arXiv subjects

Hossein Kakavand

Publications and source records attributed to Hossein Kakavand.

2 recordsLinked to original sources

arXiv2007

The Simplest Solution to an Underdetermined System of Linear Equations

Consider a d*n matrix A, with d<n. The problem of solving for x in y=Ax is underdetermined, and has infinitely many solutions (if there are any). Given y, the minimum Kolmogorov complexity solution (MKCS) of the input x is defined to be an input z (out of many) with minimum Kolmogorov-complexity that satisfies y=Az. One expects that if the actual input is simple enough, then MKCS will recover the input exactly. This paper presents a preliminary study of the existence and value of the complexity level up to which such a complexity-based recovery is possible. It is shown that for the set of all d*n binary matrices (with entries 0 or 1 and d<n), MKCS exactly recovers the input for an overwhelming fraction of the matrices provided the Kolmogorov complexity of the input is O(d). A weak converse that is loose by a log n factor is also established for this case. Finally, we investigate the difficulty of finding a matrix that has the property of recovering inputs with complexity of O(d) using MKCS.

cs.IT↗

arXiv2005

Channel Model and Upper Bound on the Information Capacity of the Fiber Optical Communication Channel Based on the Effects of XPM Induced Nonlinearity

An upper bound to the information capacity of a wavelength-division multi- plexed optical fiber communication system is derived in a model incorporating the nonlinear propagation effects of cross-phase modulation (XPM). This work is based on the paper by Mitra et al., finding lower bounds to the channel capacity, in which physical models for propagation are used to calculate statistical properties of the conditional probability distribution relating input and output in a single WDM channel. In this paper we present a tractable channel model incorporating the effects of cross phase modulation. Using this model we find an upper bound to the information capacity of the fiber optical communication channel at high SNR. The results provide physical insight into the manner in which nonlinearities degrade the information capacity.

cs.IT↗