Operational Aspects of Decision Feedback Equalizers

The central theme is the study of error propagation effects in decision feedback equalizers (DFEs). The thesis contains: a stochastic analysis of error propagation in a tuned DFE; an analysis of the effects of error propagation in a blindly adapted DFE; a deterministic analysis of error propagation through input-output stability ideas; and testing procedures for establishing correct tap convergence in blind adaptation. To a lesser extent, the decision directed equalizer (DDE) is also treated.¶ ..

Estimating Minimum Sum-rate for Cooperative Data Exchange

This paper considers how to accurately estimate the minimum sum-rate so as to reduce the complexity of solving cooperative data exchange (CDE) problems. The CDE system contains a number of geographically close clients who send packets to help the others recover an entire packet set. The minimum sum-rate is the minimum value of total number of transmissions that achieves universal recovery (the situation when all the clients recover the whole packet set). Based on a necessary and sufficient condition for a supermodular base polyhedron to be nonempty, we show that the minimum sum-rate for a CDE system can be determined by a maximization over all possible partitions of the client set. Due to the high complexity of solving this maximization problem, we propose a deterministic algorithm to approximate a lower bound on the minimum sum-rate. We show by experiments that this lower bound is much tighter than those lower bounds derived in the existing literature. We also show that the deterministic algorithm prevents from repetitively running the existing algorithms for solving CDE problems so that the overall complexity can be reduced accordingly.Comment: 6 pages, 6 figure

Iterative Merging Algorithm for Cooperative Data Exchange

We consider the problem of finding the minimum sum-rate strategy in cooperative data exchange systems that do not allow packet-splitting (NPS-CDE). In an NPS-CDE system, there are a number of geographically close cooperative clients who send packets to help the others recover a packet set. A minimum sum-rate strategy is the strategy that achieves universal recovery (the situation when all the clients recover the whole packet set) with the the minimal sum-rate (the total number of transmissions). We propose an iterative merging (IM) algorithm that recursively merges client sets based on a lower estimate of the minimum sum-rate and updates to the value of the minimum sum-rate. We also show that a minimum sum-rate strategy can be learned by allocating rates for the local recovery in each merged client set in the IM algorithm. We run an experiment to show that the complexity of the IM algorithm is lower than that of the existing deterministic algorithm when the number of clients is lower than $94$.Comment: 9 pages, 3 figure

New expression for the functional transformation of the vector Cramér-Rao lower bound

Assume that it is desired to estimate α = f(θ), where f(·) is an r-dimensional function. This paper derives the general expression for the functional transformation of the vector Cramér-Rao lower bound (CRLB). The derived bound is a tight lower bound on the estimation of uncoupled parameters, i.e., parameters that can be estimated separately. Unlike previous results in the literature, this new expression is not dependent on the inverse of the Fisher's information matrix (FIM) of the untransformed parameters, θ. Thus, it can be applied to scenarios where the FIM for θ is ill-conditioned or singular. Finally, as an application, the derived transformation is applied to determine the exact CRLB for estimation of channel parameters in amplify-and-forward relaying networks.This research was supported under Australian Research Council’s Discovery Projects funding scheme (project number DP110102548)

Centralized and Cooperative Transmission of Secure Multiple Unicasts using Network Coding

We introduce a method for securely delivering a set of messages to a group of clients over a broadcast erasure channel where each client is interested in a distinct message. Each client is able to obtain its own message but not the others'. In the proposed method the messages are combined together using a special variant of random linear network coding. Each client is provided with a private set of decoding coefficients to decode its own message. Our method provides security for the transmission sessions against computational brute-force attacks and also weakly security in information theoretic sense. As the broadcast channel is assumed to be erroneous, the missing coded packets should be recovered in some way. We consider two different scenarios. In the first scenario the missing packets are retransmitted by the base station (centralized). In the second scenario the clients cooperate with each other by exchanging packets (decentralized). In both scenarios, network coding techniques are exploited to increase the total throughput. For the case of centralized retransmissions we provide an analytical approximation for the throughput performance of instantly decodable network coded (IDNC) retransmissions as well as numerical experiments. For the decentralized scenario, we propose a new IDNC based retransmission method where its performance is evaluated via simulations and analytical approximation. Application of this method is not limited to our special problem and can be generalized to a new class of problems introduced in this paper as the cooperative index coding problem