Membership problems for data dependencies in relational expressions

In relational databases, a query can be formulated in terms of a relational algebra expression using projection, selection, restriction, cross product and union. In this paper, we consider a problem, called the membership problem, of determining whether a given dependency d is valid in a given relational expression E over a given database scheme R that is, whether every instance of the view scheme defined by E satisfies d (assuming that the underlying constraints in R are always satisfied).Consider the case where each relation scheme in R is associated with functional dependencies (FDs) as constraints, and d is an FD. Then the complement of the membership problem is NP-complete. However, if E contains no union, then the membership problem can be solved in polynomial time. Furthermore, if E contains neither a union nor a projection, then we can construct in polynomial time a cover for valid FDs in E, that is, a set of FDs which implies every valid FD in E.Consider the case where each relation scheme in R is associated with multivalued dependencies (MVDs) as well as FDs, and d is an FD or an MVD. Even if E consists of selections and cross products only, the membership problem is NP-hard. However, if E contains no union, and each relation scheme name in R occurs in E at most once, then the membership problem can be solved in polynomial time. As a corollary of this result, it can be determined in polynomial time whether a given FD or MVD is valid in $\text{R}{}_1\text{???R}{}_{\mathrm{s}}$, where R₁,…,R_s are relation schemes with FDs and MVDs, and $\text{R}{}_{\mathrm{i}}\text{?R}{}_{\mathrm{j}}$ is the natural join of R_i and R_j.     

A concatenated coded modulation scheme for error control

A concatenated coded modulation scheme is presented for error control in data communications. The scheme is achieved by concatenating a Reed-Solomon outer code and a bandwidth efficient block inner code for M-ary phase-shift keying (PSK) modulation. Error performance of the scheme is analyzed for an additive white Gaussian noise (AWGN) channel. It is shown that extremely high reliability can be attained by using a simple M-ary PSK modulation inner-code and a relatively powerful Reed-Solomon outer code. Furthermore, if an inner code of high effective rate is used, the bandwidth expansion required by the scheme due to coding will be greatly reduced. The scheme is particularly effective for high-speed satellite communications for large file transfer where high reliability is required. A simple method is also presented for constructing block codes for M-ary PSK modulation. Soome short M-ary PSK codes with good minimum squared Euclidean distance are constructed. These codes have trellis structure and hence can be decoded with a soft-decision Viterbi decoding algorithm. Furthermore, some of these codes are phase invariant under multiples of 45° rotation     

Development of a large volume zero boil-off liquid xenon storage system for muon rare decay experiment (MEG)

We have developed a new type of photon detector for an experiment aimed at searching for the lepton flavor violating decay μ⁺ → e⁺γ. In this experiment, a total of 900 L of liquid xenon is used in order for the scintillation detector to detect γ-rays with an extremely high sensitivity, where the liquid xenon is viewed by an array of 846 photomultipliers from all sides. The entire amount of xenon should be stored in certain storage systems before the start of the experiment, during detector maintenance in the period of accelerator shutdown, etc. We have developed a new liquid xenon storage system by employing the zero boil-off condition by using a pulse tube cryocooler. The details of system and its performance results are described in this article.     

On multilevel block modulation codes

The multilevel technique for combining block coding and modulation is investigated. A general formulation is presented for multilevel modulation codes in terms of component codes with appropriate distance measures. A specific method for constructing multilevel block modulation codes with interdependency among component codes is proposed. Given a multilevel block modulation code C with no interdependency among the binary component codes, the proposed method gives a multilevel block modulation code C' that has the same rate as C, a minimum squared Euclidean distance not less than that of C, a trellis diagram with the same number of states as that of C, and a smaller number of nearest neighbor codewords than that of C . Finally, a technique is presented for analyzing the error performance of block modulation codes for an additive white Gaussian noise (AWGN) channel based on soft-decision maximum likelihood decoding. Error probabilities of some specific codes are evaluated by simulation and upper bounds based on their Euclidean weight distributions     

Multistage decoding of multilevel block M-PSK modulationcodes and its performance analysis

Multistage decoding of multilevel block multilevel phase-shift keying (M-PSK) modulation codes for the additive white Gaussian noise (AWGN) channel is investigated. Several types of multistage decoding, including a suboptimum soft-decision decoding scheme, are devised and analyzed. Upper bounds on the probability of an incorrect decoding of a code are derived for the proposed multistage decoding schemes. Error probabilities of some specific multilevel block 8-PSK modulation codes are evaluated and simulated. The computation and simulation results for these codes show that with multistage decoding, significant coding gains can be achieved with large reduction in decoding complexity. In one example, it is shown that the difference in performance between the proposed suboptimum multistage soft-decision decoding and the single-stage optimum decoding is small, only a fraction of a dB loss in SNR at the block error probability of 10^-6     

An O(n) algorithm for computing the set of available expressions of D-charts

Summary In this paper, an idea for computing the set of available expressions at entrance to the nodes of D-charts is explained. An algorithm based on the idea will work in time O(n), given bit vector operations, where n is the number of nodes. D-charts are flow graphs which correspond to the programs where ifs and whiles are used as control statements. The paper is based on the authors' previous report [9].     

Error detecting capabilities of the shortened Hamming codes adoptedfor error detection in IEEE Standard 802.3

Investigates the error detecting capabilities of the shortened hamming codes adopted for error detection in IEEE Standard 802.3. These codes are also used for error detection in the data link layer of the Ethernet, a local area network. The authors compute the weight distributions for various code lengths. From the results, they show the probability of undetectable error and that of detectable error for a binary symmetric channel with bit-error rate 10^-5⩽ϵ⩽ 1/2. They also find the minimum distance of the shortened code of length n for 33 ⩽n ⩽12144 and the double-burst detecting capabilities     

A trellis-based recursive maximum-likelihood decoding algorithm forbinary linear block codes

This paper presents an efficient trellis-based maximum-likelihood decoding algorithm for binary linear block codes. This algorithm is recursive in nature and is devised based on the structural properties and optimum sectionalization of a code trellis. The complexity of the proposed decoding algorithm is analyzed. Numerical results show that the proposed decoding algorithm significantly reduces the decoding complexity. A recursive method for finding the optimum sectionalization of a trellis in terms of computational complexity is given     

An error control system with multiple-stage forward errorcorrections

A robust error control coding system is presented. This system is a cascaded FEC (forward error control) scheme supported by parity retransmissions for further error correction in the erroneous data words. The error performance and throughput efficiency of the system are analyzed. Two specific examples of the error control system are studied. The first example does not use an inner code, and the outer code, which is not interleaved, is a shortened code of the NASA standard RS code over GF(2⁸). The second example, as proposed for NASA uses the same shortened RS code as the base outer code C₂, except that it is interleaved to a depth of 2. It is shown that both examples provide high reliability and throughput efficiency even for high channel bit-error rates in the range of 10^-2