New upper and lower bounds are presented on the capacity of the free-space optical intensity channel. This channel is characterized by inputs that are nonnegative (representing the transmitted optical intensity) and by outputs that are corrupted by a
dditive white Gaussian noise (because in free space the disturbances arise from many independent sources). Due to battery and safety reasons the inputs are simultaneously constrained in both their average and peak power. For a fixed ratio of the average power to the peak power the difference between the upper and the lower bounds tends to zero as the average power tends to infinity, and the ratio of the upper and lower bounds tends to one as the average power tends to zero. The case where only an average-power constraint is imposed on the input is treated separately. In this case, the difference of the upper and lower bound tends to 0 as the average power tends to infinity, and their ratio tends to a constant as the power tends to zero.
We derive the capacity region of the Gaussian version of Willemss two-user MAC with conferencing encoders. This setting differs from the classical MAC in that, prior to each transmission block, the two transmitters can communicate with each other ove
r noise-free bit-pipes of given capacities. The derivation requires a new technique for proving the optimality of Gaussian input distributions in certain mutual information maximizations under a Markov constraint. We also consider a Costa-type extension of the Gaussian MAC with conferencing encoders. In this extension, the channel can be described as a two-user MAC with Gaussian noise and Gaussian interference where the interference is known non-causally to the encoders but not to the decoder. We show that as in Costas setting the interference sequence can be perfectly canceled, i.e., that the capacity region without interference can be achieved.
We study the high-power asymptotic behavior of the sum-rate capacity of multi-user interference networks with an equal number of transmitters and receivers. We assume that each transmitter is cognizant of the message it wishes to convey to its corres
ponding receiver and also of the messages that a subset of the other transmitters wish to send. The receivers are assumed not to be able to cooperate in any way so that they must base their decision on the signal they receive only. We focus on the networks pre-log, which is defined as the limiting ratio of the sum-rate capacity to half the logarithm of the transmitted power. We present both upper and lower bounds on the networks pre-log. The lower bounds are based on a linear partial-cancellation scheme which entails linearly transforming Gaussian codebooks so as to eliminate the interference in a subset of the receivers. Inter alias, the bounds give a complete characterization of the networks and side-information settings that result in a full pre-log, i.e., in a pre-log that is equal to the number of transmitters (and receivers) as well as a complete characterization of networks whose pre-log is equal to the full pre-log minus one. They also fully characterize networks where the full pre-log can only be achieved if each transmitter knows the messages of all users, i.e., when the side-information is full.
