The utilization of short packet transmission is primarily focused on ultra-reliable low-latency communication (URLLC), with the objective of achieving low latency. Sparse superposition codes (SSCs) have exhibited good performance in channel coding for short codeword lengths in recent years. This letter proposes a new method for constructing SSCs using Golay complementary pairs (GCPs). Furthermore, we analyze the cross-correlation properties of the constructed codewords. The simulation results indicate that, in short packet transmission scenarios, the proposed GCP-based SSCs exhibit superior performances compared to existing alternatives in the literature.

In this paper, we present a novel construction method for constructing Gaussian integer periodic Z-complementary sets (GI-PZCSs). By leveraging the technique of an extended periodic correlation operation, the proposed method generates GI-PZCSs with flexible sequence lengths. Additionally, optimal GI-PZCSs can also be constructed using the proposed method.

The widely and commonly adopted upper bound on the set size of aperiodic Z-complementary code sets (ZCCSs) in the literature has been a conjecture. In this letter, we provide detailed derivations of a conjectured bound on the set size of multiphase ZCCSs. A multiphase ZCCS is optimal when its set size reaches the upper bound. Furthermore, we propose a new construction of ZCCSs based on extended generalized Boolean functions (EGBFs). The proposed method introduces optimal ZCCSs with new parameters.

This paper presents a novel training matrix design for spatial modulation (SM) systems, by introducing a new class of two-dimensional (2D) arrays called sparse zero correlation zone (SZCZ) arrays. An SZCZ array is characterized by a majority of zero entries and exhibits the zero periodic auto-and cross-correlation zone properties across any two rows. With these unique properties, we show that SZCZ arrays can be effectively used as training matrices for SM systems. Additionally, direct constructions of SZCZ arrays with large ZCZ widths and controllable sparsity levels based on 2D restricted extended generalized Boolean functions (REGBFs) are proposed. Compared with existing training schemes, the proposed SZCZ-based training matrices have larger ZCZ widths, thereby offering greater tolerance for delay spread in multipath channels. Simulation results demonstrate that the proposed SZCZ-based training design exhibits superior channel estimation performance over frequency-selective fading channels compared to existing alternatives.

Recently, the concept of enhanced cross Z-complementary sets (E-CZCS) has been proposed for training sequence design in generalized spatial modulation (GSM). Based on generalized Boolean functions, we present a new construction of E-CZCSs having maximum zero correlation zone (ZCZ) width. Based on the proposed E-CZCSs, numerical simulation results indicate that the resultant training sequences lead to superior channel estimation performance in broadband GSM systems.

This paper presents a coding approach for achieving omnidirectional transmission of certain common signals in massive multi-input multi-output (MIMO) networks such that the received power at any direction in a cell remains constant for any given distance. Specifically, two-dimensional (2D) Golay complementary array set (GCAS) can be used to design the massive MIMO precoding matrix so as to achieve omnidirectional transmission due to its complementary autocorrelation property. In this paper, novel constructions of new 2D GCASs with arbitrary array lengths are proposed. Our key idea is to carefully truncate the columns of certain larger arrays generated by 2D generalized Boolean functions. Finally, the power radiation patterns and numerical results are provided to verify the omnidirectional property of the GCAS-based precoding. The error performances of the proposed precoding scheme are presented to validate its superiority over the existing alternatives.

This paper presents a novel class of complex-valued sparse complementary pairs (SCPs), each consisting of a number of zero values and with additional zero-correlation zone (ZCZ) property for the aperiodic autocorrelations and crosscorrelations of the two constituent sequences. Direct constructions of SCPs and their mutually-orthogonal mates based on restricted generalized Boolean functions are proposed. It is shown that such SCPs exist with arbitrary lengths and controllable sparsity levels, making them a disruptive sequence candidate for modern low-complexity, low-latency, and low-storage signal processing applications.

This paper aims to present novel constructions of Golay-ZCZ sequence sets with various set sizes and flexible lengths. A Golay-ZCZ sequence set is not only a Golay complementary set (GCS) but also a zero correlation zone (ZCZ) sequence set. Golay-ZCZ sequence sets have been employed in OFDM systems due to their low peak-to-average power ratios (PAPRs) which are upper bounded by the set sizes. Although several constructions of Golay-ZCZ sequence sets have been proposed in the literature, the known Golay-ZCZ sets cannot attain the theoretical upper bound on the ZCZ width for non-binary cases. Also, for the Golay-ZCZ sets constructed by generalized Boolean functions, parameters are limited to powers of two, such as set sizes, sequence lengths, and ZCZ widths. In this paper, constructions of Golay-ZCZ sequence sets based on the extended generalized Boolean functions are proposed, where set sizes, sequence lengths, and ZCZ widths are all flexible and not necessary to be power-of-two. Since the constructed Golay-ZCZ sets have various set sizes, their PAPR upper bounds can be tighter. In addition, the proposed Golay-ZCZ sequence sets can achieve the upper bound on the ZCZ width. Therefore, optimal and almost-optimal Golay-ZCZ sequence sets can be obtained by the proposed methods.

The cross Z-complementary pair (CZCP) has been employed for training design in spatial modulation (SM). Due to its specific zero correlation zone (ZCZ) for autocorrelation and cross-correlation sums, optimal channel estimation performance in SM over frequency-selective channels can be achieved. However, a disadvantage of the CZCP is that its ZCZ width is theoretically limited by the half sequence length. In this paper, we consider the cross Z-complementary sets (CZCSs) to aim for large ZCZ widths which can be used in SM to combat larger delay spread. A novel construction of CZCSs based on generalized Boolean functions is presented in this paper. The proposed construction leads to the so-called optimal CZCSs with the maximum ZCZ width. The simulation results demonstrate that the proposed CZCS-based training sequences can tolerate larger delay spreads to improve the channel estimation performance in SM.

This paper presents an efficient construction of two-dimensional (2D) complete complementary codes (CCCs) for their modern application as omnidirectional precoding matrices in massive MIMO systems to attain enhanced cell coverage. Unlike the traditional 1D CCCs, little progress has been made on efficient and systematic constructions of the 2D counterpart. In contrast to the existing recursive constructions with the aid of various sequence operations, certain 1D seed sequences or 2D arrays, we propose to use 2D generalized Boolean functions for direct synthesis of 2D CCCs. Simulation results show that the proposed 2D CCCs appear to be good candidates for precoding matrices to achieve omnidirectional transmission in massive MIMO systems.

Spatial modulation (SM) is one special type of multiple-input multiple-output (MIMO) technique whose advantage is that only one radio-frequency (RF) chain is needed. Recently, the so-called cross Z-complementary pair (CZCP) was proposed as the SM training sequence. Optimal channel estimation performance over frequency-selective channels can be achieved since the CZCPs have the specific zero correlation zone (ZCZ) for auto-correlation and cross-correlation sums. However, the ZCZ width of the CZCP is theoretically upper bounded by half sequence length. In this paper, the CZCP is extended to the cross Z-complementary set (CZCS) to have larger ZCZ width which can be used in SM to combat larger delay spread. Several generic constructions of CZCSs with large ZCZ widths and flexible lengths are proposed in this paper. Even the perfect CZCS, whose ZCZ width has the maximum value, can be obtained. Numerical simulations demonstrate that the proposed CZCS-based training sequence can tolerate large delay spreads to improve the channel estimation performance in SM.

The one-dimensional (1-D) Golay complementary set (GCS) has many well-known properties and has been widely employed in communications engineering. The concept of 1-D GCS can be extended to the two-dimensional (2-D) Golay complementary array set (GCAS) where the 2-D aperiodic autocorrelations of constituent arrays sum to zero except for the 2-D zero shift. The 2-D GCAS includes the 2-D Golay complementary array pair (GCAP) as a special case when the set size is 2. In this paper, 2-D generalized Boolean functions are introduced and constructions of 2-D GCAPs, 2-D GCASs, and 2-D Golay complementary array mates based on generalized Boolean functions are proposed. Explicit expressions of 2-D Boolean functions for 2-D GCAPs and 2-D GCASs are given. Therefore, they are all direct constructions without the aid of other existing 1-D or 2-D sequences. Moreover, the peak-to-average power ratio (PAPR) properties of the column sequences and row sequences of the constructed 2-D GCAPs and 2-D GCASs are investigated and the PAPRs are proved to be upper bounded.

The two-dimensional (2-D) Z-complementary array pair (ZCAP) can be viewed as an extension of the well-known one-dimensional (1-D) Z-complementary pair (ZCP). To date, most constructions of 2-D ZCAPs are indirect and based on existing 1-D sequences or 2-D arrays. In this letter, a new direct construction of 2-D ZCAPs with flexible array sizes based on 2-D generalized Boolean functions is proposed. Compared with the state-of-the-art method, the proposed 2-D ZCAPs have larger 2-D zero correlation zone (ZCZ) sizes and more flexible array sizes. Furthermore, the peak-to-average power ratio of column sequences of the proposed 2-D ZCAPs is analyzed and upper bounded by 2.

One-dimensional (1-D) Golay complementary pair (GCP) and its extension Z-complementary pair (ZCP) with additional zero autocorrelation zone property have been widely studied in the literature. Recently, the investigation of 1-D GCPs have been extended to two-dimensional (2-D) and higher dimensional Golay complementary array pairs (GCAPs). In this article, the concept of zero correlation zone (ZCZ) is applied to 2-D GCAP and the 2-D Z-complementary array pair (ZCAP) is presented. Several constructions of ZCAPs are proposed in this article and the existence of ZCAPs is discussed as well. Based on the proposed constructions, 2-D ZCAPs are shown to exist for all sizes. Furthermore, an upper bound on the rectangular ZCZ size of the 2-D ZCAP is derived when both dimensions are odd. The proposed constructions can include ZCAPs which achieve the upper bound.

The two-dimensional (2-D) Golay complementary array pair (GCAP) is an extension of the one-dimensional (1-D) Golay complementary pair (GCP). The sums of 2-D autocorrelations of constituent arrays of a GCAP are zero except for the 2-D zero shift. In this paper, the 2-D generalized Boolean function is introduced and a novel construction of 2-D GCAPs is proposed based on generalized Boolean functions. Moreover, we provide a construction of 2-D Golay complementary array mate from Boolean functions as well. One potential of 2-D GCAPs is 2-D synchronization.

One-dimensional (1-D) Z-complementary pair (ZCP) is an extension of 1-D Golay complementary pair (GCP) where the autocorrelations of constituent sequences are complementary within a zero correlation zone (ZCZ). The concept of ZCZ can be applied to two-dimensional (2-D) Golay complementary array pair to obtain the 2-D Z-complementary array pair (ZCAP). In this paper, constructions of ZCAPs are proposed based on concatenations of 1-D ZCPs or existing 2-D ZCAPs. In addition, the construction of 1-D ZCPs based on Kronecker product is modified and extended to 2-D ZCAPs. One potential application of 2-D ZCAPs is 2-D synchronization.

Two constant quality (CQ) CBR algorithms for MPEG-4 video transcoding (FLCQT and MVCQT) are proposed in this paper. These algorithms are developed based on the CQ CBR encoding algorithms. A new Laplacian rate/distortion model is developed to predict the transcoder output quality relative to the original. This model is then used by the proposed rate control algorithms to determine the frame QP (for FLCQT) or macroblock QPs (for MVCQT). Simulation results suggest that the proposed transcoding algorithms generally give a lower quality variation with similar average PSNR and lower bitrate than the reference encoding and transcoding algorithms. Like Cheng-Yu Pai et. al., (2006), an extra degree of freedom is offered so that one can trade between lower PSNR variance and higher average PSNR.

A new MPEG-4 rate control algorithm is proposed to calculate the quantization parameter for given target bit rate. The rate-distortion method models the AC DCT coefficients as Laplacian random variables. Derived from the MPEG-4 variable-length code/run-length code (VLC/ RLC) table, the new model accurately predicts the rates and the distortions of an intra frame for all range of quantization parameters. When compared with the Q2 rate-control algorithm, the proposed algorithm offers better or similar PSNR under lower bit budgets. It also features faster initialization and adaptation to sequence property changes, and meets the target bit rate more accurately than the Q2 algorithm.