Complementary sequence sets (CSSs) and complete complementary codes (CCCs) have many applications in science and engineering, especially in wireless communications. A construction of CSS and CCC, having size M = 2mand length MK, where m and K are positive integers, is presented. The proposed construction is a generalized paraunitary (PU) algorithm that greatly increases the number of permutations from K! to (mK)! compared to those of previous PU constructions. Moreover, this new construction can be generalized to the case M = pm, where p is a positive integer. The increase in the number of permutations means that a wide range of CCCs and CSSs can be obtained.

A Boolean generator for a large number of standard complementary QAM sequences of length 2Kis proposed. This Boolean generator is derived from the authors' earlier paraunitary generator, which is based on matrix multiplications. Both generators are based on unitary matrices. In contrast to previous Boolean QAM algorithms which represent complementary sequences as a weighted sum, our algorithm has a multiplicative form. Any element of a sequence can be generated efficiently by indexing the entries of unitary matrices with the binary representation of the discrete time index (which is easily implemented as a binary counter). Our 1Qum (based on one QAM unitary matrix) and 2Qum (based on two QAM unitary matrices) algorithms generate generalized Case I-III sequences and generalized Case IV and V sequences, respectively, as specified by Liu et al. in 2013, in addition to many new 2Qum sequences. The ratio of the numbers of sequences that are generated by our new construction and the previous construction increases with the constellation size. For example, for a 1024-QAM sequence of length 1024, this ratio is 4.4. However, if we compare only 2Qum sequences to Case IV and V sequences, this ratio is 267.

Owing to their ideal correlation properties, complete complementary codes (CCC) have found numerous applications in wireless engineering, in particular they have been employed to support interference-free multi-carrier code-division multiple access systems with improved spectral efficiency. In this paper, we propose a simple construction of CCCs of length Nn(n e N) based on paraunitary matrices of size N × N. This algorithm can generate CCCs from N-shift cross-orthogonal sequence sets for n > 1. Then, we introduce an easy implementation of the proposed algorithm by multiplexers and read-only memories (ROMs), i.e., a multiplier-free implementation. As multipliers are avoided, substantial reduction of construction complexity for CCCs is obtained as compared to the existing works.

A pair of sequences is called a periodic complementary pair (PCP) if the periodic autocorrelations of the constituent sequences sum up to zero for all nonzero time shifts. Owing to the scarcity of PCPs, we investigate optimal binary periodic almost-complementary pairs (BP-ACPs), each displaying correlation property closest to that of PCP. We show that an optimal BP-ACP of even length N has zero out-of-phase periodic autocorrelation sums (PACSs) except at the time shift of N/2, where the corresponding PACS has minimum magnitude of 4. We also show that for any arbitrary odd N, all the out-of-phase PACSs of an optimal BP-ACP should have identical magnitude of 2. A number of optimal BP-ACPs from analytical constructions as well as computer search are presented. In addition, our proposed optimal BP-ACPs for the even-length case lead to two new families of base-two almost difference families.

CDMA (Code Division Multiple Access) allows distinct users to communicate simultaneously on the same frequency band using binary sequences uniquely allocated to each user. For a given sequence length, we are confronted with a tradeoff between large set size (maximizing user capacity) and low maximum absolute inner product (minimizing instantaneous interference). Significant effort has been devoted to constructing upper bounds on set size and lower bounds on maximum inner products or correlation. Here we examine a common lower bound on inner products [1], show its inadequacy in certain cases, and improve it using an upper bound on set size.

For some time it has been known that, for fixed code lengthn, binary BCH codes appear to be most efficient when the number of information bitskis between1/4 nand3/4 n[1, p. 443], [2, p. 219]. In this correspondence the efficiency of block codes on an binary-quantized additive white Gaussian noise channel is analyzed as a function of the code rater = k/nfor hard decision decoding. A closed form analytical expression for the upper and lower bounds on block code performance is derived for large code lengthsn. They show that, for best codes, a relatively broad maximum occurs for rates of approximately 0.4. The performance of the BCH codes is also compared with the bounds.

In this paper a new modulator for a broad class of continuous phase modulations (CPM) is proposed that is more flexible and less complex than conventional quadrature modulators, while achieving the same or better performance. Being all-digital it is more suitable for one-chip VLSI implementation. Some design parameters are also discussed and experimental results are presented.

The coding gain of linear binary block codes on the AWGN channel is studied. Antipodal signaling and hard decision demodulation are assumed. Simple asymptotic expressions for the gain at high and low energy to noise spectral density ratios are derived. Monotonicity of the coding gain is also discussed.