Conditions for a Monotonic Channel Capacity

Motivated by results in optical communications, where the performance can degrade dramatically if the transmit power is sufficiently increased, the channel capacity is characterized for various kinds of memoryless vector channels. It is proved that for all static point-to-point channels, the channel capacity is a nondecreasing function of power. As a consequence, maximizing the mutual information over all input distributions with a certain power is for such channels equivalent to maximizing it over the larger set of input distributions with upperbounded power. For interference channels such as optical wavelength-division multiplexing systems, the primary channel capacity is always nondecreasing with power if all interferers transmit with identical distributions as the primary user. Also, if all input distributions in an interference channel are optimized jointly, then the achievable sum-rate capacity is again nondecreasing. The results generalizes to the channel capacity as a function of a wide class of costs, not only power.Comment: This is an updated and expanded version of arXiv:1108.039

Error correcting code using tree-like multilayer perceptron

An error correcting code using a tree-like multilayer perceptron is proposed. An original message \mbi{s}^0 is encoded into a codeword \boldmath{y}_0 using a tree-like committee machine (committee tree) or a tree-like parity machine (parity tree). Based on these architectures, several schemes featuring monotonic or non-monotonic units are introduced. The codeword \mbi{y}_0 is then transmitted via a Binary Asymmetric Channel (BAC) where it is corrupted by noise. The analytical performance of these schemes is investigated using the replica method of statistical mechanics. Under some specific conditions, some of the proposed schemes are shown to saturate the Shannon bound at the infinite codeword length limit. The influence of the monotonicity of the units on the performance is also discussed.Comment: 23 pages, 3 figures, Content has been extended and revise

Matrix-Monotonic Optimization for MIMO Systems

For MIMO systems, due to the deployment of multiple antennas at both the transmitter and the receiver, the design variables e.g., precoders, equalizers, training sequences, etc. are usually matrices. It is well known that matrix operations are usually more complicated compared to their vector counterparts. In order to overcome the high complexity resulting from matrix variables, in this paper we investigate a class of elegant multi-objective optimization problems, namely matrix-monotonic optimization problems (MMOPs). In our work, various representative MIMO optimization problems are unified into a framework of matrix-monotonic optimization, which includes linear transceiver design, nonlinear transceiver design, training sequence design, radar waveform optimization, the corresponding robust design and so on as its special cases. Then exploiting the framework of matrix-monotonic optimization the optimal structures of the considered matrix variables can be derived first. Based on the optimal structure, the matrix-variate optimization problems can be greatly simplified into the ones with only vector variables. In particular, the dimension of the new vector variable is equal to the minimum number of columns and rows of the original matrix variable. Finally, we also extend our work to some more general cases with multiple matrix variables.Comment: 37 Pages, 5 figures, IEEE Transactions on Signal Processing, Final Versio