S. Sridharan | Searcharxiv

arXiv2021

Dynamics of Products of Matrices in Max Algebra

The aim of this manuscript is to understand the dynamics of matrix products in a max algebra. A consequence of the Perron-Fröbenius theorem on periodic points of a nonnegative matrix is generalized to a max algebra setting. The same is then studied for a finite product associated to a $p$-lettered word on $N$ letters arising from a finite collection of nonnegative matrices, with each member having its maximum circuit geometric mean at most 1.

math.DS↗

arXiv2008

On the Capacity of Partially Cognitive Radios

This paper considers the problem of cognitive radios with partial-message information. Here, an interference channel setting is considered where one transmitter (the "cognitive" one) knows the message of the other ("legitimate" user) partially. An outer bound on the capacity region of this channel is found for the "weak" interference case (where the interference from the cognitive transmitter to the legitimate receiver is weak). This outer bound is shown for both the discrete-memoryless and the Gaussian channel cases. An achievable region is subsequently determined for a mixed interference Gaussian cognitive radio channel, where the interference from the legitimate transmitter to the cognitive receiver is "strong". It is shown that, for a class of mixed Gaussian cognitive radio channels, portions of the outer bound are achievable thus resulting in a characterization of a part of this channel's capacity region.

cs.IT↗