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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.

Ever since deoxyribonucleic acid (DNA) was considered as a next-generation data-storage medium, lots of research efforts have been made to correct errors occurred during the synthesis, storage, and sequencing processes using error correcting codes (ECCs). Previous works on recovering the data from the sequenced DNA pool with errors have utilized hard decoding algorithms based on a majority decision rule. To improve the correction capability of ECCs and robustness of the DNA storage system, we propose a new iterative soft decoding algorithm, where soft information is obtained from FASTQ files and channel statistics. In particular, we propose a new formula for log-likelihood ratio (LLR) calculation using quality scores (Q-scores) and a redecoding method which may be suitable for the error correction and detection in the DNA sequencing area. Based on the widely adopted encoding scheme of the fountain code structure proposed by Erlich et al., we use three different sets of sequenced data to show consistency for the performance evaluation. The proposed soft decoding algorithm gives 2.3% $\sim $ 7.0% improvement of the reading number reduction compared to the state-of-the-art decoding method and it is shown that it can deal with erroneous sequenced oligo reads with insertion and deletion errors.

In this paper, we propose a new coding scheme for DNA storage using low-density parity-check (LDPC) codes and interleaving techniques. While conventional coding schemes generally employ error correcting codes in both inter and intra-oligo directions, we show that inter-oligo LDPC codes, optimized by differential evolution, are sufficient in ensuring the reliability of DNA storage due to the powerful soft decoding of LDPC codes. In addition, we apply interleaving techniques for handling non-uniform error characteristics of DNA storage to enhance the decoding performance. Consequently, the proposed coding scheme reduces the required number of oligo reads for perfect recovery by 26.25% ~ 38.5% compared to existing state-of-the-art coding schemes. Moreover, we develop an analytical DNA channel model in terms of non-uniform binary symmetric channels. This mathematical model allows us to demonstrate the superiority of the proposed coding scheme while isolating the experimental variation, as well as confirm the independent effects of LDPC codes and interleaving techniques.

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.

In this letter, we investigate the min-sum (MS) and neural MS (NMS) decoding algorithms for generalized low-density parity-check (GLDPC) codes. Although the MS decoder is much simpler than the a posteriori probability (APP) decoder commonly used for GLDPC codes, the MS decoder has not been considered mainly due to its inferior decoding performance. However, we show that the performance can be improved by i) employing the NMS decoding algorithm and ii) optimizing the component parity check matrix (PCM). For the four representative short GLDPC codes in the literature, experimental results show that the NMS decoding performance with the optimized component PCM significantly outperforms the MS decoding performance and even outperforms the APP decoding performance for some cases.

The comparison operation for two numbers is one of the most frequently used operations in several applications, including deep learning. As such, lots of research has been conducted with the goal of efficiently evaluating the comparison operation in homomorphic encryption schemes. Recently, Cheon et al. (Asiacrypt 2020) proposed new comparison methods that approximated the sign function on homomorphically encrypted data using composite polynomials and proved that these methods had optimal asymptotic complexity. In this article, we propose a practically optimal method that approximates the sign function using compositions of minimax approximation polynomials. We prove that this approximation method is optimal with respect to depth consumption and the number of non-scalar multiplications. In addition, we propose a polynomial-time algorithm that determines the optimal composition of minimax approximation polynomials for the proposed homomorphic comparison operation using dynamic programming. The numerical analysis demonstrates that when minimizing runtime, the proposed comparison operation reduces the runtime by approximately 45 percent on average when compared to the previous algorithm. Likewise, when minimizing depth consumption, the proposed algorithm reduces the runtime by approximately 41 percent on average. In addition, when high precision in the comparison operation is required, the previous algorithm does not achieve 128-bit security, while the proposed algorithm does due to its small depth consumption.

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 this paper, we introduce new codes for the private information retrieval (PIR). The conventional Tian-Sun-Chen (TSC) scheme achieves PIR capacity under the perfect privacy condition with the minimum message length. Based on the TSC scheme, weakly PIR (WPIR) studies have been developed to benefit download costs by relaxing privacy. We show that the proposed scheme has lower download cost than the TSC scheme in the weak privacy setting. While our scheme is not capacity-achieving under perfect privacy, it has smaller message sizes compared with the TSC scheme.

In this paper, we investigate degrees of freedom (DoF) of the M × N single input single output (SISO) X channel with alternating channel state information at the transmitter (CSIT). It is known that sum DoF of 2-user SISO X channel with synergistic alternating CSIT is the same as the sum DoF of 2-user (M = N = 2) SISO X channel with perfect CSIT [8]. As an extension of the 2-user case, achievable schemes of the M × N SISO X channel with synergistic alternating CSIT are proposed. It is shown that the proposed M × N X channel schemes with synergistic alternating CSIT achieve the sum DoF 2M/(M + 1), which is better than the weighted sum DoF of the conventional schemes for M <; N. The DoF of the proposed scheme with M = N = K is strictly better than the best known DoF for the K-user X channel with delayed CSIT.

Write-once memory (WOM) codes aim to extend the lifetime and improve the writing efficiency of storage devices such as NAND flash memory by reducing the number of erase operations. In this paper, a new rewriting scheme for NAND flash memory is proposed, which supports two writes (or only one rewrite) and allows the second write incrementally done multiple times by using raptor-like codes as rate-compatible (RC) low-density generator matrix (LDGM) codes. The proposed scheme improves writing efficiency of the NAND flash memory when combined with a proper page selection method. It is verified via numerical analysis that the proposed WOM codes outperform the conventional WOM codes in terms of writing efficiency.

In this paper, a new decoding scheme is proposed to improve the error correcting performance of low-density parity-check (LDPC) codes in high signal-to-noise ratio (SNR) region by using post-processing. It behaves as follows: First, a conventional LDPC decoding is applied to received LDPC codewords one by one. Then, we count the number of word errors in a predetermined number of decoded codewords. If there is no word error, nothing needs to be done and we can move to the next group of codewords with no delay. Otherwise, we perform a proper post-processing which pro-ducesa new soft-valued codeword (this will befully explained in the main body of this paper) and then apply the conventional LDPC decoding to it again to recover the unsuccessfully decoded codewords. For the proposed decoding scheme, we adopt a simple product code structure which contains LDPC codes and simple algebraic codes as its horizontal and vertical codes, respectively. The decoding capability of the proposed decoding scheme is defined and analyzed using the parity-check matrices of vertical codes and, especially, the combined-decodability is derived for the case of single parity-check (SPC) codes and Hamming codes used as vertical codes. It is also shown that the proposed decoding scheme achieves much better error correcting capability in high SNR region with little additional decoding complexity, compared with the conventional LDPC decoding scheme.

In this paper, a cooperative relaying protocol called soft-decision-and-forward (SDF) with multiple antennas in each node is introduced. SDF protocol exploits the soft decision source symbol values from the received signal at the relay node. For orthogonal transmission (OT), orthogonal codes including Alamouti code are used and for non-orthogonal transmission (NT), distributed space-time codes are designed by using a quasi-orthogonal space-time block code. The optimal maximum likelihood (ML) decoders for the proposed protocol with low de coding complexity are proposed. For OT, the ML decoders are derived as symbolwise decoders while for NT, the ML decoders are derived as pairwise decoders. It can be seen through simulations that SDF protocol outperforms AF protocol for both OT and NT.

In this paper, a new distributed space-time coded (DS-TCed) non-orthogonal decode-and-forward (NDF) protocol with source antenna switching (SAS) is proposed, where two antennas associated with each radio frequency chain can be alternatively used in the first and second phases. Several DSTC schemes for the NDF with SAS (NDF-SAS) protocol are proposed and their average pairwise error probability for the error-free source-relay (SR) channel is also derived. The simulation results show that the NDF-SAS protocol achieves larger diversity order than the NDF protocol under the error-free and erroneous SR channels.

In this paper, using binary (N, M, L, є) low correlation zone (LCZ) sequence sets, we construct new quaternary LCZ sequence sets with parameters (2N, 2M, L, 2є). Binary LCZ sequences for the construction should have period N ≡ 3 mod 4, L|N, and the balance property. The proposed method corresponds to a quaternary extension of the extended construction of binary LCZ sequence sets proposed by Kim, Jang, No, and Chung [1].

Orthogonal frequency division multiplexing (OFDM) has been adopted as a standard for various high data rate wireless communication systems due to the spectral bandwidth efficiency, robustness to frequency selective fading channels, etc. However, implementation of the OFDM system entails several difficulties. One of the major drawbacks is the high peak-to-average power ratio (PAPR), which results in intercarrier interference, high out-of-band radiation, and bit error rate performance degradation, mainly due to the nonlinearity of the high power amplifier. This paper reviews the conventional PAPR reduction schemes and their modifications for achieving the low computational complexity required for practical implementation in wireless communication systems.

In this paper, the performance of generic orthogonal space-time block codes (OSTBCs) introduced by Alamouti [2], Tarokh [3], and Su and Xia [11] is analyzed. We first define one-dimensional component symbol error function (ODSEF) from the exact expression of the pairwise error probability of an OSTBC. Utilizing the ODSEF and the bit error probability (BEP) expression for quadrature amplitude modulation (QAM) introduced by Cho and Yoon [9], the exact closed-form expressions for the BEP of linear OSTBCs with QAM in quasi-static Rayleigh fading channel are derived. We also derive the exact closed-form of the BEP for some OSTBCs which have at least one message symbol transmitted with unequal power via all transmit antennas.

In this paper, for a prime power q, new cyclic difference sets with Singer para- meters ((qn−1/q−1), (qn−1−1/q−1), (qn−2−1/q−1)) are constructed by using q-ary sequences (d-homogeneous functions) of period qn−1 and the generalization of GMW difference sets is proposed by combining the generation methods of d-form sequences and extended sequences. When qis a power of 3, new cyclic difference sets with Singer parameters ((qn−1/q−1), (qn−1−1/q−1), (qn−2−1/q−1)) are constructed from the ternary sequences of period qn−1 with ideal autocorrelation introduced by Helleseth, Kumar, and Martinsen.

In this paper, the p-ranks and characteristic polynomials of cyclic difference sets are derived by expanding the trace expressions of their characteristic sequences. Using this method, it is shown that the 3-ranks and characteristic polynomials of the Helleseth–Kumar–Martinsen (HKM) difference set and the Lin difference set can be easily obtained. Also, the p-rank of a Singer difference set is reviewed and the characteristic polynomial is calculated using our approach.