Index Coding—An Interference Alignment Perspective
TL;DR: An equivalence is established between the capacity of multiple unicast index coding and groupcast index coding, which settles the heretofore open question of insufficiency of linear codes for the multiple unicasts index coding problem by equivalence with groupcast settings.
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Abstract: Author(s): Maleki, H; Cadambe, VR; Jafar, SA | Abstract: The index coding problem is studied from an interference alignment perspective providing new results as well as new insights into, and generalizations of, previously known results. An equivalence is established between the capacity of multiple unicast index coding (where each message is desired by exactly one receiver), and groupcast index coding (where a message can be desired by multiple receivers), which settles the heretofore open question of insufficiency of linear codes for the multiple unicast index coding problem by equivalence with groupcast settings, where this question has previously been answered. Necessary and sufficient conditions for the achievability of rate half per message in the index coding problem are shown to be a natural consequence of interference alignment constraints, and generalizations to feasibility of rate 1/(L+1)per message when each destination desires at least L messages, are similarly obtained. Finally, capacity optimal solutions are presented to a series of symmetric index coding problems inspired by the local connectivity and local interference characteristics of wireless networks. The solutions are based on vector linear coding. © 1963-2012 IEEE.
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Citations
Asymptotic Interference Alignment for Optimal Repair of MDS Codes in Distributed Storage
TL;DR: This paper addresses exact repair MDS codes, which allow for any single failed node to be repaired exactly with access to any arbitrary set of d survivor nodes, and characterize the capacity of a class of multisource nonmulticast networks.
289
Finite-Length Analysis of Caching-Aided Coded Multicasting
TL;DR: This paper designs a new random placement and an efficient clique cover-based delivery scheme that achieves this lower bound approximately and provides tight concentration results that show that the average number of transmissions concentrates very well requiring only a polynomial number of packets in the rest of the system parameters.
On the capacity region for index coding
Fatemeh Arbabjolfaei,Bernd Bandemer,Young-Han Kim,Eren Sasoglu,Lele Wang +4 more
- 07 Jul 2013
TL;DR: A new inner bound on the capacity region of the general index coding problem is established, which relies on a random coding scheme and optimal decoding, and has a simple polymatroidal single-letter expression.
188
Local graph coloring and index coding
Karthikeyan Shanmugam,Alexandros G. Dimakis,Michael Langberg +2 more
- 07 Jul 2013
TL;DR: In this paper, an upper bound for the optimal index coding rate using a graph theoretic quantity called the local chromatic number (LQN) is presented, which is used as an alignment guide to assign index coding vectors from a general position MDS code.
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Finite Length Analysis of Caching-Aided Coded Multicasting
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References
Interference Alignment and Degrees of Freedom of the $K$ -User Interference Channel
Viveck R. Cadambe,Syed A. Jafar +1 more
TL;DR: For the fully connected K user wireless interference channel where the channel coefficients are time-varying and are drawn from a continuous distribution, the sum capacity is characterized as C(SNR)=K/2log (SNR)+o(log( SNR), which almost surely has K/2 degrees of freedom.
A Random Linear Network Coding Approach to Multicast
TL;DR: This work presents a distributed random linear network coding approach for transmission and compression of information in general multisource multicast networks, and shows that this approach can take advantage of redundant network capacity for improved success probability and robustness.
Coding for Errors and Erasures in Random Network Coding
TL;DR: A Reed-Solomon-like code construction, related to Gabidulin's construction of maximum rank-distance codes, is described and a Sudan-style ldquolist-1rdquo minimum-distance decoding algorithm is provided.
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Interference channels
TL;DR: General bounds on the capacity region are obtained for discrete memoryless interference channels and for linear-superposition interference channels with additive white Gaussian noise.
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A Survey on Network Codes for Distributed Storage
Alexandros G. Dimakis,Kannan Ramchandran,Yunnan Wu,Changho Suh +3 more
- 04 Feb 2011
TL;DR: In this paper, the authors provide an overview of the research results on network coding for distributed storage systems and provide a comparison between erasure codes and network coding techniques, showing that maintenance bandwidth can be reduced by orders of magnitude compared to standard erasure code.
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