Distance Properties of Short LDPC Codes and their Impact on the BP, ML and Near-ML Decoding Performance

Parameters of LDPC codes, such as minimum distance, stopping distance, stopping redundancy, girth of the Tanner graph, and their influence on the frame error rate performance of the BP, ML and near-ML decoding over a BEC and an AWGN channel are studied. Both random and structured LDPC codes are considered. In particular, the BP decoding is applied to the code parity-check matrices with an increasing number of redundant rows, and the convergence of the performance to that of the ML decoding is analyzed. A comparison of the simulated BP, ML, and near-ML performance with the improved theoretical bounds on the error probability based on the exact weight spectrum coefficients and the exact stopping size spectrum coefficients is presented. It is observed that decoding performance very close to the ML decoding performance can be achieved with a relatively small number of redundant rows for some codes, for both the BEC and the AWGN channels

Robust Physical Layer Security for Power Domain Non-Orthogonal Multiple Access-Based HetNets and HUDNs: SIC Avoidance at Eavesdroppers

In this paper, we investigate the physical layer security in downlink of Power Domain Non-Orthogonal Multiple Access (PD-NOMA)-based heterogeneous cellular network (HetNet). In this paper, we assume two categories of users are available: 1) Trusted users and 2) untrusted users (eavesdroppers) at which transparency of users is not clear for the BSs, i.e., they are potential eavesdroppers. Our aim is to maximize the sum secrecy rate of the network. To this end, we formulate joint subcarrier and power allocation optimization problems to increase sum secrecy rate. Moreover, we propose a novel scheme at which the eavesdroppers are prevented from doing Successive Interference Cancellation (SIC), while legitimate users are able to do it. In practical systems, perfectly availability of all eavesdroppers' Channel State Information (CSI) at legitimate transmitters are impractical. Also CSIs of legitimate users may be also imperfect due to the error of channel estimation. Hence, we study two cases of CSI availability: 1) Perfect CSI of nodes (legitimate users and eavesdroppers) are available at the BSs and 2) imperfect CSI of nodes are available at the BSs. Since the proposed optimization problems are non-convex, we adopt the well-known iterative algorithm called Alternative Search Method (ASM). In this algorithm, the optimization problems are converted to two subproblems, power allocation and subcarrier allocation. We solve the power allocation problem by the Successive Convex Approximation approach and solve the subcarrier allocation subproblem, by exploiting the Mesh Adaptive Direct Search algorithm (MADS). Moreover, in order to study the optimality gap of the proposed solution method, we apply the monotonic optimization method. Moreover, we evaluate the proposed scheme for secure massive connectivity in Heterogeneous Ultra Dense Networks (HUDNs). Furthermore, we investigate multiple antennas base stations scenario in this literature. Finally, we numerically compare the proposed scheme with the conventional case at which the eavesdroppers are able to apply SIC. Numerical results highlight that the proposed scheme significantly improves the sum secrecy rate compared with the conventional case

Analysis of finite unreliable sensor grids

Abstract — Asymptotic analysis of unreliable sensor grides has been studied previously. Some analytic results for sensor grids have been reported for the case where the number of nodes n in the network tends to infinity (large-scale grids). This includes connectivity, coverage, and diameter of the networks. These results have not been extended for small or moderate values of n, although in many practical sensor grids, n might not be very large. In this paper, we first show that previous asymptotic results may provide poor approximations for the finite grids (small-scale grids). We then aim to develop a methodology to analytically study unreliable sensor grids properties without assuming that n is large. We prove some properties of finite sensor grids. We show that a large class of network parameters can be expressed as piecewise constant functions of communication and sensing radii. We obtain simple analytic expressions for connectivity and coverage probabilities of finite sensor grids. Using simulations, we show that the expressions give good estimates of these probabilities. I