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This paper provides an explicit expression for the capacity region of the two-user broadcast Z channel and proves that the optimal boundary can be achieved by independent encoding of each user. Specifically, the information messages corresponding to each user are encoded independently and the OR of these two encoded streams is transmitted. Nonlinear turbo codes that provide a controlled distribution of ones and zeros are used to demonstrate a low-complexity scheme that operates close to the optimal boundary. Index Terms--Broadcast channel, broadcast Z channel, capacity region, nonlinear turbo codes, turbo codes.

Based on random codes and typical set decoding, an alternative proof of Root and Varaiya's compound channel coding theorem for linear Gaussian channels is presented. The performance limit of codes with finite block length under a compound channel is studied through error bounds and simulation. Although the theorem promises uniform convergence of the probability of error as the block length approaches infinity, with short block lengths the performance can differ considerably for individual channels. Simulation results show that universal performance can be a practical goal as the block lengths become large. Index Terms--Compound channel, random coding bound, sphere-packing bound (SPB), universal code.

We study the maximum flow possible between a single-source and multiple terminals in a weighted random graph (modeling a wired network) and a weighted random geometric graph (modeling an ad-hoc wireless network) using network coding. For the weighted random graph model, we show that the network coding capacity concentrates around the expected number of nearest neighbors of the source and the terminals. Specifically, for a network with a single source, l terminals, and n relay nodes such that the link capacities between any two nodes is independent and identically distributed (i.i.d.) ~ X, the maximum flow between the source and the terminals is approximately [.sub.n]E[X] with high probability. For the weighted random geometric graph model where two nodes are connected if they are within a certain distance of each other we show that with high probability the network coding capacity is greater than or equal to the expected number of nearest neighbors of the node with the least coverage area. Index Terms--Minimum cut, multicast, network coding, random geometric graphs, random graphs.

This correspondence gives practical examples of space-time trellis codes performing as predicted by Root and Varaiya's compound channel theorem. Specifically, 32-state and 64-state 2 x 2 space-time trellis codes are presented that provide a bit-error rate (BER) of [10.sup.-5] on all 2 x 2 matrix channels with an excess mutual information (MI) within 8% of the excess MI required by standard trellis codes of the same complexity operating only in additive white Gaussian noise (AWGN). Not surprisingly, the universal space-time trellis-coded modulations (ST-TCMs) provide average bit- and frame-error rates in quasi-static Rayleigh fading (QRF) that are comparable to those achieved by ST-TCMs designed specifically for QRF as well as standard TCMs followed by the Alamouti space-time block code. However, all of these other schemes require more excess MI in the worst case, and some have a significantly wider variation in the required excess MI. The correspondence also compares the universal and quasi-static Rayleigh fading design approaches analytically and bounds the worst case distance of a trellis code on a 2 x 2 channel using the distances of the code on singular and unitary channels. This bound is extended to the more general [n.sub.T] x [n.sub.R] scenario. Index Terms--Compound channel, outage, quasi-static Rayleigh fading, space-time trellis codes.

We consider the problem of binary hypothesis testing using binary decisions from independent and identically distributed (i.i.d). sensors. Identical likelihood-ratio quantizers with threshold [lambda] are used at the sensors to obtain sensor decisions. Under this condition, the optimal fusion rule is known to be a [kappa]-out-of-n rule with threshold [kappa]. For the Bayesian detection problem, we show that given [kappa], the probability of error is a quasi-convex function of [kappa] and has a single minimum that is achieved by the unique optimal [[lambda].sub.opt]. Except for the trivial situation where one hypothesis is always decided, we obtain a sufficient and necessary condition on [[lambda].sub.opt], and show that [[lambda.sub.opt] can be efficiently obtained via the SECANT algorithm. The overall optimal solution is obtained by optimizing every pair of ([kappa], [lambda]). For the Neyman-Pearson detection problem, we show that the use of the Lagrange multiplier method is justified for a given fixed [kappa] since the objective function is a quasi-convex function of [lambda]. We further show that the receiver operating characteristic (ROC) for a fixed [kappa] is concave downward. Index Terms--Decision-making, multisensor systems, quantization, signal detection.

This paper investigates optimal constellation labeling in the context of the edge profile. A constellation's edge profile lists the minimum-distance edge for each binary symbol error. The paper introduces the symmetric-ultracomposite (SU) labeling structure and shows that this structure provides undominated edge profiles for [2.sup.n]-PSK, [2.sup.n]-PAM, and [2.sup.2n]-point square QAM. The SU structure is a generalization of the commonly used reflected binary Gray code. With the proper choice of basis vectors, SU labeling can support either set-partition or Gray-code labeling of [2.sup.n]-PSK, [2.sup.n]-PAM, and [2.sup.2n]-point square QAM. Notably, there are Gray-code and set-partition labelings that do not have the SU structure. These labelings yield inferior edge profiles. The SU structure does not apply to cross constellations. However, for any standard cross constellation with 32 or more points, a quasi-SU labeling structure can approximate the SU structure. With the correct choice of basis, quasi-SU labelings produce quasi-Gray labelings. However, the quasi-SU structure cannot support set-partition labeling. In fact, the quasi-SU structure provides a better edge profile than standard set-partition labeling. Thus, for cross constellations there is a choice between edge profile optimality and the group structure provided by set-partitioning. Here, the correct choice depends on whether the encoder trellis has parallel branches. Index Terms--Binary reflected labeling, coded modulation, constellation labeling, fading channels, Gray code, set-partition.

In this correspondence, we present a technique to find the optimal threshold [Tau] for the binary hypothesis detection problem with n identical and independent sensors. The sensors all use an identical and single threshold [Tau] to make local decisions, and the fusion center makes a global decision based on the n local binary decisions. For generalized Gaussian noises and some non-Gaussian noise distributions, we show that for any admissible fusion rule, the probability of error is a quasi-convex function of threshold [Tau]. Hence, the problem decomposes into a series of n quasi-convex optimization problems that may be solved using well-known techniques. Assuming equal a priori probability, we give a sufficient condition of the non-Gaussian noise distribution g(x) for the probability of error to be quasi-convex. Furthermore, this technique is extended to Bayes risk and Neyman-Pearson criteria. We also demonstrate that, in practice, it takes fewer than twice as many binary sensors to give the performance of infinite precision sensors in our scenario. Index Terms--Distributed detection, fusion rule, generalized Gaussian noise, hard decision, non-Gaussian noise.

Focuses on the use of binary decisions from independent and identically distributed sensors for binary hypothesis testing. Discussion on the Bayesian detection problem; Formulation of the Neyman-Pearson problem; Facts on the use of the SECANT algorithm.