Based on the number of cyclotomy of order eight, a class of balanced almost 8-QAM sequences with odd prime periods is presented. The resultant sequences have low two-level nontrivial autocorrelation values, and their distribution is determined. Furthermore, the smallest possible absolute sidelobes (SPASs) of autocorrelation functions of balanced almost 8-QAM sequences are derived. Compared with the obtained SPASs, some of the proposed sequences is optimal or suboptimal.

Block compressed sensing with random permutation (BCS-RP) has been shown to be very effective for image Encryption-then-Compression (ETC) applications. However, in the BCS-RP scheme, the statistical information of the blocks is disclosed, because the encryption is conducted within each small block of the image. To solve this problem, a two-dimension compressed sensing (2DCS) with 2D random permutation (2DRP) strategy for image ETC applications is proposed in this letter, where the 2DRP strategy is used for encrypting the image and the 2DCS scheme is used for compressing the encrypted image. Compared with the BCS-RP scheme, the proposed approach has two benefits. Firstly, it offers better security. Secondly, it obtains a significant gain of peak signal-to-noise ratio (PSNR) of the reconstructed-images.

The approximately synchronized code-division multiple-access (CDMA) communication system, using the QAM sequences with zero correlation zone (ZCZ) as its spreading sequences, not only can remove the multiple access interference (MAI) and multi-path interference (MPI) synchronously, but also has a higher transmission data rate than the one using traditional ZCZ sequences with the same sequence length. Based on Gray mapping and the known binary ZCZ sequences, in this letter, six families of 16-QAM sequences with ZCZ are presented. When the binary ZCZ sequences employed by this letter arrive at the theoretical bound on the binary ZCZ sequences, and their family size is a multiple of 4 or 2, two of the resultant six 16-QAM sequence sets satisfy the bound referred to above as well.

Multi-dimensional (MD) periodic complementary array sets (CASs) with impulse-like MD periodic autocorrelation function are naturally generalized to (one dimensional) periodic complementary sequence sets, and such array sets are widely applied to communication, radar, sonar, coded aperture imaging, and so forth. In this letter, based on multi-dimensional perfect arrays (MD PAs), a method for constructing MD periodic CASs is presented, which is carried out by sampling MD PAs. It is particularly worth mentioning that the numbers and sizes of sub-arrays in the proposed MD periodic CASs can be freely changed within the range of possibilities. In particular, for arbitrarily given positive integers M and L, two-dimensional periodic polyphase CASs with the number M2 and size L L of sub-arrays can be produced by the proposed method. And analogously, pseudo-random MD periodic CASs can be given when pseudo-random MD arrays are sampled. Finally, the proposed method's validity is made sure by a given example.

A novel construction of complementary sequences with multi-width zero cross-correlation zone (ZCCZ) is presented based on the interleaving iteration of a basic kernel set. The presented multi-width ZCCZ complementary (MWZC) sequences can be divided into multiple sequence groups, the correlation functions of which possess one-width intragroup ZCCZ and multi-width intergroup ZCCZ. When an arbitrary orthogonal sequence set with set size equal to sequence length is used as a basic kernel set, the constructed MWZC sequence set and the combination sets of specific subsets with each subset including several groups can be optimal with respect to the theoretical bound on set size. In addition, the MWZC sequence set includes complementary sequence sets with one-width or two-width ZCCZ as special subsets, and allows a more flexible choice of sequence parameters.

In an OFDM communication system using quadrature amplitude modulation (QAM) signals, peak envelope powers (PEPs) of the transmitted signals can be well controlled by using QAM Golay complementary sequence pairs (CSPs). In this letter, by making use of a new construction, a family of new 16-QAM Golay CSPs of length N=2m (integer m≥2) with binary inputs is presented, and all the resultant pairs have the PEP upper bound 2N. However, in the existing such pairs from other references their PEP upper bounds can arrive at 3.6N when the worst case happens. In this sense, novel pairs are good candidates for OFDM applications.

In DS-CDMA systems and DS-UWB radios, low correlation of spreading sequences can greatly help to minimize multiple access interference (MAI) and large linear span of spreading sequences can reduce their predictability. In this letter, new sequence sets with low correlation and large linear span are proposed. Based on the construction Tr1m[Trmn(αbt+γiαdt)]r for generating p-ary sequences of period pn-1, where n=2m, d=upm v, b=u v, γi GF(pn), and p is an arbitrary prime number, several methods to choose the parameter d are provided. The obtained sequences with family size pn are of four-valued, five-valued, six-valued or seven-valued correlation and the maximum nontrivial correlation value is (u+v-1)pm-1. The simulation by a computer shows that the linear span of the new sequences is larger than that of the sequences with Niho-type and Welch-type decimations, and similar to that of [10].

The mappings from independent binary variables to quadrature amplitude modulation (QAM) symbols are developed. Based the proposed mappings and the existing binary mutually uncorrelated complementary sequence sets (MUCSSs), a construction producing QAM periodic complementary sequence sets (PCSSs) is presented. The resultant QAM PCSSs have the same numbers and periods of sub-sequences as the binary MUCSSs employed, and the family size of new sequence sets is increased with exponent of periods of sub-sequences. The proposed QAM PCSSs can be applied to CDMA or OFDM communication systems so as to suppress multiple access interference (MAI) or to reduce peak-to-mean envelope power ratio (PMEPR), respectively.

In contemporary communications, Golay, periodic and Z- complementary sequence sets play a very important role, since such sequence sets possess impulse-like or zero correlation zone (ZCZ) autocorrelation. On the other hand, the advantages of the signals over the quadrature amplitude modulation (QAM) constellation are more and more prominent. Hence, the design of such sequence sets over the QAM constellation has turned into one of the all-important issues in communications. Therefore, the construction methods of such sequence sets over the 16-QAM constellation are investigated, in this letter, and our goals are arrived at by the known quaternary Golay, periodic and Z- complementary sequence sets. Finally, many examples illuminate the validity of the proposed methods.

For various applications in image, communications and signal processing, two-dimensional (2-D) generalized orthogonal (GO) sequences, that is, 2-D sequences with zero correlation zone (ZCZ) and 2-D complementary orthogonal (CO) sequences with ZCZ, are widely investigated. New lower bounds for 2-D GO sequences, based on matrix theory on rank, are derived and presented, some examples that attain these lower bounds are given. As a direct application to our results, upper bound on family size of 2-D mutually complementary orthogonal (MCO) codes defined by Luke [9] is proposed.

In the letter, properties of m-sequence are derived, based on these properties, a family of binary nonlinear constant weight codes is presented, these binary nonlinear constant weight codes can apply to automatic repeat request (ARQ) communication system, as detecting-error codes.

Perfect arrays are widely applied to high-dimensional communications, time-frequency-coding, spatial correlation or map matching, built-in tests of VLSI-circuits, radar, and so on. The letter investigates perfect arrays over the 8-QAM+ constellation, and two constructions for yielding such arrays are presented. Furthermore, the family size of the proposed arrays is determined as well.

In a direct-sequence spread spectrum communication system, its multiple access interference, security and user number are mainly decided by correlation, linear span and family size of spreading sequences employed by such a system, respectively. In this letter, based on several families of the known sequences, a method for improving their linear span and family sizes is presented. It is worthy of mentioning that although the number of the proposed sequences with linear span not less than that of the known sequences is enormously increased, the former's correlation distribution is the same as the latter's one. In addition, the proposed sequences include No sequences and the known sequences mentioned above as special cases.