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10
New Complete Complementary Codes for PeaktoMean Power Control in MultiCarrier CDMA
"... Owing to the zero nontrivial aperiodic correlation sum properties, complete complementary codes (CCC) have been applied to asynchronous multicarrier codedivision multipleaccess (MCCDMA) communications in order to provide zero interference performance. When each complementary code is arranged to ..."
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Owing to the zero nontrivial aperiodic correlation sum properties, complete complementary codes (CCC) have been applied to asynchronous multicarrier codedivision multipleaccess (MCCDMA) communications in order to provide zero interference performance. When each complementary code is arranged to be a matrix, the peaktomean envelope power ratio (PMEPR) of the CCCMCCDMA system is determined by the column sequences of the complementary matrices. The existing CCC have the column sequence PMEPR of M, where M denotes the number of subcarriers in a CCCMCCDMA system. In practice, M is generally large and a PMEPR approaching this value is unacceptable. To solve this problem, a new class of CCC using generalized Boolean functions and with a column sequence PMEPR of at most 2 is proposed in this paper.
Dense ErrorCorrecting Codes in the Lee Metric
 ITW 2010
, 2010
"... Several new applications and a number of new mathematical techniques have increased the research on errorcorrecting codes in the Lee metric in the last decade. In this work we consider several coding problems and constructions of errorcorrecting codes in the Lee metric. First, we consider constru ..."
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Several new applications and a number of new mathematical techniques have increased the research on errorcorrecting codes in the Lee metric in the last decade. In this work we consider several coding problems and constructions of errorcorrecting codes in the Lee metric. First, we consider constructions of dense errorcorrecting codes in relatively small dimensions over small alphabets. The second problem we solve is construction of diametric perfect codes with minimum distance four. We will construct such codes over various lengths and alphabet sizes. The third problem is to transfer an ndimensional Lee sphere with large radius into a shape, with the same volume, located in a relatively small box. Hadamard matrices play an essential role in the solutions for all three problems. A construction of codes based on Hadamard matrices will start our discussion. These codes approach the sphere packing bound for very high rate range and appear to be the best known codes over some sets of parameters.
Generalised complementary arrays
 Lecture Notes in Computer Science, LNCS 7089
, 2011
"... Abstract. We present a generalised setting for the construction of complementary array pairs and its proof, using a unitary matrix notation. When the unitaries comprise multivariate polynomials in complex space, we show that four definitions of conjugation imply four types of complementary pair typ ..."
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Abstract. We present a generalised setting for the construction of complementary array pairs and its proof, using a unitary matrix notation. When the unitaries comprise multivariate polynomials in complex space, we show that four definitions of conjugation imply four types of complementary pair types I, II, III, and IV. We provide a construction for complementary pairs of types I, II, and III over {1, −1}, and further specialize to a construction for all known 2 × 2 ×... × 2 complementary array pairs of types I, II, and III over {1, −1}. We present a construction for typeIV complementary array pairs, and call them Rayleigh quotient pairs. We then generalise to complementary array sets, provide a construction for complementary sets of types I, II, and III over {1, −1}, further specialize to a construction for all known 2 × 2 ×... × 2 complementary array sets of types I, II, and III over {1, −1}, and derive closedform Boolean formulas for these cases.
Nearcomplementary Sequences With Low PMEPR for Peak Power Control in Multicarrier Communications
, 2009
"... New families of nearcomplementary sequences are presented for peak power control in multicarrier communications. A framework for nearcomplementary sequences is given by the explicit Boolean expression and the equivalent array structure. The framework transforms the seed pairs to nearcomplementary ..."
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New families of nearcomplementary sequences are presented for peak power control in multicarrier communications. A framework for nearcomplementary sequences is given by the explicit Boolean expression and the equivalent array structure. The framework transforms the seed pairs to nearcomplementary sequences by the aid of Golay complementary sequences. As the first example, a new sequence family of length 2m and peaktomean envelope power ratio (PMEPR) ≤ 4 is presented, where the family produces more distinct sequences than any other known near complementary sequences of the same lengths and PMEPR bound. An efficient generation algorithm for permutations is developed for the distinct sequences. In addition, new families of nearcomplementary sequences of various lengths and PMEPR < 4 are also presented, where the sequences are constructed by the framework employing the seeds of shortened or extended Golay complementary pairs. The families present in a constructive way a large number of sequences of PMEPR < 4 for the lengths (< 100) of
A fast algorithm for designing complementary sets of sequences,
 Signal Processing
, 2013
"... a b s t r a c t In this paper, we introduce a fast computational frequencydomain approach for designing complementary sets of sequences. Following the basic idea of CANbased algorithms, we propose an extension of the CAN algorithm to complementary sets of sequences (which we call CANARY). Moreove ..."
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a b s t r a c t In this paper, we introduce a fast computational frequencydomain approach for designing complementary sets of sequences. Following the basic idea of CANbased algorithms, we propose an extension of the CAN algorithm to complementary sets of sequences (which we call CANARY). Moreover, modified versions of the proposed algorithm are derived to tackle the complementary set design problems in which low peaktoaveragepower ratio (PAR), unimodular or phasequantized sequences are of interest. Several numerical examples are provided to show the performance of CANARY.
On the PeaktoMean Envelope Power Ratio of PhaseShifted Binary Codes
 IEEE TRANSACTIONS ON COMMUNICATIONS
, 2008
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Complete complementary codes and generalized reedmuller codes
 IEEE Commun. Lett
, 2008
"... Abstract—Due to ideal autocorrelation and crosscorrelation properties, complete complementary codes (CCCs) can be employed in CDMA systems to eliminate the multipleaccess interference. In this letter, we propose a direct general construction of CCCs from cosets of the firstorder ReedMuller cod ..."
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Abstract—Due to ideal autocorrelation and crosscorrelation properties, complete complementary codes (CCCs) can be employed in CDMA systems to eliminate the multipleaccess interference. In this letter, we propose a direct general construction of CCCs from cosets of the firstorder ReedMuller codes, which includes previous results as a special case. The larger number of CCCs constructed by our method can provide advantages in applications to cellular CDMA systems. Index Terms—Complete complementary codes, Golay complementary sets, ReedMuller codes, CDMA.
Coding for the Lee and Manhattan Metrics with Weighing Matrices
"... AbstractThis paper has two goals. The first one is to discuss good codes for packing problems in the Lee and Manhattan metrics. The second one is to consider weighing matrices for some of these coding problems. Weighing matrices were considered as building blocks for codes in the Hamming metric in ..."
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AbstractThis paper has two goals. The first one is to discuss good codes for packing problems in the Lee and Manhattan metrics. The second one is to consider weighing matrices for some of these coding problems. Weighing matrices were considered as building blocks for codes in the Hamming metric in various constructions. In this paper we will consider mainly two types of weighing matrices, namely conference matrices and Hadamard matrices, to construct codes in the Lee (and Manhattan) metric. We will show that these matrices have some desirable properties when considered as generator matrices for codes in these metrics. Two related packing problems will be considered. The first one is to find good codes for errorcorrection (i.e. dense packings of Lee spheres). The second one is to transform the space in a way that volumes are preserved and each Lee sphere (or conscribed crosspolytope), in the space, will be transformed into a shape inscribed in a small cube.