Importance Sampling Simulation of the Stack Algorithm with Application to Sequential Decoding

Importance sampling is a Monte Carlo variance reduction technique which in many applications has resulted in a significant reduction in computational cost required to obtain accurate Monte Carlo estimates. The basic idea is to generate the random inputs using a biased simulation distribution. That is, one that differs from the true underlying probability model. Simulation data is then weighted by an appropriate likelihood ratio in order to obtain an unbiased estimate of the desired parameter. This thesis presents new importance sampling techniques for the simulation of systems that employ the stack algorithm. The stack algorithm is primarily used in digital communications to decode convolutional codes, but there are also other applications. For example, sequential edge linking is a method of finding edges in images that employs the stack algorithm. In brief, the stack algorithm is an algorithm that attempts to find the maximum metric path through a large decision tree. There are two quantities that characterize its performance. First there is the probability of a branching error. The second quantity is the distribution of computation. It turns out that the number of tree nodes examined in order to make a specific branching decision is a random variable. The distribution of computation is the distribution of this random variable. The estimation of the distribution of computation, and parameters derived from this distribution, is the main goal of this work. We present two new importance sampling schemes (including some variations) for estimating the distribution of computation of the stack algorithm. The first general method is called the reference path method. This method biases noise inputs using the weight distribution of the associated convolutional code. The second method is the partitioning method. This method uses a stationary biasing of noise inputs that alters the drift of the node metric process in an ensemble average sense. The biasing is applied only up to a certain point in time; the point where the correct path node metric minimum occurs. This method is inspired by both information theory and large deviations theory. This thesis also presents another two importance sampling techniques. The first is called the error events simulation method. This scheme will be used to estimate the error probabilities of stack algorithm decoders. The second method that we shall present is a new importance sampling technique for simulating the sequential edge linking algorithm. The main goal of this presentation will be the development of the basic theory that is relevant to this simulation problem, and to discuss some of the key issues that are related to the sequential edge linking simulation

High Speed Railway Wireless Communications: Efficiency v.s. Fairness

High speed railways (HSRs) have been deployed widely all over the world in recent years. Different from traditional cellular communication, its high mobility makes it essential to implement power allocation along the time. In the HSR case, the transmission rate depends greatly on the distance between the base station (BS) and the train. As a result, the train receives a time varying data rate service when passing by a BS. It is clear that the most efficient power allocation will spend all the power when the train is nearest from the BS, which will cause great unfairness along the time. On the other hand, the channel inversion allocation achieves the best fairness in terms of constant rate transmission. However, its power efficiency is much lower. Therefore, the power efficiency and the fairness along time are two incompatible objects. For the HSR cellular system considered in this paper, a trade-off between the two is achieved by proposing a temporal proportional fair power allocation scheme. Besides, near optimal closed form solution and one algorithm finding the $\epsilon$-optimal allocation are presented.Comment: 16 pages, 6 figure

Wireless Information and Energy Transfer for Two-Hop Non-Regenerative MIMO-OFDM Relay Networks

This paper investigates the simultaneous wireless information and energy transfer for the non-regenerative multipleinput multiple-output orthogonal frequency-division multiplexing (MIMO-OFDM) relaying system. By considering two practical receiver architectures, we present two protocols, time switchingbased relaying (TSR) and power splitting-based relaying (PSR). To explore the system performance limit, we formulate two optimization problems to maximize the end-to-end achievable information rate with the full channel state information (CSI) assumption. Since both problems are non-convex and have no known solution method, we firstly derive some explicit results by theoretical analysis and then design effective algorithms for them. Numerical results show that the performances of both protocols are greatly affected by the relay position. Specifically, PSR and TSR show very different behaviors to the variation of relay position. The achievable information rate of PSR monotonically decreases when the relay moves from the source towards the destination, but for TSR, the performance is relatively worse when the relay is placed in the middle of the source and the destination. This is the first time to observe such a phenomenon. In addition, it is also shown that PSR always outperforms TSR in such a MIMO-OFDM relaying system. Moreover, the effect of the number of antennas and the number of subcarriers are also discussed.Comment: 16 pages, 12 figures, to appear in IEEE Selected Areas in Communication