Many artificial intelligence technologies have been applied for extracting useful information from massive industrial big data. However, the privacy issues are usually overlooked in many existing methods. In this article, we propose an anonymous and privacy-preserving federated learning scheme for the mining of industrial big data. We explored the effect of the proportion of shared parameters on the accuracy through experiments, and found that sharing partial parameters can almost achieve the accuracy of sharing all the parameters. On this basis, our proposed federated learning scheme reduces the privacy leakage by sharing fewer parameters between the server and each participant. Specifically, we leverage differential privacy on shared parameters with Gaussian mechanism to provide strict privacy preservation; the effect of different ε and δ on accuracy is tested; and we keep track of δ-when it reaches a certain threshold, training shall be stopped. What's more, we employ a proxy server as the middle layer between the server and all the participants to achieve anonymity of participants; it is worth noting that this can also reduce the communication burden on the federated learning server. Finally, we provide the security analysis and performance evaluations by comparing with other schemes.

A new method to construct q-ary complementary sequence sets (CSSs) and complete complementary codes (CCCs) of size N is proposed by using desired para-unitary (PU) matrices. The concept of seed PU matrices is introduced and a systematic approach on how to compute the explicit forms of the functions in constructed CSSs and CCCs from the seed PU matrices is given. A general form of these functions only depends on a basis of the functions from \mathbb Z _N to \mathbb Z _q and representatives in the equivalent class of Butson-type Hadamard (BH) matrices. Especially, the realization of Golay pairs from our general form exactly coincides with the standard Golay pairs. The realization of ternary complementary sequences of size 3 is first reported here. For the realization of the quaternary complementary sequences of size 4, almost all the sequences derived here are never reported before. Generalized seed PU matrices and the recursive constructions of the desired PU matrices are also studied, and a large number of new constructions of CSSs and CCCs are given accordingly. From the perspective of this paper, all the known results of CSSs and CCCs with explicit GBF form in the literature (except non-standard Golay pairs) are constructed from the WHT matrices. This suggests that the proposed method with other BH matrices will yield a large number of new CSSs and CCCs with the significantly increasing number of the sequences of low peak-to-mean envelope power ratio.

There is a significant recent interest in collaboratively training a machine learning (ML) model without collecting data to a central server. Federated learning (FL) emerges as an efficient solution mitigating systemic privacy risks and communication costs. However, conventional FL inherited from parameter server designs relies too much on a central server, which may lead to privacy risks, communication bottlenecks, or a single point of failure. In this paper, we propose an asynchronous and hierarchical local gradient aggregation and global model update algorithm, FedDual, under three different security considerations for FL in large decentralized networks. Particularly, FedDual preserves privacy by introducing local differential privacy (LDP) and aggregates local gradients asynchronously and hierarchically via a pair-wise gossip algorithm, which is more competitive than previous gossip-based decentralized FL methods in terms of privacy preservation and communication efficiency, and offers more computational efficiency compared to existing blockchain-assisted decentralized FL methods. Further, we devise a noise cutting trick based on Private Set Intersection (PSI) to mitigate the prediction performance loss of the global model caused by the leveraged LDP. Rigorous analyses show that FedDual helps decentralized FL achieve the same convergence rate of $\mathcal {O}\left({\frac {1}{T}}\right) $ as centralized ML theoretically. Ingenious experiments on MNIST, CIFAR-10, and FEMNIST confirm that the model prediction performance gained from FedDual is close to centralized ML. More importantly, the proposed noise cutting trick helps FedDual to train better global models than LDP-based FL methods in terms of prediction performance and convergence rate.

Federated learning (FL), an attractive and promising distributed machine learning paradigm, has sparked extensive interest in exploiting tremendous data stored on ubiquitous mobile devices. However, conventional FL suffers severely from resource heterogeneity, as clients with weak computational and communication capabilities may be unable to complete local training using the same local training hyper-parameters. In this article, we propose Dap-FL, a deep deterministic policy gradient (DDPG)-assisted adaptive FL system, in which local learning rates and local training epochs are adaptively adjusted by all resource-heterogeneous clients through locally deployed DDPG-assisted adaptive hyper-parameter selection schemes. Particularly, the rationality of the proposed hyper-parameter selection scheme is confirmed through rigorous mathematical proof. Besides, due to the thoughtlessness of security consideration of adaptive FL systems in previous studies, we introduce the Paillier cryptosystem to aggregate local models in a secure and privacy-preserving manner. Rigorous analyses show that the proposed Dap-FL system could protect clients’ private local models against chosen-plaintext attacks and chosen-message attacks in a widely used honest-but-curious participants and active adversaries security model. More importantly, through ingenious and extensive experiments, the proposed Dap-FL achieves higher model prediction accuracy than two state-of-the-art RL-assisted FL methods, i.e., 6.03% higher than DDPG-based FL and 7.85% higher than DQN-based FL. In addition, experimental results also show that the proposed Dap-FL achieves higher global model prediction accuracy and faster convergence rates than conventional FL, and the comprehensiveness of the adjusted local training hyper-parameters is validated.

In this paper, we further investigate the constructions of complementary sequence sets (CSSs) and complete complementary codes (CCCs) by Butson-type Hadamard matrices. By taking the algebraic structure of Butson-type Hadamard (BH) matrices into consideration, we obtain the explicit representation of the δ-linear terms and δ-quadratic terms, which are ingredients to construct CSSs and CCCs. In particular, we derive the δ-quadratic terms determined by DFT matrices and BH matrices constructed from 2-level autocorrelation sequences, which yields two type of new contructions. We show that inequivalent BH matrices produce different CSSs and CCCs, which proves that our constructed CSSs and CCCs are new. As a consequence of the first type of the constructions, not only a large number of p -ary CSSs and CCCs of size p ( p prime) have been proposed, which were never reported in the literature, but also a theory linking these CSSs of p -ary sequences and the generalized Reed-Muller codes proposed by Kasami et al . is shown. These codes enjoy good error-correcting capability, tightly controlled PMEPR, and significantly extend the range of coding options for applications of OFDM using pⁿ subcarriers. As a consequence of the second type of the constructions, we reveal an extremely fascinating hidden connection between the sequences in aperiodic CSSs and CCCs and the sequences with ideal period 2-level autocorrelation, through their trace representations and permutation polynomials over finite fields.

In this paper, some questions on the distribution of the peak-to-mean envelope power ratio (PMEPR) of standard binary Golay sequences are solved. For n odd, we prove that the PMEPR of each standard binary Golay sequence of length 2ⁿ is exactly 2, and determine the location(s), where peaks occur for each sequence. For n even, we prove that the envelope power of such sequences can never reach 2ⁿ⁺¹ at time points t ∈ {(v/2^u)|0 ≤ v ≤ 2^u, v,u ∈ N}. We further identify eight sequences of length 2⁴ and eight sequences of length 2⁶ that have PMEPR exactly 2, and raise the question whether, asymptotically, it is possible for standard binary Golay sequences to have PMEPR less than 2 - ϵ, where, ϵ > 0.