In this letter, a new design of blockwise interleaved ideal low-rank parity-check (BII-LRPC) codes is proposed for a fast cryptographic application. We show that the proposed ideal LRPC codes can be ...used as a key encapsulation mechanism (KEM) for post-quantum cryptography (PQC). The simulation results show that the KEM constructed from the proposed BII-LRPC codes is faster by 30-70% than the ROLLO-I algorithm, an existing LRPC-based cryptosystem.
New constructions of binary and ternary locally repairable codes (LRCs) using cyclic codes and their concatenation are proposed. The proposed binary LRCs with d = 4 and some r and with d ≥ 5 and some ...n are shown to be optimal in terms of the upper bounds. In addition, the similar method of the binary case is applied to construct the ternary LRCs with good parameters.
In this letter, we propose a new design method for protograph-based partially doped generalized low-density parity-check (PD-GLDPC) codes over the binary erasure channel (BEC). By extending the ...block-error threshold condition proposed by A. K. Pradhan et al. for conventional GLDPC codes, we optimize medium to high-rate PD-GLDPC codes with degree-1 variable nodes and multi-types of component codes (MCC). It is shown that the optimized PD-GLDPC codes outperform the conventional LDPC and GLDPC codes at the frame error rate 10−4 over the BEC while having comparable decoding complexity.
Fully homomorphic encryption (FHE) is a prospective tool for privacy-preserving machine learning (PPML). Several PPML models have been proposed based on various FHE schemes and approaches. Although ...FHE schemes are suitable as tools for implementing PPML models, previous PPML models based on FHE, such as CryptoNet, SEALion, and CryptoDL, are limited to simple and nonstandard types of machine learning models; they have not proven to be efficient and accurate with more practical and advanced datasets. Previous PPML schemes replaced non-arithmetic activation functions with simple arithmetic functions instead of adopting approximation methods and did not use bootstrapping, which enables continuous homomorphic evaluations. Thus, they could neither use standard activation functions nor employ large numbers of layers. In this work, we first implement the standard ResNet-20 model with the RNS-CKKS FHE with bootstrapping and verify the implemented model with the CIFAR-10 dataset and plaintext model parameters. Instead of replacing the non-arithmetic functions with simple arithmetic functions, we use state-of-the-art approximation methods to evaluate these non-arithmetic functions, such as ReLU and Softmax, with sufficient precision. Further, for the first time, we use the bootstrapping technique of the RNS-CKKS scheme in the proposed model, which enables us to evaluate an arbitrary deep learning model on encrypted data. We numerically verify that the proposed model with the CIFAR-10 dataset shows 98.43% identical results to the original ResNet-20 model with non-encrypted data. The classification accuracy of the proposed model is 92.43%±2.65%, which is quite close to that of the original ResNet-20 CNN model (91.89%). It takes approximately 3 h for inference on a dual Intel Xeon Platinum 8280 CPU (112 cores) with 172 GB of memory. We believe that this opens the possibility of applying FHE to an advanced deep PPML model.
New constructions of linear binary locally repairable codes (LRCs) with disjoint repair groups, locality 3, and minimum Hamming distance larger than or equal to six are proposed by using existing ...binary LRCs. The proposed linear binary LRCs are optimal or near-optimal in terms of the bound of binary LRCs with disjoint repair groups.
In this paper, we propose an optimization method for protograph-based spatially coupled low-density parity-check (SC-LDPC) codes under window decoding (WD). Previous works on constructing SC-LDPC ...codes for WD typically focused on optimizing asymptotic performance metrics such as the WD threshold. However, in this paper, it is observed that the WD threshold is not an appropriate metric to sufficiently explain the finite-length behavior of SC-LDPC codes under WD. Thus, we propose a new performance metric, called the window mean parameter, based on a scaling analysis to capture the WD performance more accurately and formulate a code optimization algorithm that optimizes the proposed performance metric. Since the proposed metric depends on the window size, the optimization algorithm can provide a code family of SC-LDPC codes optimized for various target window sizes. Simulation results confirm that the improvement in the proposed metric leads to a finite-length performance improvement, resulting in one to two orders of the frame error rate gain over the conventional SC-LDPC codes for a wide range of window sizes. Furthermore, we investigate structural characteristics of the proposed codes to provide a supplementary explanation for the performance improvement, which also promotes a better understanding of SC-LDPC codes for WD.
In this paper, we propose new design algorithms of irregular spatially-coupled low-density parity-check (SC-LDPC) codes with non-uniform degree distributions using linear programming (LP). In ...general, irregular SC-LDPC codes with non-uniform degree distributions are difficult to design with low complexity because their density evolution equations are multi-dimensional. To overcome this problem, proposed design algorithms are based on three main ideas: a local design of degree distributions, pre-computation of the input/output message relationship, and selection of a proper objective function. These ideas make it possible to design degree distributions of irregular SC-LDPC codes by solving low-complexity LP problems over the binary erasure channel (BEC). It is shown that the proposed irregular SC-LDPC codes designed by the proposed algorithms are superior to regular SC-LDPC codes in terms of both asymptotic and finite-length performances over the BEC. We also confirm that the proposed irregular SC-LDPC code achieves better performance compared with an optimized irregular block LDPC code in the same blocklength, which implies that the proposed design algorithms also provide a new way to construct capacity-approaching block LDPC codes.
In this paper, linear index codes with multiple senders are studied, where every receiver receives encoded messages from all senders. A new fitting matrix for the multiple senders is proposed and it ...is proved that the minimum rank of the proposed fitting matrices is the optimal codelength of linear index codes for the multiple senders. In addition, a new type of a side information graph related with the optimal codelength is proposed and whether given side information is critical or not is studied. Furthermore, linear index codes for the cellular network scenario are studied, where each receiver can receive a subset of sub-codewords. Since some receivers cannot receive the entire codeword in the cellular network scenario, the encoding method based on the fitting matrix has to be modified. In the cellular network scenario, we propose another fitting matrix and prove that an optimal generator matrix can be found based on these fitting matrices. In addition, some properties on the optimal codelength of linear index codes for the cellular network case are studied.
In this letter, we propose new protograph low-density parity-check (LDPC) codes of high code rates using resolvable block designs (RBDs) for block fading (BF) channels. To analyze the performance of ...the proposed LDPC codes, we derive an upper bound on bit error rate (BER) using the novel method, called the gamma evolution. Finally, we numerically show that the frame error rate (FER) of the proposed LDPC codes has a slope approaching the channel outage probability.
In orthogonal frequency division multiplexing (OFDM) systems, high peak-to-average power ratio (PAPR) of OFDM signals is one of the most important problems. As a solution to the PAPR problem in OFDM ...systems, the partial transmit sequence (PTS) is a fairly suitable scheme due to its PAPR reduction performance and distortionless characteristic. However, high computational complexity is a serious problem in the PTS scheme. In this paper, in an effort to reduce its computational complexity, new PTS schemes are proposed using dominant time-domain samples of OFDM signals. Although the proposed PTS schemes use dominant time-domain samples in a manner similar to several existing low-complexity PTS schemes, we propose more efficient selection methods for dominant time-domain samples. The proposed PTS schemes lower the computational complexity compared to the conventional PTS schemes while achieving the optimal PAPR reduction performance.
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