This paper proposes a novel approach to low complexity soft input decoding for lattice reduction-aided MIMO receivers. The proposed approach feeds a soft input decoder with soft signals made from hard decision signals generated by using a lattice reduction-aided linear detector. The soft signal is a weighted-sum of some candidate vectors that are near by the hard decision signal coming out from the lattice reduction-aided linear detector. This paper proposes a technique to adjust the weight adapt to the channel for the higher transmission performance. Furthermore, we propose to introduce a coefficient that is used for the weights in order to enhance the transmission performance. The transmission performance is evaluated in a 4×4 MIMO channel. When a linear MMSE filter or a serial interference canceller is used as the linear detector, the proposed technique achieves about 1.0dB better transmission performance at the BER of 10-5 than the decoder fed with the hard decision signals. In addition, the low computational complexity of the proposed technique is quantitatively evaluated.

This paper proposes a novel flexible receiver with virtual channels for overloaded multiple-input multiple-output (MIMO) channels. The receiver applies extended rotation matrices proposed in the paper for the flexibility. In addition, adaptive selection of the extended rotation matrices is proposed for further performance improvement. We propose two techniques to reduce the computational complexity of the adaptive selection. As a result, the proposed receiver gives us an option to reduce the complexity with a slight decrease in the transmission performance by changing receiver configuration parameters. A computer simulation reveals that the adaptive selection attains a gain of about 3dB at the BER of 10-3.

Non-linear precoding (NLP) scheme for downlink multi-user multiple-input multiple-output (DL-MU-MIMO) transmission has received much attention as a promising technology to achieve high capacity within the limited bandwidths available to radio access systems. In order to minimize the required transmission power for DL-MU-MIMO and achieve high spectrum efficiency, Vector Perturbation (VP) was proposed as an optimal NLP scheme. Unfortunately, the original VP suffers from significant computation complexity in detecting the optimal perturbation vector from an infinite number of the candidates. To reduce the complexity with near transmission performance of VP, several recent studies investigated various efficient NLP schemes based on the concept of Tomlinson-Harashima precoding (THP) that applies successive pre-cancellation of inter-user interference (IUI) and offsets the transmission vector based on a modulo operation. In order to attain transmission performance improvement over the original THP, a previous work proposed Minimum Mean Square Error based THP (MMSE-THP) employing IUI successive pre-cancellation based on MMSE criteria. On the other hand, to improve the transmission performance of MMSE-THP, other previous works proposed Ordered MMSE-THP and Lattice-Reduction-Aided MMSE-THP (LRA MMSE-THP). This paper investigates the further transmission performance improvement of Ordered MMSE-THP and LRA MMSE-THP. This paper starts by proposing an extension of MMSE-THP employing a perturbation vector search (PVS), called PVS MMSE-THP as a novel NLP scheme, where the modulo operation is substituted by PVS and a subtraction operation from the transmit signal vector. Then, it introduces an efficient search algorithm of appropriate perturbation vector based on a depth-first branch-and-bound search for PVS MMSE-THP. Next, it also evaluates the transmission performance of PVS MMSE-THP with the appropriate perturbation vector detected by the efficient search algorithm. Computer simulations quantitatively clarify that PVS MMSE-THP achieves better transmission performance than the conventional NLP schemes. Moreover, it also clarifies that PVS MMSE-THP increases the effect of required transmission power reduction with the number of transmit antennas compared to the conventional NLP schemes.

In this paper, an improved lattice reduction (LR)-aided soft-output multiple-input multiple-output (MIMO) detector is proposed. Conventional LR-aided soft-output MIMO detectors involve the empty set problem (ESP), in which an entry with a particular bit in the candidate list might not exist. To overcome the performance degradation resulting from this ESP, a post-processing algorithm that modifies the candidate list is proposed. The proposed algorithm efficiently resolves the ESP by utilizing the near-orthogonality of the lattice-reduced system model so that the bit error rate (BER) performance is enhanced. In addition, as the complexity of the candidate list generation is reduced with the aid of the post-processing algorithm, the overall complexity is also reduced. Simulation results and the complexity comparisons demonstrate that our proposed method lowers the required Eb/No by 4-5 dB at the BER of 10-5 and the complexity by 13%-55%, compared to the conventional method.

The breadth-first tree searching (BFTS) detection algorithm such as the QR decomposition with M algorithm (QRD-M) which is the generally K-best detection algorithm is suboptimal, but has high complexity. In this letter, the K-best BFTS detection algorithm having reduced complexity is proposed. The proposed detection algorithm calculates the channel condition to decide the thresholds for regulating complexity and performance and from the simulation results, it has good error performance with very low complexity.

In this paper, we propose an overloaded multiple-input multiple-output (MIMO) signal detection scheme with slab decoding and lattice reduction (LR). The proposed scheme firstly splits the transmitted signal vector into two parts, the post-voting vector composed of the same number of signal elements as that of receive antennas, and the pre-voting vector composed of the remaining elements. Secondly, it reduces the candidates of the pre-voting vector using slab decoding and determines the post-voting vectors for each pre-voting vector candidate by LR-aided minimum mean square error (MMSE)-successive interference cancellation (SIC) detection. From the performance analysis of the proposed scheme, we derive an upper bound of the error probability and show that it can achieve the full diversity order. Simulation results show that the proposed scheme can achieve almost the same performance as the optimal ML detection while reducing the required computational complexity.

In this letter, we propose a lattice reduction (LR) aided joint precoding design for MIMO-relay broadcast communication with the average bit error rate (BER) criterion. We jointly design the signal process flow at both the base station (BS), and the relay station (RS), using the reduced basis of two-stage channel matrices. We further modify the basic precoding design with a novel shift method and a modulo method to improve the power efficiency at the BS and the RS respectively. In addition, the MMSE-SIC algorithm is employed to improve the performance of precoding. Simulations show that, the proposed schemes achieve higher diversity order than the traditional precoding without LR, and the modified schemes significantly outperform the basic design, proving the effectiveness of the proposed methods.

In this letter, an enhanced detection scheme using threshold and lattice-reduction algorithm is proposed. The first step of the proposed detection scheme finds another basis channel matrix H' which has good properties from the channel matrix H by using lattice-reduction algorithm. And QRD-M detection scheme using threshold algorithm is executed in the next step. Simulation results show that the proposed method has better performance than the conventional QRD-M detection scheme at high SNR. Also, it reduces candidate symbols because of the threshold algorithm.

When Zero-Forcing (ZF) is adopted as a detector, decreasing the condition number of the channel matrix increases the BER performance. In this paper, we propose a new detection algorithm which reduces the condition number of channel matrix down to nearly 2 on average. Since the least singular value of the channel matrix is a major factor determining the condition number, we, first, project the received signal into a space spanned by singular vectors that are orthogonal to the one corresponding to the least singular value. Then, LR decomposition is performed to reduce further the condition number of the projected channel matrix. Computer simulations show that the performance of the proposed algorithm is comparable to that of the ML detector for both correlated and uncorrelated channels. And also the proposed algorithm provides an at least 2dB improvement compared to the conventional LR-based Ordered Successive Interference Cancellation (LR-OSIC) detector with a Bit Error Rate (BER) of 10-3 and a comparable computation load.

We consider some attacks on multi-prime RSA (MPRSA) with a modulus N = p1p2 . . . pr (r ≥ 3). It is believed that the small private exponent attack on the MPRSA is less effective than that on RSA (see Hinek et al.'s work at SAC 2003), which means smaller private exponents can be used in the MPRSA to speed up the decryption process. Our work shows that even if a private exponent is significantly beyond Hinek et al.'s bound, it still may be insecure if the prime difference Δ (Δ = pr - p1 = Nγ, supposing p1 < p2 < … < pr) is small, i.e. 0 < γ < 1/r. Specifically, by taking full advantage of prime properties, our small private exponent attack reveals that the MPRSA is insecure when $delta<1-sqrt{1+2gamma-3/r}$ (if $gammagerac{3}{2r}-rac{1+delta}{4}$) or $deltale rac{3}{r}-rac{1}{4}-2gamma$ (if $gamma < rac{3}{2r}-rac{1+delta}{4}$), where δ is the exponential of the private exponent d with base N, i.e., d = Nδ. In addition, we present a Fermat-like factoring attack which factors N efficiently when Δ < N1/r2. These proposed attacks surpass previous works (e.g. Bahig et al.'s at ICICS 2012), and are proved effective in practice.

Although the QR decomposition M algorithm (QRD-M) detection reduces the complexity and achieves near-optimal detection performance, its complexity is still very high. In the proposed scheme, the received symbols through bad channel conditions are arranged in reverse order due to the performance of a system depending on the detection capability of the first layer. Simulation results show that the proposed scheme provides almost the same performance as the QRD-M. Moreover, the complexity is about 33.6% of the QRD-M for a bit error rate (BER) with 4×4 multi input multi output (MIMO) system.

Given an integer n-dimensional lattice basis, the random sampling reduction was proven to find a short vector in arithmetic steps with an integer k, which is freely chosen by users. This paper introduces new random sampling reduction using precomputation techniques. The computation cost is almost independent of the lattice dimension number. The new method is therefore especially advantageous to find a short lattice vector in higher dimensions. The arithmetic operation number of our new method is about 20% of the random sampling reduction with 200 dimensions, and with 1000 dimensions it is less than 1% ( 1/130) of that of the random sampling reduction with representative parameter settings under reasonable assumptions.

This paper proposes a lattice-reduction-aided MIMO-OFDM receiver with virtual channels; the receiver enables an increase in the downlink transmission speed for a user where the number of transmit antennas is considerably higher than that of the receive antennas. However, the receiver has a higher computational complexity than conventional lattice-reduction-aided MIMO receivers. Accordingly, we also propose novel techniques to reduce the computational complexity for the lattice-reduction-aided MIMO receivers with virtual channels. The proposed MIMO receiver achieves superior performance in 102 MIMO-OFDM systems. Furthermore, the proposed techniques are shown to reduce the computational complexity to approximately 40% of the original configuration in the 102 MIMO-OFDM systems.

The subset sum problem, which is often called as the knapsack problem, is known as an NP-hard problem, and there are several cryptosystems based on the problem. Assuming an oracle for shortest vector problem of lattice, the low-density attack algorithm by Lagarias and Odlyzko and its variants solve the subset sum problem efficiently, when the “density” of the given problem is smaller than some threshold. When we define the density in the context of knapsack-type cryptosystems, weights are usually assumed to be chosen uniformly at random from the same interval. In this paper, we focus on general subset sum problems, where this assumption may not hold. We assume that weights are chosen from different intervals, and make analysis of the effect on the success probability of above algorithms both theoretically and experimentally. Possible application of our result in the context of knapsack cryptosystems is the security analysis when we reduce the data size of public keys.

Multi-user multi-input multi-output (MIMO) system has been attracting much attention due to its high spectrum efficiency. Non-linear MIMO signal detection methods with less computational complexity have been widely studied for single-user MIMO systems. In this paper, we investigate how a lattice reduction (LR)-aided detection and a maximum likelihood detection (MLD) employing the QR decomposition and M-algorithm (QRM-MLD), which are commonly known as non-linear MIMO signal detection methods, improve the uplink capacity of a multi-user MIMO-OFDM cellular system, compared to simple linear detection methods such as zero-forcing detection (ZFD) and minimum mean square error detection (MMSED). We show that both LR-aided linear detection and QRM-MLD can achieve higher uplink capacity than simple linear detection at the cost of moderate increase of computational complexity. Furthermore, QRM-MLD can obtain the same uplink capacity as MLD.

This investigation proposes two methods for embedding backdoors in the RSA modulus N=pq rather than in the public exponent e. This strategy not only permits manufacturers to embed backdoors in an RSA system, but also allows users to choose any desired public exponent, such as e=216+1, to ensure efficient encryption. This work utilizes lattice attack and exhaustive attack to embed backdoors in two proposed methods, called RSASBLT and RSASBES, respectively. Both approaches involve straightforward steps, making their running time roughly the same as that of normal RSA key-generation time, implying that no one can detect the backdoor by observing time imparity.

A reduced complexity quantization error correction method for lattice reduction aided (LRA) vector precoding is proposed. For LRA vector precoding,Babai's approximation procedure can generate quantization errors leading to performance loss. Instead of making a list to correct all possible errors as is done in the existing scheme, we propose a novel method in which only a subset of all possible errors are corrected. The size of the subset is determined by the probability distribution of the number of actual errors. Thus, the computation complexity of our correction procedure is reduced with little performance loss compared with the existing correction scheme.

In this letter, a pre-processed lattice reduction (PLR) scheme is developed for the lattice reduction aided (LRA) detection of multiple input multiple-output (MIMO) systems in spatially correlated channel. The PLR computes the LLL-reduced matrix of the equivalent matrix, which is the product of the present channel matrix and unimodular transformation matrix for LR of spatial correlation matrix, rather than the present channel matrix itself. In conjunction with PLR followed by recursive lattice reduction (RLR) scheme [7], pre-processed RLR (PRLR) is shown to efficiently carry out the LR of the channel matrix, especially for the burst packet message in spatially and temporally correlated channel while matching the performance of conventional LRA detection.

In this letter, we propose two computationally efficient precoding algorithms that achieve near-ML performance for multiuser MIMO downlink. The proposed algorithms perform tree expansion after lattice reduction. The first full expansion is tried by selecting the first level node with a minimum metric, constituting a reference metric. To find an optimal sequence, they iteratively visit each node and terminate the expansion by comparing node metrics with the calculated reference metric. By doing this, they significantly reduce the number of undesirable node visit. Monte-Carlo simulations show that both proposed algorithms yield near-ML performance with considerable reduction in complexity compared with that of the conventional schemes such as sphere encoding.

In this letter, a lattice-reduction-aided (LRA) minimum mean square error (MMSE) Tomlinson-Harashima precoding (THP) is proposed for multiple input multiple output (MIMO) systems. The extended channel is exploited to develop the LRA MMSE-THP based on the lattice reduction method. Simulation results show that the proposed scheme significantly outperforms the conventional MMSE THP and the LRA zero-forcing (ZF) THP and achieves full diversity order.