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Articles 1 - 8 of 8
Full-Text Articles in Mathematics
Peak-To-Mean Power Control In Ofdm, Golay Complementary Sequences, And Reed–Muller Codes, James A. Davis, Jonathan Jedwab
Peak-To-Mean Power Control In Ofdm, Golay Complementary Sequences, And Reed–Muller Codes, James A. Davis, Jonathan Jedwab
Department of Math & Statistics Faculty Publications
We present a range of coding schemes for OFDM transmission using binary, quaternary, octary, and higher order modulation that give high code rates for moderate numbers of carriers. These schemes have tightly bounded peak-to-mean envelope power ratio (PMEPR) and simultaneously have good error correction capability. The key theoretical result is a previously unrecognized connection between Golay complementary sequences and second-order Reed–Muller codes over alphabets ℤ2h. We obtain additional flexibility in trading off code rate, PMEPR, and error correction capability by partitioning the second-order Reed–Muller code into cosets such that codewords with large values of PMEPR are isolated. …
A New Family Of Relative Difference Sets In 2-Groups, James A. Davis, Jonathan Jedwab
A New Family Of Relative Difference Sets In 2-Groups, James A. Davis, Jonathan Jedwab
Department of Math & Statistics Faculty Publications
We recursively construct a new family of (26d+4, 8, 26d+4, 26d+1) semi-regular relative difference sets in abelian groups G relative to an elementary abelian subgroup U. The initial case d = 0 of the recursion comprises examples of (16, 8, 16, 2) relative difference sets for four distinct pairs (G, U).
Some Recent Developments In Difference Sets, James A. Davis, Jonathan Jedwab
Some Recent Developments In Difference Sets, James A. Davis, Jonathan Jedwab
Department of Math & Statistics Faculty Publications
There are five known parameter families for (v, k, λ, n)- difference sets satisfying gcd(v, n)>1: the Hadamard, McFarland, Spence, Davis-Jedwab, and Chen families. The authors recently gave a recursive unifying construction for difference sets from the first four families which relies on relative difference sets. We give an overview of this construction and show that, by modifying it to use divisible difference sets in place of relative difference sets, the recent difference set discoveries of Chen can be brought within the unifying framework. We also demonstrate the recursive use of an auxiliary construction for …
Codes, Correlations And Power Control In Ofdm, James A. Davis, Jonathan Jedwab, Kenneth G. Paterson
Codes, Correlations And Power Control In Ofdm, James A. Davis, Jonathan Jedwab, Kenneth G. Paterson
Department of Math & Statistics Faculty Publications
Practical communications engineering is continually producing problems of interest to the coding theory community. A recent example is the power-control problem in Orthogonal Frequency Division Multiplexing (OFDM). We report recent work which gives a mathematical framework for generating solutions to this notorious problem that are suited to low-cost wireless applications. The key result is a connection between Golay complementary sequences and Reed-Muller codes. The former are almost ideal for OFDM transmissions because they have a very low peak-to-mean envelope power ratio (PMEPR), while the latter have efficient encoding and decoding algorithms and good error correction capability. This result is then …
A Unified Approach To Difference Sets With Gcd(V, N) > 1, James A. Davis, Jonathan Jedwab
A Unified Approach To Difference Sets With Gcd(V, N) > 1, James A. Davis, Jonathan Jedwab
Department of Math & Statistics Faculty Publications
The five known families of difference sets whose parameters (v, k, λ; n) satisfy the condition gcd(v,n) > 1 are the McFarland, Spence, Davis-Jedwab, Hadamard and Chen families. We survey recent work which uses recursive techniques to unify these difference set families, placing particular emphasis on examples. This unified approach has also proved useful for studying semi-regular relative difference sets and for constructing new symmetric designs.
Bayes Estimation Of A Distribution Function Using Ranked Set Samples, Paul H. Kvam, Ram C. Tiwari
Bayes Estimation Of A Distribution Function Using Ranked Set Samples, Paul H. Kvam, Ram C. Tiwari
Department of Math & Statistics Faculty Publications
Aranked set sample (RSS), if not balanced, is simply a sample of independent order statistics generated from the same underlying distribution F. Kvam and Samaniego (1994) derived maximum likelihood estimates of F for a general RSS. In many applications, including some in the environmental sciences, prior information about F is available to supplement the data-based inference. In such cases, Bayes estimators should be considered for improved estimation. Bayes estimation (using the squared error loss function) of the unknown distribution function F is investigated with such samples. Additionally, the Bayes generalized maximum likelihood estimator (GMLE) is derived. An iterative scheme based …
Fisher Information In Weighted Distributions, Satish Iyengar, Paul H. Kvam, Harshinder Singh
Fisher Information In Weighted Distributions, Satish Iyengar, Paul H. Kvam, Harshinder Singh
Department of Math & Statistics Faculty Publications
Standard inference procedures assume a random sample from a population with density fμ(x) for estimating the parameter μ. However, there are many applications in which the available data are a biased sample instead. Fisher modeled biased sampling using a weight function w(x) ¸ 0, and constructed a weighted distribution with a density fμw(x) that is proportional to w(x)fμ(x). In this paper, we assume that fμ(x) belongs to an exponential family, and study the Fisher information about μ in observations obtained from some commonly arising weighted distributions: (i) the kth order …
A Quantile‐Based Approach For Relative Efficiency Measurement, Paul M. Griffin, Paul H. Kvam
A Quantile‐Based Approach For Relative Efficiency Measurement, Paul M. Griffin, Paul H. Kvam
Department of Math & Statistics Faculty Publications
Two popular approaches for efficiency measurement are a non‐stochastic approach called data envelopment analysis (DEA) and a parametric approach called stochastic frontier analysis (SFA). Both approaches have modeling difficulty, particularly for ranking firm efficiencies. In this paper, a new parametric approach using quantile statistics is developed. The quantile statistic relies less on the stochastic model than SFA methods, and accounts for a firm's relationship to the other firms in the study by acknowledging the firm's influence on the empirical model, and its relationship, in terms of similarity of input levels, to the other firms.