We prove that any IN-rational sequence s = (sn) n1 of non-negative integers satisfying the Kraft strict inequality P n1 snk ?n < 1 is the enumerative sequence of leaves by height of a rational k-ary tree. Particular cases of this result had been previously proven. We give some partial results in the equality case.

The performance analysis of a system employing co-ordinate interleaving and constellation rotation, over Nakagami-m fading channels, in the presence of phase noise as well as additive white Gaussian noise, is presented. An upper bound for the average probability of bit error for M-ary phase shift keying is derived. It is shown that the derived upper bound is tight for high signal-to-noise ratio...

The performance of moment generating function approaches, specifically Chernoff bound (CB) and modified (MCB), is examined improved in this study. We evaluates enhances the a wavelength division multiplexing (WDM) technique for free-space optical (FSO) fibre communications based on passive network (PON) using M-ary digital pulse-position modulation (M-ary DPPM) schemes under amplified spontaneo...

We consider a sequence of probability measures n obtained by conditioning a random and give several suucient conditions on the distribution of X for n to be stochastically increasing in n. The problem is motivated by an interacting particle system on the homogeneous tree in which each vertex has d + 1 neighbors. This system is a variant of the contact process, and was studied recently by A. Puh...

Abstract A number of recent papers have estimated ratios the partition function $p(n-j)/p(n)$ , which appear in many applications. Here, we prove an easy-to-use effective bound on these ratios. Using this, then study second shifted difference partitions, $f(\,j,n) := p(n) -2p(n-j) +p(n-2j)$ and give another estimate $f(\,j,n)$ . As applications these, a convexity property $p(n)$ as well giving ...

The parity based divide and conquer recursion trees are introduced where the sizes of the tree do not grow monotonically as n grows. These non-monotonic recursive functions called fogk(n) and f̃ogk(n) are strictly less than linear, o(n) but greater than logarithm, Ω(logn). Properties of fogk(n) such as non-monotonicity, upper and lower bounds, etc. are examined and proven. These functions are us...

In this paper we compute the number of reduced decompositions of certain permutations ∈ Sn as a product of transpositions (1; 2), (1; 3), : : :, (1; n). We present several combinatorial correspondences between these decompositions and combinatorial objects such as Catalan paths and k-ary trees. c © 1999 Elsevier Science B.V. All rights reserved

An analvtic techniaue is Dresented for comwhere Q, is the channel rrain. and w, is an additive Gaus" I puting the performance of trellis coded q-ary PSK in Rayleigh fading. A contour-integral expression for the pairwise error probability (PEP) is used to define a transfer function, enabling the union bound to be evaluated exactly for the ideal CSI (channel state information) case and imperfect-...

Using modular arithmetic we introduce a simple bound which applies to a wide range of bin-packing like problems. This bound must hold if a problem is to be soluble. When it fails, search can therefore be pruned. We show the value of such pruning in a greedy backtracking algorithm for number partitioning problems. As the bound can be used when solving inexact as well as exact partitioning proble...