Topic
Complementary sequences
About: Complementary sequences is a research topic. Over the lifetime, 1540 publications have been published within this topic receiving 26864 citations.
Papers published on a yearly basis
1 / 2
Papers
[...]
1 Apr 1961
TL;DR: These series, which were originally conceived in connection with the optical problem of multislit spectrometry, also have possible applications in communication engineering, for when the two kinds of elements of these series are taken to be +1 and -1, it follows immediately from their definition that the sum of their two respective autocorrelation series is zero everywhere, except for the center term.
Abstract: A set of complementary series is defined as a pair of equally long, finite sequences of two kinds of elements which have the property that the number of pairs of like elements with any one given separation in one series is equal to the number of pairs of unlike elements with the same given separation in the other series. (For instance the two series, 1001010001 and 1000000110 have, respectively, three pairs of like and three pairs of unlike adjacent elements, four pairs of like and four pairs of unlike alternate elements, and so forth for all possible separations.) These series, which were originally conceived in connection with the optical problem of multislit spectrometry, also have possible applications in communication engineering, for when the two kinds of elements of these series are taken to be +1 and -1, it follows immediately from their definition that the sum of their two respective autocorrelation series is zero everywhere, except for the center term. Several propositions relative to these series, to their permissible number of elements, and to their synthesis are demonstrated.
1,693 citations
1 Dec 1976
TL;DR: A simple description of pseudo-random sequences, or maximal-length shift-register sequences, and two-dimensional arrays of area n = 2lm- 1 with the same property.
Abstract: Binary sequences of length n = 2m- 1 whose autocorrelation function is either 1 or -1/n have been known for a long time, and are called pseudo-random (or PN) sequences, or maximal-length shift-register sequences. Two-dimensional arrays of area n = 2lm- 1 with the same property have rcently been found by several authors. This paper gives a simple description of such sequences and arrays and their many nice properties.
848 citations
TL;DR: It is shown that matrices consisting of mutually orthogonal complementary sets of sequences can be used as operators so as to per form transformations and inverse transformations on a one- or two-dimensional array of real time or spatial functions.
Abstract: A set of equally long finite sequences, the elements of which are either + 1 or - 1, is said to be a complementary set of sequences if the sum of autocorrelation functions of the sequences in that set is zero except for a zero-shift term. A complementary set of sequences is said to be a mate of another set if the sum of the cross-correlation functions of the corresponding sequences in these two sets is zero everywhere. Complementary sets of sequences are said to be mutually orthogonal complementary sets if any two of them are mates to each other. In this paper we discuss the properties of such complementary sets of sequences. Algorithms for synthesizing new sets from a given set are given. Recursive formulas for constructing mutually orthogonal complementary sets are presented. It is shown that matrices consisting of mutually orthogonal complementary sets of sequences can be used as operators so as to per form transformations and inverse transformations on a one- or two-dimensional array of real time or spatial functions. The similarity between such new transformations and the Hadamard transformation suggests applications of such new transformations to signal processing and image coding.
685 citations
TL;DR: In this article, it was shown that the dispersion of the (t, s)-sequences constructed here has the smallest possible order of magnitude among any sequences in the s-dimensional unit cube.
557 citations
16 Aug 1998
TL;DR: A powerful theory linking Golay complementary sets of polyphase sequences and Reed-Muller codes is developed and shows that any second-order coset of a q-ary generalization of the first order Reed-muller code can be partitioned into Golay additive sets whose size depends only on a single parameter that is easily computed from a graph associated with the coset.
Abstract: Controlling the peak-to-mean envelope power ratio (PMEPR) of orthogonal frequency-division multiplexed (OFDM) transmissions is a notoriously difficult problem, though one which is of vital importance for the practical application of OFDM in low-cost applications The utility of Golay complementary sequences in solving this problem has been recognized for some time In this paper, a powerful theory linking Golay complementary sets of polyphase sequences and Reed-Muller codes is developed Our main result shows that any second-order coset of a q-ary generalization of the first order Reed-Muller code can be partitioned into Golay complementary sets whose size depends only on a single parameter that is easily computed from a graph associated with the coset As a first consequence, recent results of Davis and Jedwab (see Electron Lett, vol33, p267-8, 1997) on Golay pairs, as well as earlier constructions of Golay (1949, 1951, 1961), Budisin (1990) and Sivaswamy (1978) are shown to arise as special cases of a unified theory for Golay complementary sets As a second consequence, the main result directly yields bounds on the PMEPRs of codes formed from selected cosets of the generalized first order Reed-Muller code These codes enjoy efficient encoding, good error-correcting capability, and tightly controlled PMEPR, and significantly extend the range of coding options for applications of OFDM using small numbers of carriers
532 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 3 |
| 2024 | 4 |
| 2023 | 24 |
| 2022 | 47 |
| 2021 | 19 |
| 2020 | 28 |