Nehari's problem and competing species systems

We consider an optimal partition problem in N-dimensional domains related to a method introduced by Nehari [22]. We prove existence of the minimal partition and some extremality conditions. Moreover we show some connections between the variational problem, the behaviour of competing species systems with large interaction and changing sign solutions to elliptic superlinear equations.     

Coulomb energy of3He and charge-symmetry breaking in nuclear forces

We report a calculation of Coulomb energy of³He with two-term separable potentials of a form proposed recently, and a perturbative calculation of the charge-symmetry-breaking potential, again in a two-term separable form. By using potential sets adjusted to various values of proton-neutron effective range difference, some limit is sought to be placed on this quantity, about which nothing is known experimentally.     

一种基于代数编码理论的签名、加密和纠错公钥体制

本文基于代数编码理论中关于一般线性码的译码是非确定型多项式完全问题,提出了一种能实现签名、加密和纠错的公钥密码体制。     

Maximum Distance Separable Codes in the ρ Metric over Arbitrary Alphabets

We give a bound for codes over an arbitrary alphabet in a non-Hamming metric and define MDS codes as codes meeting this bound. We show that MDS codes are precisely those codes that are uniformly distributed and show that their weight enumerators based on this metric are uniquely determined.     

Turbo码中交织器和子码的综合设计

分析了距离谱和交织器结构对 Ｔｕｒｂｏ码性能的影响，介绍了高斯信道中一种新的 Ｔｕｒｂｏ码设计方法。该方法对交织器及子码进行综合设计，并给出了交织器的设计方法。仿真结果表明，通过交织器和子码的综合设计可以获得优异的误比特率性能。     

Design of Embedded Self-Testing Checkers for t-UED and BUED Codes

In this article we present a new method for designing self-testing checkers for t-UED and BUED codes. The main idea of this method is to map words of the considered code to words of a code of the same type in which the value of t or the number of check bits is reduced and repeating this with the obtained words until a parity code is obtained, or to translate the code words into words of a code for which such a mapping is possible. First we consider Borden codes for t = 2 ^k – 1, Bose, and Bose-Lin codes. The mapping operation is realized by averaging weights and check symbol values of the code words. The resulting checkers have a simple and regular structure. This structure is independent on the set of code words that is provided by the circuit under check. The checkers are very well suited for use as embedded checkers since they are self-testing with respect to single stuck-at faults under very weak assumptions. All three checker types can be tested with 2 or 3 code words. We also propose a novel approach to design checkers for Blaum codes that require much less code word tests than existing solutions.     

Generalized Steiner Triple Systems with Group Size g ≡0, 3 (mod 6)

Generalized Steirier triple systems, GS(2,3,n,g), are equivalent to maximum constant weight codes over an alphabet of size g 1 with distance 3 and weight 3 in which each codeword has length n. The necessary conditions for the existence of a GS(2,3,n,g) are (n-1)g≡0 (mod 2), n(n-1)g2≡0 (mod 6), and n≥g 2. These necessary conditions are shown to be sufficient by several authors for 2≤g≤11. In this paper, three new results are obtained. First, it is shown that for any given g, g≡0 (mod 6) and g≥12, if there exists a GS(2.3.n.g) for all n, g 2≤n≤7g 13. then the necessary conditions are also sufficient. Next, it is also shown that for any given g, g≡3 (mod 6) and g≥15, if there exists a GS(2,3,n,g) for all n, n≡1 (mod 2) and g 2≤n≤7g 6, then the necessary conditions are also sufficient. Finally, as an application, it is proved that the necessary conditions for the existence of a GS(2,3,n,g) are also sufficient for g=12,15.     

Azumaya Categories

We define the notions of Azumaya category and Brauer group in category theory enriched over some very general base category V. We prove the equivalence of various definitions, in particular in terms of separable categories or progenerating bimodules. When V is the category of modules over a commutative ring R with unit, we recapture the classical notions of Azumaya algebra and Brauer group and provide an alternative, purely categorical treatment of those theories. But our theory applies as well to the cases of topological, metric or Banach modules, to the sheaves of such structures or graded such structures, and many other examples.     

Adaptive Channel Estimation Aided Log-Map Turbo Decoder Implementation for DS-CDMA Based Mobile Systems

Practical implementation of convolutional turbo codec is impeded by the difficulty of real-time execution in high transmission rate communication systems due to high computational complexity, iterative block decoding structure, as well as the requirement of accurate on-line channel reliability estimation for maximum-likelihood decoding. Relying on innovative channel estimation techniques involving DS-CDMA specific noise/interference variance estimation and fading channel variation tracking, this paper provides a low-complexity all-digital design of an iterative SISO log-MAP turbo decoder for DS-CDMA based mobile communication systems. The issues of quantization and data flow in both pre-decoder processing module and iterative trellis decoding module are prudently addressed to ensure highly efficient hardware implementation. The efficient design strategies applied confine the decoding complexity while leading to an excellent performance within 0.2 dB of the software decoder.