Cyclic liftings are proposed to lower the error floor of low-density parity-check (LDPC) codes. The liftings are designed to eliminate dominant trapping sets of the base code by removing the short cycles which are part of the trapping sets. We derive a necessary and sufficient condition for the cyclic permutations assigned to the edges of a cycle ξ of length l(ξ) in the base graph such that the inverse image of ξ in the lifted graph consists of only cycles of length strictly larger than l(ξ). The proposed method is universal in the sense that it can be applied to any LDPC code over any channel and for any iterative decoding algorithm. It also preserves important properties of the base code such as degree distributions, and in some cases, the code rate. The constructed codes are quasi-cyclic and thus attractive from a practical point of view. The proposed method is applied to both structured and random codes over the binary symmetric channel (BSC). The error floor improves consistently by increasing the lifting degree, and the results show significant improvements in the error floor compared to the base code, a random code of the same degree distribution and block length, and a random lifting of the same degree. Similar improvements are also observed when the codes designed for the BSC are applied to the additive white Gaussian noise (AWGN) channel.

The progressive-edge-growth (PEG) algorithm of Hu et al. is modified to improve the error floor performance of the constructed low-density parity-check (LDPC) codes. To improve the error floor, the original PEG algorithm is equipped with an efficient algorithm to find the dominant elementary trapping sets (ETS's) that are added to the Tanner graph of the under-construction code by the addition of each variable node and its adjacent edges. The aim is to select the edges, among the candidates available at each step of the original PEG algorithm, that prevent the creation of dominant ETS's. The proposed method is applicable to both regular and irregular variable node degree distributions. Simulation results are presented to demonstrate the superior ETS distribution and error floor performance of the constructed codes compared to similar codes constructed by the original and other modifications of the PEG algorithm.

In this paper, we propose a rate-compatible puncturing scheme for finite-length low-density parity-check (LDPC) codes over the additive white Gaussian noise (AWGN) channel. The proposed method is applicable to any LDPC mother code, both regular and irregular, and constructs punctured codes which perform well in both the waterfall and the error floor regions for a wide range of code rates. The scheme selects code bits to be punctured one at a time and based on a sequence of criteria. An important selection criterion is the number of short cycles with low approximate cycle extrinsic message degree (ACE) in which a candidate bit node participates. Simulation results demonstrate that the ACE measure, which is most often the determining criterion in the final selection of the puncturing candidates, plays an important role in improving the performance of the codes in both the waterfall and the error-floor regions. These results also demonstrate that the proposed scheme is superior to the existing puncturing methods, particularly when a wide range of code rates is desirable.

We propose a technique to design finite-length irregular low-density parity-check (LDPC) codes over the binary-input additive white Gaussian noise (AWGN) channel with good performance in both the waterfall and the error floor region. The design process starts from a protograph which embodies a desirable degree distribution. This protograph is then lifted cyclically to a certain block length of interest. The lift is designed carefully to maximize the components of the approximate cycle extrinsic message degree (ACE) spectrum of the code's Tanner graph in a greedy fashion. As a consequence, the designed code would perform well in the error floor region. Moreover, the proposed construction results in quasi-cyclic codes which are attractive in practice due to simple encoder and decoder implementation. Simulation results are provided to demonstrate the effectiveness of the proposed construction in comparison with similar existing constructions.

The approach of factor-graphs (FGs) is applied in the context of power control and user pairing in Device-to-Device (D2D) communications as an effective underlay concept in wireless cellular networks. D2D communications can increase the spectral efficiency of wireless cellular networks by establishing a direct link between devices with limited help from the evolved node base stations (eNBs). A well-designed user pairing and power allocation scheme with low complexity can remarkably improve the system's performance. In this paper, a simple and distributed FG based approach is utilized for power control and user pairing implementation in an underlay cellular network with D2D communications. A max-min criterion is proposed to maximize the minimum rate of all active users in the network, including the cellular and multiple D2D co-channel links in the uplink direction. An associated message-passing (MP) algorithm is presented to distributedly solve the resultant NP-hard maximization problem, with a guaranteed convergence compared to game theoretic and Q-learning based methods. The complexity and convergence of the proposed method is analyzed and numerical results confirm that the proposed scheme outperforms alternative algorithms in terms of complexity, while keeping the sum-rate of users nearly the same as centralized counterpart methods.

In this paper, we propose an efficient method that specifies the minimum number of samples and their locations to measure the spherical near-field (SNF) of antennas utilizing information theoretic tools. To this end, spherical harmonics are investigated from the information theoretic point of view. Our study determines the minimum required samples and provides a validation tool to assess the ability of a sampling scheme to recover the antenna characteristics by the measured data. Further, an optimum sampling scheme is proposed by clustering the energy of vector spherical harmonics using the frame theory without any time-consuming iterative which leads to a highly efficient SNF measurement procedure. The number of samples determined by the proposed method is only 50% of the Nyquist method which provides significant advantages for storage and processing time. Our method additionally shows a great promise for recovery of far-field radiation pattern from near-field samples with the same performance as the Nyquist sampling on a sphere. To derive the proposed sampling scheme with the minimum redundancy, no prior information on the antenna is assumed. Finally, the proposed sampling scheme is validated on measurement data.