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.

Cross Z-complementary sets (CZCSs) are useful for optimal training design in spatial modulation (SM) system over frequency-selective channels. Recently, several generic constructions of CZCSs have been proposed based on special sequences. Based on the algebraic tool of generalized Boolean functions, we make the first attempt for two constructions of CZCSs having flexible non-power-of-two lengths and large zero correlation zone properties. It is shown that the proposed CZCSs lead to optimal SM training sequences which can achieve the minimum mean square error of channel estimation performance in frequency-selective channels.

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.

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.