1 Entropy, source coding Problem 1 (Alternative definition of unique decodability) An f : X → Y∗ code is called uniquely decodable if for any messages u = u1 · · ·uk and v = v1 · · · vk (where u1, vi, . . . , uk, vk ∈ X ) with f(u1)f(u2) · · · f(uk) = f(v1)f(v2) · · · f(vk), we have ui = vi for all i. That is, as opposed to the definition given in class, we require that the codes of any pair of...

In this chapter, we present constrained simulated annealing (CSA), an algorithm that extends conventional simulated annealing to look for constrained local minima of constrained optimization problems. The algorithm is based on the theory of extended saddle points (ESPs) that shows the one-to-one correspondence between a constrained local minimum of the problem and an ESP of the corresponding pe...

A chain probe graph is a graph that admits an independent set S of vertices and a set F of pairs of elements of S such that G+ F is a chain graph (i.e., a 2K2-free bipartite graph). We show that chain probe graphs are exactly the bipartite graphs that do not contain as an induced subgraph a member of a family of six forbidden subgraphs, and deduce an O(n2) recognition algorithm. Given a class C...

Definition 1. Given a undirected graph G = (V,E), two vertices are adjacent when they are both incident to a common edge. A path in an undirected graph is a sequence of vertices P = (v1, v2, . . . , vn) ∈ V n such that vi is adjacent to vi+1 for 1 ≤ i < n. Such a path P is called a path of length n from v1 to vn. Let ei,j be the edge incident to both vi and vj. Given a real-valued weight functi...

Graphs in this paper are finite and undirected and may have loops or multiple edges. The vertexand edge-sets of a graph G are denoted by V(G) and E(G). If G, = ( V1, E,), G2 = ( V2, E2) are subgraphs of a graph G, we denote the graphs (V1n V2,E1nE,) and (V,u V2, EluEZ) by G,nG, and G, u GZ, respectively. A separation of a graph G is a pair (G,, G2) of subgraphs with G1 u G2 = G and E(G1 n G2) =...

For every positive integers n, m and every even positive integer δ, we derive inequalities satisfied by the Walsh transforms of all vectorial (n,m)-functions and prove that the case of equality characterizes differential δ-uniformity. This provides a generalization to all differentially δ-uniform functions of the characterization of APN (n, n)-functions due to Chabaud and Vaudenay, by means of ...

Feedback with Carry Shift Registers (FCSRs) have previously been available in two configurations, the Fibonacci and Galois architectures. Recently, a generalized and unifying FCSR structure and theory was presented. The new ring FCSRs model repairs some weaknesses of the older architectures. Most notably, the carry cell bias property that was exploited for an attack on the eSTREAM final portfol...

Algorithm S1 Œis algorithm calculates S of a network alignment. Let G1(V1, E1) and G2(V2, E2) be two networks and f : V1 → V2 be an alignment between the two networks. We calculate S 3 by creating the alignment graph (described below) and using the alignment graph to calculate the number of conserved and non-conserved edges. Œe alignment graph, GA(VA, EA), is the graph inwhich each aligned pair...

I n this paper, we present a novel algorithmic approach, the hybrid matrix geometric/invariant subspace method, f o r finding the stationary probability distribut ion of the f inite QBD process which arises in performance analysis of computer and communication systems. Assuming that the QBD state space i s defined in two dimensions with m phases and K f 1 levels, the solution Vector for level k...