicast link. However, achievable schemes proposed to date have been shown to achieve the proved order-optimal performance only in the asymptotic regime in which the number of packets per requested item goes to infinity. In this paper, we first extend the asymptotic analysis of the achievable scheme in [1], [2] to the case of heterogeneous cache sizes and demand distributions, providing the best known upper bound on the fundamental limiting performance when the number of packets goes to infinity. We then show that the scheme achieving this upper bound quickly loses its multiplicative caching gain for finite content packetization. To overcome this limitation, we design a novel polynomial-time algorithm based on random greedy graph-coloring that, while keeping the same finite content packetization, recovers a significant part of the multiplicative caching gain. Our results show that the order-optimal coded multicasting schemes proposed to date, while useful in quantifying the fundamental limiting performance, must be properly designed for practical regimes of finite packetization.
    Computer Communications Workshops (INFOCOM WKSHPS), 2015 IEEE Conference on, Hong Kong; 04/2015
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