We consider the problem of private multiple linear computation (PMLC) over a replicated storage system with colluding and unresponsive constraints. In this scenario, the user wishes to privately compute$P$linear combinations of$M$files from a set of$N$replicated servers without revealing any information about the coefficients of these linear combinations to any$T$colluding servers, in the presence of$S$unresponsive servers that do not provide any information in response to user queries. Our focus is on more general performance metrics where the communication and computational overheads incurred by the user are not neglected. Additionally, the communication and computational overheads for servers are also taken into consideration. Unlike most previous literature that primarily focused on download cost from servers as a performance metric, we propose a novel PMLC scheme to establish a flexible tradeoff between communication costs and computational complexities.

Sequences play an important role in many engineering applications. Searching sequences with desired properties has long been an intriguing but also challenging research topic. This article proposes a novel method, called HpGAN, to search desired sequences algorithmically using generative adversarial networks (GANs). HpGAN is based on the idea of zero-sum game to train a generative model, which can generate sequences with characteristics similar to the training sequences. In HpGAN, we design the Hopfield network as an encoder to avoid the limitations of GAN in generating discrete data. Compared with traditional sequence construction by algebraic tools, HpGAN is particularly suitable for complex problems which are intractable by mathematical analysis. We demonstrate the search capabilities of HpGAN in two applications: 1) HpGAN successfully found many different mutually orthogonal complementary sequence sets (MOCSSs) and optimal odd-length binary Z-complementary pairs (OB-ZCPs) which are not part of the training set. In the literature, both MOCSSs and OB-ZCPs have found wide applications in wireless communications and 2) HpGAN found new sequences which achieve a four-times increase of signal-to-interference ratio-benchmarked against the well-known Legendre sequences-of a mismatched filter (MMF) estimator in pulse compression radar systems. These sequences outperform those found by AlphaSeq.

A pair of sequences of lengthLis called a Z-complementary pair (ZCP) with zero correlation zone (ZCZ)Zif the sequences have zero aperiodic autocorrelation sums at eachof the non-zero time-shifts smaller thanZ. Such a pair is denoted byan(L,Z)-ZCP for short. In this letter, we propose a construction ofZCPs via properly cascading sequences from a Golay complemen-tary pair (GCP). The proposed construction leads to(3N,2N)-ZCPs,(5N,3N)-ZCPs,(7N,4N)-ZCPs,(9N,5N)-ZCPs,(11N,6N)-ZCPs,(12N,10N)-ZCPs,(13N,7N)-ZCPsand(14N,12N)- ZCPs, whereNis the length of the chosen GCP. Itturns out that the resultant ZCPs have low peak-to-mean envelopepower ratios.

In many applications, including integer-forcing linear multiple-input and multiple-output (MIMO) receiver design, one needs to solve a successive minima problem (SMP) on an n-dimensional lattice to get an optimal integer coefficient matrix A* ∈ Zn×n. In this paper, we first propose an efficient optimal SMP algorithm with an O(n2) memory complexity. The main idea behind the new algorithm is it first initializes with a suitable suboptimal solution, which is then updated via a novel algorithm with only O(n2) flops in each updating, until A* is obtained. Different from existing algorithms which find A* column by column through using a sphere decoding search strategy n times, the new algorithm uses a search strategy once only. We then rigorously prove the optimality of the proposed algorithm. Furthermore, we theoretically analyze its complexity. In particular, we not only show that the new algorithm is Ω(n) times faster than the most efficient existing algorithm with polynomial memory complexity, but also assert that it is even more efficient than the most efficient existing algorithm with exponential memory complexity. Finally, numerical simulations are presented to illustrate the optimality and efficiency of our novel SMP algorithm.

The integer-forcing (IF) linear multiple-input and multiple-output (MIMO) receiver is a recently proposed suboptimal receiver which nearly reaches the performance of the optimal maximum likelihood receiver for the entire signal-to-noise ratio (SNR) range and achieves the optimal diversity multiplexing tradeoff for the standard MIMO channel with no coding across transmit antennas in the high SNR regime. The optimal integer coefficient matrix A* ϵ ZNt×Ntfor IF maximizes the total achievable rate, where Nt is the column dimension of the channel matrix. To obtain A*, a successive minima problem (SMP) on an Nt-dimensional lattice that is suspected to be NP-hard needs to be solved. In this paper, an efficient exact algorithm for the SMP is proposed. For efficiency, our algorithm first uses the LLL reduction to reduce the SMP. Then, different from existing SMP algorithms which form the transformed A*column by column in Ntiterations, it first initializes with a suboptimal matrix which is the Nt× Ntidentity matrix with certain column permutations that guarantee this suboptimal matrix is a good initial solution of the reduced SMP. The suboptimal matrix is then updated, by utilizing the integer vectors obtained by employing an improved Schnorr-Euchner search algorithm to search the candidate integer vectors within a certain hyper-ellipsoid, via a novel and efficient algorithm until the transformed A*is obtained in only one iteration. Finally, the algorithm returns the matrix obtained by left multiplying the solution of the reduced SMP with the unimodular matrix that is generated by the LLL reduction. Simulation results show the optimality of our novel algorithm and indicates that the new one is much more efficient than existing optimal algorithms.