arXiv subjects

Sreeram Kannan

Publications and source records attributed to Sreeram Kannan.

58 records · Page 4Linked to original sources

arXiv2013

Interactive Interference Alignment

We study interference channels (IFC) where interaction among sources and destinations is enabled, e.g., both sources and destinations can talk to each other using full-duplex radios. The interaction can come in two ways: 1) {\em In-band interaction:} sources and destinations can transmit and listen in the same channel simultaneously, enabling interaction. 2) {\em out-of-band interaction:} destinations talk back to the sources on an out-of-band channel, possible from white-space channels. The flexibility afforded by interaction among sources and destinations allows for the derivation of interference alignment (IA) strategies that have desirable "engineering properties": insensitivity to the rationality or irrationality of channel parameters, small block lengths and finite SNR operations. We show that for several classes of interference channels the interactive interference alignment scheme can achieve the optimal degrees of freedom. In particular, we show the {\em first simple scheme} (having finite block length, for channels having no diversity) for $K=3,4$ that can achieve the optimal degrees of freedom of $\frac{K}{2}$ even after accounting for the cost of interaction. We also give simulation results on the finite SNR performance of interactive alignment under some settings. On the technical side, we show using a Gröbner basis argument that in a general network potentially utilizing cooperation and feedback, the optimal degrees of freedom under linear schemes of a fixed block length is the same for channel coefficients with probability 1. Furthermore, a numerical method to estimate this value is also presented. These tools have potentially wider utility in studying other wireless networks as well.

cs.IT↗

arXiv2011

Capacity of Multiple Unicast in Wireless Networks: A Polymatroidal Approach

A classical result in undirected wireline networks is the near optimality of routing (flow) for multiple-unicast traffic (multiple sources communicating independent messages to multiple destinations): the min cut upper bound is within a logarithmic factor of the number of sources of the max flow. In this paper we "extend" the wireline result to the wireless context. Our main result is the approximate optimality of a simple layering principle: {\em local physical-layer schemes combined with global routing}. We use the {\em reciprocity} of the wireless channel critically in this result. Our formal result is in the context of channel models for which "good" local schemes, that achieve the cut-set bound, exist (such as Gaussian MAC and broadcast channels, broadcast erasure networks, fast fading Gaussian networks). Layered architectures, common in the engineering-design of wireless networks, can have near-optimal performance if the {\em locality} over which physical-layer schemes should operate is carefully designed. Feedback is shown to play a critical role in enabling the separation between the physical and the network layers. The key technical idea is the modeling of a wireless network by an undirected "polymatroidal" network, for which we establish a max-flow min-cut approximation theorem.

cs.IT↗

arXiv2011

Multicommodity Flows and Cuts in Polymatroidal Networks

We consider multicommodity flow and cut problems in {\em polymatroidal} networks where there are submodular capacity constraints on the edges incident to a node. Polymatroidal networks were introduced by Lawler and Martel and Hassin in the single-commodity setting and are closely related to the submodular flow model of Edmonds and Giles; the well-known maxflow-mincut theorem holds in this more general setting. Polymatroidal networks for the multicommodity case have not, as far as the authors are aware, been previously explored. Our work is primarily motivated by applications to information flow in wireless networks. We also consider the notion of undirected polymatroidal networks and observe that they provide a natural way to generalize flows and cuts in edge and node capacitated undirected networks. We establish poly-logarithmic flow-cut gap results in several scenarios that have been previously considered in the standard network flow models where capacities are on the edges or nodes. Our results have already found aplications in wireless network information flow and we anticipate more in the future. On the technical side our key tools are the formulation and analysis of the dual of the flow relaxations via continuous extensions of submodular functions, in particular the Lovász extension. For directed graphs we rely on a simple yet useful reduction from polymatroidal networks to standard networks. For undirected graphs we rely on the interplay between the Lovász extension of a submodular function and line embeddings with low average distortion introduced by Matousek and Rabinovich; this connection is inspired by, and generalizes, the work of Feige, Hajiaghayi and Lee on node-capacitated multicommodity flows and cuts. The applicability of embeddings to polymatroidal networks is of independent mathematical interest.

cs.DS↗

arXiv2010

Approximately Optimal Wireless Broadcasting

We study a wireless broadcast network, where a single source reliably communicates independent messages to multiple destinations, with the aid of relays and cooperation between destinations. The wireless nature of the medium is captured by the broadcast nature of transmissions as well as the superposition of all transmit signals plus independent Gaussian noise at the received signal at any radio. We propose a scheme that can achieve rate tuples within a constant gap away from the cut-set bound, where the constant is independent of channel coefficients and power constraints. The proposed scheme operates in two steps. The inner code, in which the relays perform a quantize-and-encode operation, is constructed by lifting a scheme designed for a corresponding discrete superposition network. The outer code is a Marton code for the non-Gaussian vector broadcast channel induced by the relaying scheme, and is constructed by adopting a ``receiver-centric'' viewpoint.

cs.IT↗