Enabling decentralized wireless index coding in practice

Index coding is a problem in theoretical computer science and network information theory that studies the optimal coding scheme for transmitting multiple messages across a network to receivers with different side information. The ultimate goal of index coding is to reduce transmission time in a communication network by minimizing the number of messages based on shared information. Index coding theory extends to several key engineering problems in network communication including peer to peer communication, distributed broadcast networks, and interference alignment. Although the theoretical connection between index coding and wireless networks is valuable, we focus on finding index coding strategies for a realistic wireless network. More specifically, we investigate how index coding can be applied to an OFDMA downlink network during the retransmission phase. An orthogonal frequency-division multiple access (OFDMA) downlink network is a network where data is sent downward from a designated higher-level transmitter to a group of receiving nodes. In addition, receivers can often decode the other receivers' physical layer signals on the other sub-channels that can be exploited as side information. If this side information is sent back to the transmitter, it can then be coded to cancel the interference in subsequent retransmission phases resulting in fewer retransmission messages. In this report, we explain the coding model and characterize the benefits of index coding for retransmissions within an OFDMA downlink network. In addition, we demonstrate the results of applying this index coding scheme in such network in both simulation and in an active wireless mesh network.Electrical and Computer Engineerin

Maximum Likelihood Decoder for Index Coded PSK Modulation for Priority Ordered Receivers

Index coded PSK modulation over an AWGN broadcast channel, for a given index coding problem (ICP) is studied. For a chosen index code and an arbitrary mapping (of broadcast vectors to PSK signal points), we have derived a decision rule for the maximum likelihood (ML) decoder. The message error performance of a receiver at high SNR is characterized by a parameter called PSK Index Coding Gain (PSK-ICG). The PSK-ICG of a receiver is determined by a metric called minimum inter-set distance. For a given ICP with an order of priority among the receivers, and a chosen $2^N$-PSK constellation we propose an algorithm to find (index code, mapping) pairs, each of which gives the best performance in terms of PSK-ICG of the receivers. No other pair of index code (of length $N$ with $2^N$ broadcast vectors) and mapping can give a better PSK-ICG for the highest priority receiver. Also, given that the highest priority receiver achieves its best performance, the next highest priority receiver achieves its maximum gain possible and so on in the specified order or priority.Comment: 9 pages, 6 figures and 2 table

The Minrank of Random Graphs

The minrank of a graph $G$ is the minimum rank of a matrix $M$ that can be obtained from the adjacency matrix of $G$ by switching some ones to zeros (i.e., deleting edges) and then setting all diagonal entries to one. This quantity is closely related to the fundamental information-theoretic problems of (linear) index coding (Bar-Yossef et al., FOCS'06), network coding and distributed storage, and to Valiant's approach for proving superlinear circuit lower bounds (Valiant, Boolean Function Complexity '92). We prove tight bounds on the minrank of random Erd\H{o}s-R\'enyi graphs $G(n,p)$ for all regimes of $p\in[0,1]$. In particular, for any constant $p$, we show that $\mathsf{minrk}(G) = \Theta(n/\log n)$ with high probability, where $G$ is chosen from $G(n,p)$. This bound gives a near quadratic improvement over the previous best lower bound of $\Omega(\sqrt{n})$ (Haviv and Langberg, ISIT'12), and partially settles an open problem raised by Lubetzky and Stav (FOCS '07). Our lower bound matches the well-known upper bound obtained by the "clique covering" solution, and settles the linear index coding problem for random graphs. Finally, our result suggests a new avenue of attack, via derandomization, on Valiant's approach for proving superlinear lower bounds for logarithmic-depth semilinear circuits