Sampling Large Data on Graphs

We consider the problem of sampling from data defined on the nodes of a weighted graph, where the edge weights capture the data correlation structure. As shown recently, using spectral graph theory one can define a cut-off frequency for the bandlimited graph signals that can be reconstructed from a given set of samples (i.e., graph nodes). In this work, we show how this cut-off frequency can be computed exactly. Using this characterization, we provide efficient algorithms for finding the subset of nodes of a given size with the largest cut-off frequency and for finding the smallest subset of nodes with a given cut-off frequency. In addition, we study the performance of random uniform sampling when compared to the centralized optimal sampling provided by the proposed algorithms.Comment: To be presented at GlobalSIP 201

Degrees of Freedom of Two-Hop Wireless Networks: "Everyone Gets the Entire Cake"

We show that fully connected two-hop wireless networks with K sources, K relays and K destinations have K degrees of freedom both in the case of time-varying channel coefficients and in the case of constant channel coefficients (in which case the result holds for almost all values of constant channel coefficients). Our main contribution is a new achievability scheme which we call Aligned Network Diagonalization. This scheme allows the data streams transmitted by the sources to undergo a diagonal linear transformation from the sources to the destinations, thus being received free of interference by their intended destination. In addition, we extend our scheme to multi-hop networks with fully connected hops, and multi-hop networks with MIMO nodes, for which the degrees of freedom are also fully characterized.Comment: Presented at the 2012 Allerton Conference. Submitted to IEEE Transactions on Information Theor

Do Read Errors Matter for Genome Assembly?

While most current high-throughput DNA sequencing technologies generate short reads with low error rates, emerging sequencing technologies generate long reads with high error rates. A basic question of interest is the tradeoff between read length and error rate in terms of the information needed for the perfect assembly of the genome. Using an adversarial erasure error model, we make progress on this problem by establishing a critical read length, as a function of the genome and the error rate, above which perfect assembly is guaranteed. For several real genomes, including those from the GAGE dataset, we verify that this critical read length is not significantly greater than the read length required for perfect assembly from reads without errors.Comment: Submitted to ISIT 201

A Generalized Cut-Set Bound for Deterministic Multi-Flow Networks and its Applications

We present a new outer bound for the sum capacity of general multi-unicast deterministic networks. Intuitively, this bound can be understood as applying the cut-set bound to concatenated copies of the original network with a special restriction on the allowed transmit signal distributions. We first study applications to finite-field networks, where we obtain a general outer-bound expression in terms of ranks of the transfer matrices. We then show that, even though our outer bound is for deterministic networks, a recent result relating the capacity of AWGN KxKxK networks and the capacity of a deterministic counterpart allows us to establish an outer bound to the DoF of KxKxK wireless networks with general connectivity. This bound is tight in the case of the "adjacent-cell interference" topology, and yields graph-theoretic necessary and sufficient conditions for K DoF to be achievable in general topologies.Comment: A shorter version of this paper will appear in the Proceedings of ISIT 201