A method to construct Boolean functions with maximum algebraic immunity have been proposed in . Based on that method, we propose a different method to construct Boolean functions on even variables with maximum algebraic immunity in this letter. By counting on our construction, a lower bound of the number of such Boolean functions is derived, which is the best among all the existing lower bounds.

In this paper, we study lower bounds on the query complexity of testing algorithms for various problems. Given an oracle that returns information of an input object, a testing algorithm distinguishes the case that the object has a given property P from the case that it has a large distance to having P with probability at least . The query complexity of an algorithm is measured by the number of accesses to the oracle. We introduce two reductions that preserve the query complexity. One is derived from the gap-preserving local reduction and the other is from the L-reduction. By using the former reduction, we show linear lower bounds on the query complexity for testing basic NP-complete properties, i.e., 3-edge-colorability, directed Hamiltonian path/cycle, undirected Hamiltonian path/cycle, 3-dimensional matching and NP-complete generalized satisfiability problems. Also, using the second reduction, we show a linear lower bound on the query complexity of approximating the size of the maximum 3-dimensional matching.

In this paper, we investigate the smallest value of p for which a (J,L,p)-QC LDPC code with girth 6 exists for J=3 and J=4. For J=3, we determine the smallest value of p for any L. For J=4, we determine the smallest value of p for L ≤ 301. Furthermore we provide examples of specific constructions meeting these smallest values of p.

By using multiple repeated signal replicas to formulate the accumulative observed noisy signal sequence (AONSS) or the differential observed noisy signal sequence (DONSS) in the hybrid ARQ system, a novel data-aided maximum likelihood (DA ML) SNR estimation and a blind ML SNR estimation technique are proposed for the AWGN channel. It is revealed that the conventional DA ML estimate is a special case of the novel DA ML estimate, and both the proposed DA ML and the proposed blind ML SNR estimation techniques can offer satisfactory SNR estimation without introducing significant additional complexity to the existing hybrid ARQ scheme. Based on the AONSS, both the generalized deterministic and the random Cramer-Rao lower bounds (GCRLBs), which include the traditional Cramer-Rao lower bounds (CRLBs) as special cases, are also derived. Finally, the applicability of the proposed SNR estimation techniques based on the AONSS and the DONSS are validated through numerical analysis and simulation results.

We compare the convergence performance of different numerical schemes for computing the fundamental matrix from point correspondences over two images. First, we state the problem and the associated KCR lower bound. Then, we describe the algorithms of three well-known methods: FNS, HEIV, and renormalization. We also introduce Gauss-Newton iterations as a new method for fundamental matrix computation. For initial values, we test random choice, least squares, and Taubin's method. Experiments using simulated and real images reveal different characteristics of each method. Overall, FNS exhibits the best convergence properties.

Assume that each vertex of a graph G is assigned a constant number q of nonnegative integer weights, and that q pairs of nonnegative integers li and ui, 1 ≤ i ≤ q, are given. One wishes to partition G into connected components by deleting edges from G so that the total i-th weights of all vertices in each component is at least li and at most ui for each index i, 1 ≤ i ≤ q. The problem of finding such a "uniform" partition is NP-hard for series-parallel graphs, and is strongly NP-hard for general graphs even for q = 1. In this paper we show that the problem and many variants can be solved in pseudo-polynomial time for series-parallel graphs and partial k-trees, that is, graphs with bounded tree-width.

For fitting an ellipse to a point sequence, ML (maximum likelihood) has been regarded as having the highest accuracy. In this paper, we demonstrate the existence of a "hyperaccurate" method which outperforms ML. This is made possible by error analysis of ML followed by subtraction of high-order bias terms. Since ML nearly achieves the theoretical accuracy bound (the KCR lower bound), the resulting improvement is very small. Nevertheless, our analysis has theoretical significance, illuminating the relationship between ML and the KCR lower bound.

Let A(n, d, w) denote the maximum possible number of code words in binary (n,d,w) constant weight codes. For smaller instances of (n, d, w)s, many improvements have occurred over the decades. However, unknown instances still remain for larger (n, d, w)s (for example, those of n > 30 and d > 10). In this paper, we propose a new class of binary constant weight codes that fill in the remaining blank instances of (n, d, w)s. Specifically, we establish several new non-trivial lower bounds such as 336 for A(64, 12, 8), etc. (listed in Table 2). To obtain these results, we have developed a new systematic technique for construction by means of groups acting on some sets. The new technique is performed by considering a triad (G, Ω, f) := ("Group G," "Set Ω," "Action f on Ω") simultaneously. Our results described in Sect. 3 are obtained by using permutations of the elements of a set that include ∞ homogeneously like the other elements, which play a role to improve their randomness. Specifically, in our examples, we adopt the following model such as (PGL2(Fq), P1(Fq), "linear fractional action of subgroups of PGL2(Fq) on P1(Fq)") as a typical construction model. Moreover, as an application, the essential examples in [7] constructed by using an alternating group are again reconstructed with our new technique of a triad model, after which they are all systematically understood in the context of finite subgroups that act fractionally on a projective space over a finite field.

The Schaub bound is one of well-known lower bounds of the minimum distance for given cyclic code C, and defined as the minimum value, which is a lower bound on rank of matrix corresponding a codeword, in defining sequence for all sub-cyclic codes of given code C. In this paper, we will try to show relationships between the Schaub bound, the Roos bound and the shift bound from numerical experiments. In order to reduce computational time for the Schaub bound, we claim one conjecture, from numerical examples in binary and ternary cases with short code length that the Schaub bound can be set the value from only defining sequence of given code C.

In this paper, we treat a design problem for IIR digital filters described by rational transfer function in discrete space. First, we form the filter design problem using the modified least-squares (MLS) criterion and express it as the quadratic form with respect to the numerator and denominator coefficients. Next, we show the relaxation method using the Lagrange multiplier method in order to search for the good solution efficiently. Additionally we can check the filter stability when designing the denominator coefficients. Finally, we show the effectiveness of the proposed method using a numerical example.

In this paper, we consider the problem of multicast routing and wavelength assignment (MC-RWA) in multi-fiber all-optical WDM networks. Two main network design system comprehensively investigated here are mesh and multi-ring designs. Given the multicast traffic demands, we present new ILP formulations to solve the MC-RWA problem with an objective to determine the minimal number of fibers needed to support the multicast requests. Unlike previous studies, our ILP formulations are not only capable of finding the optimal multicast routing and wavelength assignment pattern to the light-trees, but also finding the optimal light-tree structures simultaneously. Since broadcast and unicast communications are special cases of multicast communications, our ILP models are actually the generalized RWA mathematical models of optical WDM networks. In addition to proposing the ILP models, this paper takes two main issues affecting the network capacity requirement into account, that is, the splitting degree level of optical splitters and techniques of wavelength assignment to the light-trees. Three multicast wavelength assignment techniques studied in this paper are Light-Tree (LT), Virtual Light-Tree (VLT) and Partial Virtual Light-Tree (PVLT) techniques. Due to the NP-completeness of the MC-RWA problem, the ILP formulations can reasonably cope with small and moderate networks. To work with large networks, this paper presents alternative MC-RWA ILP-based heuristic algorithms for the PVLT and LT networks and develops lower bound techniques to characterize the performance of our algorithms. Using existing large backbone networks, numerical results are reported to analyze such aspects as multiple fiber systems, the benefits of using optical splitters and wavelength converters, and the capacity difference between the mesh and multi-ring designs. Finally, this paper provides an analysis of the influence of network connectivity on the network implementation under the constraints of mesh and multi-ring design schemes.

Group multicasting is a generalization of multicasting whereby every member of a group is allowed to multicast messages to other members that belongs to the same group. The group multicast routing problem (GMRP) is that of finding a set of multicast trees with bandwidth requirements, each rooted at a member of the group, for multicasting messages to other members of the group. An optimal solution to GMRP is a set of trees, one for each member of the group, that incurs the least overall cost. This problem is known to be NP-complete and hence heuristic algorithms are likely to be the only viable approach for computing near optimal solutions in practice. In this paper, we derive a lower bound on the cost of an optimal solution to GMRP by using Lagrangean Relaxation and Subgradient Optimization. This lower bound is used to evaluate the two existing heuristic algorithms in terms of their ability to find close-to-optimal solutions.

This letter presents a lower bound and approximation for the coverage probability of the pilot channel that can be used for a CDMA downlink design. The approximation of a compound truncated Poisson distribution is used to obtain a closed form equation for the coverage probability of the pilot channel. Computer simulations show that our lower bound curve is truly less than the empirical curve, and our proposed approximation agrees well with the empirical result.

This paper presents a comprehensive investigation of three optical wavelength-division multiplexed (WDM) mesh network protection approaches, namely minimal cost, single link basis and disjoint path approaches. The operation of each approach is described and their performances are extensively evaluated and compared. Key aspects that are taken into the consideration and comparison of the designs include a spare capacity requirement, ease of operation and practical feasibility. A mathematical model based on integer linear programming is introduced to obtain a lower bound on the spare capacity requirement for full protection against all single link failures. Two heuristic algorithms have also been developed to perform wavelength resource allocation under both normal and failure conditions for both systems with and without wavelength conversion capability. It is shown that the minimal cost approach can accomplish the lowest extra cost requirement for protection, but this approach is considered not appropriate for practical applications due to complicated restoration and management. The single link basis scheme is on the other hand more practical and very cost efficient. For the disjoint path technique, the cost for spare capacity is generally slightly greater than that of the single link basis scheme. Its main advantages lie in the simple re-configuration and inherent protection against node failure for in-transit traffic. Finally, a new framework for obtaining a good spare capacity cost estimate of a mesh restorable network is presented.

Sequence estimation (SE) of narrow-band digital FM signals, such as CPFSK and GMSK, with non-coherent limiter/discriminator (L/D) and integrate and dump (I&D) detection is investigated in detail using both analysis and simulation. The BER is studied from approximate upper and lower bounds obtained through Chernoff bounding techniques and minimum error event path probability along with a Gaussian noise assumption for high SNR. Various IF filters and the dependence of the error probability upon modulation index are considered. The results show an optimum modulation index around h 0.55, and clearly demonstrate the effectiveness and limitations of sequence estimation.

A modified version of the SAGE algorithm is presented for joint delay-azimuth-attenuation parameters' estimation in a multiuser DS-CDMA system. The introduced modification consists of using different time interval lengths when calculating the time correlations for optimizing the different channel parameters. This modification was proposed for the purpose of a further reduction in the algorithm's computational weight in case of receiving sufficiently resolvable waves. Specifically, we found that short interval windows are sufficient for estimating delays and azimuth angles, which is quite effective in reducing the computational burden in their optimization processes. As for the estimation of the attenuation parameters, a longer time window, equal to the preamble length, is considered for more accurate estimation. Also two other estimators are proposed. The first one combining the modified SAGE with a sequential estimation of the attenuation parameters, suitable for slowly varying channels. Another one, similar to the first, and primarily designed to alleviate the influence of present strong interferers. Through a numerical example, the performances of the three presented estimation schemes, in terms of their near-far resistance, are compared. And it is shown that the proposed second combined estimator outperforms the modified SAGE in environments with high MAI levels.

In this paper, we propose path accommodation methods for unidirectional rings based on an optical compression time-division multiplexing (OCTDM) technology. We first derive a theoretical lower bound on the numbers of slots and frames, in order to allocate all paths among nodes. Three path accommodation algorithms for the all-optical access are next proposed to achieve the lower bound as closely as possible. Path splitting is next considered to improve the traffic accommodation. Finally, we analyze the packet delay time for given numbers of slots/frames, which are decided by our proposed algorithms. Numerical examples are also shown to examine the effectiveness of our proposed algorithms including path accommodation and path splitting methods.

The minimum number of comparators in a (6,6)-merging network is shown to be 17. The number has been known to be either 16 or 17 [See Knuth, The Art of Computer Programming Vol. 3: Sorting and Searching, p. 230]. Minimum numbers for (n,n)-merging netwerks, 1 n 9, n 6, were already known. The problem had been open for more than two decades.

A binary moment diagram, which was proposed for arithmetic circuit verification, is a directed acyclic graph representing a function from binary-vectors to integers (f : {0,1}n Z). A multiplicative binary moment diagram is an extension of a binary moment diagram with edge weights attached. A multiplicative binary moment diagram can represent addition, multiplication and many other functions with polynomial numbers of vertices. Lower bounds for division, however, had not been investigated. In this paper, we show an exponential lower bound on the number of vertices of a multiplicative binary moment diagram representing a quotient function or a remainder function.

All-terminal reliability is one of the measurements to evaluate the reliability for network systems. Since it may need exponential time of the network size to compute the exact value of all-terminal reliability, it is important to calculate its tight approximate value, especially its lower bound, at a moderate calculation time. Ramanathan and Colbourn have proposed approaches for lower bounds of all-terminal reliability by using arc-packings but their approaches are not detailed enough to construct concrete algorithms and they have just evaluated their approaches for a particular network. In this paper, we construct concrete algorithms based on their approaches and suggest new algorithms. We also execute computational experiments for general networks in order to evaluate the lower bounds by the algorithms and show the effectiveness of our new algorithms.