The outage behaviour of the single cell DSCDMA uplink is investigated for flat Rayleigh fading channels. Goal of the work is to find an analytical way for the optimisation of the system spectral efficiency under some outage probability constraint by adjusting parameters such as modulation, spreading factor, code rate and number of codes per user. Therefore, the results of the asymptotic analysi...

Over ten years ago Wright [4] proved a fundamental theorem in the theory of random graphs. He showed that if M = M(n) is such that almost no labelled graph of order n and size M has two isolated vertices or two vertices of degree n — 1, then the number of labelled graphs of order n and size M divided by the number of unlabelled graphs of order n and size M is asymptotic to n\. The result is bes...

Given any integer d ≥ 3, let k be the smallest integer such that d < 2k log k. We prove that with high probability the chromatic number of a random d-regular graph is k, k + 1, or k + 2.

The domatic number of a graph G is the maximum number of dominating sets into which the vertex set of G can be partitioned. We show that the domatic number of a random r-regular graph is almost surely at most r, and that for 3-regular random graphs, the domatic number is almost surely equal to 3. We also give a lower bound on the domatic number of a graph in terms of order, minimum degree and m...

We prove that any irreducible triangulation on n vertices has O(4.6807) regular edge labelings and that there are irreducible triangulations on n vertices with Ω(3.0426) regular edge labelings. Our upper bound relies on a novel application of Shearer’s entropy lemma. As an example of the wider applicability of this technique, we also improve the upper bound on the number of 2-orientations of a ...

Multi-connectivity is considered to be key for enabling reliable transmissions and enhancing data rates in future wireless networks. In this work, we quantify the communication performance by the outage probability and the system throughput. We establish a remarkably simple, yet accurate analytical framework based on distributed source coding to describe the outage probability and the system th...