Abstract. -An approach to analyze the performance of the code division multiple access (CDMA) scheme, which is a core technology used in modern wireless communication systems, is provided. The approach characterizes the objective system by the eigenvalue spectrum of a cross-correlation matrix composed of signature sequences used in CDMA communication, which enable us to handle a wider class of CDMA systems beyond the basic model reported by Tanaka in Europhys. Lett., 54 (2001) 540. The utility of the scheme is shown by analyzing a system in which the generation of signature sequences is designed for enhancing the orthogonality.Introduction. -Over the last decade, the scope of statistical mechanics has rapidly expanded beyond its original goal of analyzing many-body problems that arise when dealing with material objects. Information theory is a major source of problems, and research activity aimed at solving these problems is becoming popular. Identifying information bits with Ising spins, many problems in information theory, such as error correcting/compression codes [1-10] and cryptosystems [11,12], can be formulated as virtual many-body systems that are subject to disordered interactions. Analysis of the formulated problems using techniques of statistical mechanics has provided various nontrivial results that have not been obtained by conventional methods of information theory [13,14].Code division multiple access (CDMA), which is a core technology used in modern wireless communication, is an example of the successful application of such a statistical mechanical approach. This technology realizes simultaneous communication between multiple users and a single base station by modulating each user's bit signal (symbol) into a sequence of random pattern, termed the signature sequence [15]. CDMA has already been employed in thirdgeneration mobile phone systems and wireless LANs.Tanaka (2001) showed that the replica method of statistical mechanics enables the accurate assessment of the communication performance of a basic CDMA model in which users' sequences are generated independently of each other in a large system limit [16,17]. This research
Abstract. Although the Bayesian approach provides optimal performance for many inference problems, the computation cost is sometimes impractical. We herein develop a practical algorithm by which to approximate Bayesian inference in large single-layer feed-forward networks (perceptrons) based on belief propagation (BP). Although direct application of BP to the inference problem remains computationally difficult, by introducing methods and concepts from statistical mechanics that are related to the central limit theorem and the law of large numbers, the proposed BP-based algorithm exhibits nearly optimal performance in a practical time scale for ideal large networks. In order to demonstrate the practical significance of the proposed algorithm, an application to a problem that arises in a mobile communications system is also presented.
The demand for extracting rules from high dimensional real world data is increasing in various fields. However, the possible redundancy of such data sometimes makes it difficult to obtain a good generalization ability for novel samples. To resolve this problem, we provide a scheme that reduces the effective dimensions of data by pruning redundant components for bicategorical classification based on the Bayesian framework. First, the potential of the proposed method is confirmed in ideal situations using the replica method. Unfortunately, performing the scheme exactly is computationally difficult. So, we next develop a tractable approximation algorithm, which turns out to offer nearly optimal performance in ideal cases when the system size is large. Finally, the efficacy of the developed classifier is experimentally examined for a real world problem of colon cancer classification, which shows that the developed method can be practically useful.
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