New Non-asymptotic Random Channel Coding Theorems

New non-asymptotic random coding theorems (with error probability $\epsilon$ and finite block length $n$) based on Gallager parity check ensemble and Shannon random code ensemble with a fixed codeword type are established for discrete input arbitrary output channels. The resulting non-asymptotic achievability bounds, when combined with non-asymptotic equipartition properties developed in the paper, can be easily computed. Analytically, these non-asymptotic achievability bounds are shown to be asymptotically tight up to the second order of the coding rate as $n$ goes to infinity with either constant or sub-exponentially decreasing $\epsilon$. Numerically, they are also compared favourably, for finite $n$ and $\epsilon$ of practical interest, with existing non-asymptotic achievability bounds in the literature in general.Comment: 48 pages and 12 figure

Approximate expressions for modulation speed and threshold for performance optimization of biaxially compressive strain quantum-well lasers

Simple analytical expressions for transparency, threshold, and relaxation oscillation corner frequency are derived for biaxial strain quantum-well lasers. An optimal operating point loss for high speed operation (in the absence of nonlinear gain) is established which varies as the square root of the number of quantum wells. The corresponding relaxation oscillation frequency is found to depend only on fundamental quantities. Its power dependence is [vR(max) = (87 GHz õm^3/mW) (Powerout/Vmode)^1/2) where Vmode is the mode volume

Localization of electric field distribution in graded core-shell metamaterials

The local electric field distribution has been investigated in a core-shell cylindrical metamaterial structure under the illumination of a uniform incident optical field. The structure consists of a homogeneous dielectric core, a shell of graded metal-dielectric metamaterial, embedded in a uniform matrix. In the quasi-static limit, the permittivity of the metamaterial is given by the graded Drude model. The local electric potentials and hence the electric fields have been derived exactly and analytically in terms of hyper-geometric functions. Our results showed that the peak of the electric field inside the cylindrical shell can be confined in a desired position by varying the frequency of the optical field and the parameters of the graded profiles. Thus, by fabricating graded metamaterials, it is possible to control electric field distribution spatially. We offer an intuitive explanation for the gradation-controlled electric field distribution