No Arabic abstract
The demand for flexible broadband wireless services makes the pruning technique, including both shortening and puncturing, an indispensable component of error correcting codes. The analysis of the pruning process for structured lowdensity parity-check (LDPC) codes can be considerably simplified with their equivalent representations through base-matrices or protographs. In this letter, we evaluate the thresholds of the pruned base-matrices by using protograph based on extrinsic information transfer (PEXIT). We also provide an efficient method to optimize the pruning patterns, which can significantly improve the thresholds of both the full-length patterns and the sub-patterns. Numerical results show that the structured LDPC codes pruned by the improved patterns outperform those with the existing patterns.
This paper considers the optimization of multi-edge type low-density parity-check (METLDPC) codes to maximize the decoding threshold. We propose an algorithm to jointly optimize the node degree distribution and the multi-edge structure of MET-LDPC codes for given values of the maximum number of edge-types and maximum node degrees. This joint optimization is particularly important for MET-LDPC codes as it is not clear a priori which structures will be good. Using several examples, we demonstrate that the MET-LDPC codes designed by the proposed joint optimization algorithm exhibit improved decoding thresholds compared to previously reported MET-LDPC codes.
Quantum LDPC codes are a promising direction for low overhead quantum computing. In this paper, we propose a generalization of the Union-Find decoder as adecoder for quantum LDPC codes. We prove that this decoder corrects all errors with weight up to An^{alpha} for some A, {alpha} > 0 for different classes of quantum LDPC codes such as toric codes and hyperbolic codes in any dimension D geq 3 and quantum expander codes. To prove this result, we introduce a notion of covering radius which measures the spread of an error from its syndrome. We believe this notion could find application beyond the decoding problem. We also perform numerical simulations, which show that our Union-Find decoder outperforms the belief propagation decoder in the low error rate regime in the case of a quantum LDPC code with length 3600.
In order to further exploit the potential of joint multi-antenna radar-communication (RadCom) system, we propose two transmission techniques respectively based on separated and shared antenna deployments. Both techniques are designed to maximize the weighted sum rate (WSR) and the probing power at targets location under average power constraints at the antennas such that the system can simultaneously communicate with downlink users and detect the target within the same frequency band. Based on a Weighted Minimized Mean Square Errors (WMMSE) method, the separated deployment transmission is designed via semidefinite programming (SDP) while the shared deployment problem is solved by majorization-minimization (MM) algorithm. Numerical results show that the shared deployment outperforms the separated deployment in radar beamforming. The tradeoffs between WSR and probing power at target are compared among both proposed transmissions and two practically simpler dual-function implementations i.e., time division and frequency division. Results show that although the separated deployment enables spectrum sharing, it experiences a performance loss compared with frequency division, while the shared deployment outperforms both and surpasses time division in certain conditions.
The combination of non-orthogonal multiple access (NOMA) and intelligent reflecting surface (IRS) is an efficient solution to significantly enhance the energy efficiency of the wireless communication system. In this paper, we focus on a downlink multi-cluster NOMA network, where each cluster is supported by one IRS. We aim to minimize the transmit power by jointly optimizing the beamforming, the power allocation and the phase shift of each IRS. The formulated problem is non-convex and challenging to solve due to the coupled variables, i.e., the beamforming vector, the power allocation coefficient and the phase shift matrix. To address this non-convex problem, we propose an alternating optimization based algorithm. Specifically, we divide the primal problem into the two subproblems for beamforming optimization and phase shifting feasiblity, where the two subproblems are solved iteratively. Moreover, to guarantee the feasibility of the beamforming optimization problem, an iterative algorithm is proposed to search the feasible initial points. To reduce the complexity, we also propose a simplified algorithm based on partial exhaustive search for this system model. Simulation results demonstrate that the proposed alternating algorithm can yield a better performance gain than the partial exhaustive search algorithm, OMA-IRS, and NOMA with random IRS phase shift.
We utilize a concatenation scheme to construct new families of quantum error correction codes that include the Bacon-Shor codes. We show that our scheme can lead to asymptotically good quantum codes while Bacon-Shor codes cannot. Further, the concatenation scheme allows us to derive quantum LDPC codes of distance $Omega(N^{2/3}/loglog N)$ which can improve Hastingss recent result [arXiv:2102.10030] by a polylogarithmic factor. Moreover, assisted by the Evra-Kaufman-Zemor distance balancing construction, our concatenation scheme can yield quantum LDPC codes with non-vanishing code rates and better minimum distance upper bound than the hypergraph product quantum LDPC codes. Finally, we derive a family of fast encodable and decodable quantum concatenated codes with parameters ${Q}=[[N,Omega(sqrt{N}),Omega( sqrt{N})]]$ and they also belong to the Bacon-Shor codes. We show that ${Q}$ can be encoded very efficiently by circuits of size $O(N)$ and depth $O(sqrt{N})$, and can correct any adversarial error of weight up to half the minimum distance bound in $O(sqrt{N})$ time. To the best of our knowledge, they are the most powerful quantum codes for correcting so many adversarial errors in sublinear time by far.