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

Discriminatory Source Coding for a Noiseless Broadcast Channel

We introduce a new problem of broadcast source coding with a discrimination requirement --- there is an eavesdropping user from whom we wish to withhold the true message in an entropic sense. Binning can achieve the Slepian-Wolf rate, but at the cost of full information leakage to the eavesdropper. Our main result is a lower bound that implies that any entropically efficient broadcast scheme must be "like binning" in that it also must leak significant information to eavesdroppers I

Diversity-Multiplexing Tradeoff in ISI Channels

The optimal diversity-multiplexing tradeoff curve for the intersymbol interference (ISI) channel is computed and various equalizers are analyzed using this performance metric. Maximum-likelihood signal decoding (MLSD) and decision feedback equalization (DFE) equalizers achieve the optimal tradeoff without coding, but zero forcing (ZF) and minimum mean-square-error (MMSE) equalizers do not. However if each transmission block is ended with a period of silence lasting the coherence time of the channel, both ZF and MMSE equalizers become diversity-multiplexing optimal. This suggests that the bulk of the performance gain obtained by replacing linear decoders with computationally intensive ones such as orthogonal frequency-division multiplexing (OFDM) or Viterbi, can be realized in much simpler fashion-with a small modification to the transmit scheme

Spectrum Sharing Between Wireless Networks

Abstract-We consider the problem of two wireless networks operating on the same (presumably unlicensed) frequency band. Pairs within a given network cooperate to schedule transmissions, but between networks there is competition for spectrum. To make the problem tractable, we assume transmissions are scheduled according to a random access protocol where each network chooses an access probability for its users. A game between the two networks is defined. We characterize the Nash Equilibrium behavior of the system. Three regimes are identified: one in which both networks simultaneously schedule all transmissions, one in which the denser network schedules all transmissions and the sparser only schedules a fraction, and one in which both networks schedule only a fraction of their transmissions. The regime of operation depends on the path loss exponent , the latter regime being desirable but attainable only for > 4. This suggests that in certain environments, rival wireless networks may end up naturally cooperating. To substantiate our analytical results, we simulate a system where networks iteratively optimize their access probabilities in a greedy manner. We also discuss a distributed scheduling protocol that employs carrier sensing and demonstrate via simulations that again a near cooperative equilibrium exists for sufficiently large . Index Terms-Carrier sensing, game theory, Nash equilibrium (N.E.), price of anarchy, random access, spectrum sharing, wireless ad hoc networks