Information Theoretic Operating Regimes of Large Wireless Networks

In analyzing the point-to-point wireless channel, insights about two qualitatively different operating regimes--bandwidth- and power-limited--have proven indispensable in the design of good communication schemes. In this paper, we propose a new scaling law formulation for wireless networks that allows us to develop a theory that is analogous to the point-to-point case. We identify fundamental operating regimes of wireless networks and derive architectural guidelines for the design of optimal schemes. Our analysis shows that in a given wireless network with arbitrary size, area, power, bandwidth, etc., there are three parameters of importance: the short-distance SNR, the long-distance SNR, and the power path loss exponent of the environment. Depending on these parameters we identify four qualitatively different regimes. One of these regimes is especially interesting since it is fundamentally a consequence of the heterogeneous nature of links in a network and does not occur in the point-to-point case; the network capacity is {\em both} power and bandwidth limited. This regime has thus far remained hidden due to the limitations of the existing formulation. Existing schemes, either multihop transmission or hierarchical cooperation, fail to achieve capacity in this regime; we propose a new hybrid scheme that achieves capacity.Comment: 12 pages, 5 figures, to appear in IEEE Transactions on Information Theor

Fundamental Constraints on Multicast Capacity Regions

Much of the existing work on the broadcast channel focuses only on the sending of private messages. In this work we examine the scenario where the sender also wishes to transmit common messages to subsets of receivers. For an L user broadcast channel there are 2L - 1 subsets of receivers and correspondingly 2L - 1 independent messages. The set of achievable rates for this channel is a 2L - 1 dimensional region. There are fundamental constraints on the geometry of this region. For example, observe that if the transmitter is able to simultaneously send L rate-one private messages, error-free to all receivers, then by sending the same information in each message, it must be able to send a single rate-one common message, error-free to all receivers. This swapping of private and common messages illustrates that for any broadcast channel, the inclusion of a point R* in the achievable rate region implies the achievability of a set of other points that are not merely component-wise less than R*. We formerly define this set and characterize it for L = 2 and L = 3. Whereas for L = 2 all the points in the set arise only from operations relating to swapping private and common messages, for L = 3 a form of network coding is required

Two-Way Interference Channel Capacity: How to Have the Cake and Eat it Too

Two-way communication is prevalent and its fundamental limits are first studied in the point-to-point setting by Shannon [1]. One natural extension is a two-way interference channel (IC) with four independent messages: two associated with each direction of communication. In this work, we explore a deterministic two-way IC which captures key properties of the wireless Gaussian channel. Our main contribution lies in the complete capacity region characterization of the two-way IC (w.r.t. the forward and backward sum-rate pair) via a new achievable scheme and a new converse. One surprising consequence of this result is that not only we can get an interaction gain over the one-way non-feedback capacities, we can sometimes get all the way to perfect feedback capacities in both directions simultaneously. In addition, our novel outer bound characterizes channel regimes in which interaction has no bearing on capacity.Comment: Presented in part in the IEEE International Symposium on Information Theory 201

Efficient File Synchronization: a Distributed Source Coding Approach

The problem of reconstructing a source sequence with the presence of decoder side-information that is mis-synchronized to the source due to deletions is studied in a distributed source coding framework. Motivated by practical applications, the deletion process is assumed to be bursty and is modeled by a Markov chain. The minimum rate needed to reconstruct the source sequence with high probability is characterized in terms of an information theoretic expression, which is interpreted as the amount of information of the deleted content and the locations of deletions, subtracting "nature's secret", that is, the uncertainty of the locations given the source and side-information. For small bursty deletion probability, the asymptotic expansion of the minimum rate is computed.Comment: 9 pages, 2 figures. A shorter version will appear in IEEE International Symposium on Information Theory (ISIT), 201