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

Wireless Network Information Flow: A Deterministic Approach

In a wireless network with a single source and a single destination and an arbitrary number of relay nodes, what is the maximum rate of information flow achievable? We make progress on this long standing problem through a two-step approach. First we propose a deterministic channel model which captures the key wireless properties of signal strength, broadcast and superposition. We obtain an exact characterization of the capacity of a network with nodes connected by such deterministic channels. This result is a natural generalization of the celebrated max-flow min-cut theorem for wired networks. Second, we use the insights obtained from the deterministic analysis to design a new quantize-map-and-forward scheme for Gaussian networks. In this scheme, each relay quantizes the received signal at the noise level and maps it to a random Gaussian codeword for forwarding, and the final destination decodes the source's message based on the received signal. We show that, in contrast to existing schemes, this scheme can achieve the cut-set upper bound to within a gap which is independent of the channel parameters. In the case of the relay channel with a single relay as well as the two-relay Gaussian diamond network, the gap is 1 bit/s/Hz. Moreover, the scheme is universal in the sense that the relays need no knowledge of the values of the channel parameters to (approximately) achieve the rate supportable by the network. We also present extensions of the results to multicast networks, half-duplex networks and ergodic networks.Comment: To appear in IEEE transactions on Information Theory, Vol 57, No 4, April 201