This paper is concerned with construction and structural analysis of both cyclic and quasi-cyclic codes, particularly low-density parity-check (LDPC) codes. It consists of three parts. The first part shows that a cyclic code given by a parity-check matrix in circulant form can be decomposed into descendant cyclic and quasi-cyclic codes of various lengths and rates. Some fundamental structural properties of these descendant codes are developed, including the characterization of the roots of the generator polynomial of a cyclic descendant code. The second part of the paper shows that cyclic and quasi-cyclic descendant LDPC codes can be derived from cyclic finite-geometry LDPC codes using the results developed in the first part of the paper. This enlarges the repertoire of cyclic LDPC codes. The third part of the paper analyzes the trapping set structure of regular LDPC codes whose parity-check matrices satisfy a certain constraint on their rows and columns. Several classes of finite-geometry and finite-field cyclic and quasi-cyclic LDPC codes with large minimum distances are shown to have no harmful trapping sets of size smaller than their minimum distances. Consequently, their error-floor performances are dominated by their minimum distances.

In this paper, we consider a cooperative communication network where multiple low-Earth-orbit (LEO) satellites provide services to multiple ground users (GUs) cooperatively at the same time and on the same frequency. The multi-satellite cooperation has great potential in extending communication coverage and increasing spectral efficiency. Considering that the on-board radio-frequency circuit resources and computation resources on each satellite are restricted, we aim to propose a low-complexity yet efficient multi-satellite cooperative transmission framework. Specifically, we first propose a hybrid beamforming method consisting of analog beamforming for beam alignment and digital beamforming for interference mitigation. Then, to establish appropriate connections between the satellites and GUs, we propose a heuristic user scheduling algorithm which determines the connections according to the total spectral efficiency increment of the multi-satellite cooperative network. Next, considering the intrinsic connection between beamforming and user scheduling, a joint hybrid beamforming and user scheduling (JHU) scheme is proposed to dramatically improve the performance of the multi-satellite cooperative network. In addition to the single-connection scenario, we also consider the multi-connection case using the JHU scheme. Extensive simulations conducted over different LEO satellite constellations and across various GU locations demonstrate the superiority of the proposed schemes in both overall and per-user spectral efficiencies.

This paper proposes an integrated sensing and communications (ISAC) system based on affine frequency division multiplexing (AFDM) waveform. To this end, a metric set is designed according to not only the maximum tolerable delay/Doppler, but also the weighted spectral efficiency as well as the outage/error probability of sensing and communications. This enables the analytical investigation of the performance trade-offs of AFDM-ISAC system using the derived analytical relation among metrics and AFDM waveform parameters. Moreover, by revealing that delay and the integral/fractional parts of normalized Doppler can be decoupled in the affine Fourier transform-Doppler domain, an efficient estimation method is proposed for our AFDM-ISAC system, whose unambiguous Doppler can break through the limitation of subcarrier spacing. Theoretical analyses and numerical results verify that our proposed AFDM-ISAC system may significantly enlarge unambiguous delay/Doppler while possessing good spectral efficiency and peak-to-sidelobe level ratio in high-mobility scenarios.

This paper presents two packings derived from balanced incomplete block designs to construct quasi-cyclic spatially coupled LDPC convolutional codes (SC-LDPC-CCs). The construction gives time-invariant codes, since the sub-blocks corresponding to each time instant of the parity-check matrix are identical. Moreover, it provides flexible design rates and constraint lengths. Simulation results show that the proposed packing-based SC-LDPC-CCs outperform the existing time-invariant codes and perform closely to the time-varying protograph-based codes.

Piggybacking is an efficient framework to reduce the repair bandwidth of distributed storage systems, especially, when the systems meet the settings-maximum distance separable (MDS), high code rate, and a small number of substripes. Through an analysis on the repair ratio of a piggybacking construction, this paper reveals that the proportion p _p of piggybacking protected stripes is the key to significantly decrease the repair bandwidth. Based on this analysis, this paper proposes a repair efficient coding under piggybacking framework (REPB) by considering various piggybacking protected stripes and MDS only protected stripes. The repair ratio of REPB tends to 0 and is close to theoretical cut-set bound, as the proportion p _p is no longer fixed at 1/2. Furthermore, the proposed REPB codes enjoy low computational complexity in repair operation.

This paper constructs an objective function for symbol flipping decoding algorithms, considering not only soft reliability, but also hard reliability. The maximization of this objective function indicates that the flipping metric should involve both the information before and after symbol flipping, while the existing algorithms consider the information before symbol flipping. Theoretical analysis shows that such prediction mechanism, together with hard reliability, can significantly improve the error performance of symbol flipping algorithms. Simulation results show that the proposed algorithms provide effective tradeoff between error performance and complexity for decoding non-binary LDPC codes.