Cong Ling

Complex Lattice Reduction Algorithm for Low-Complexity Full-Diversity MIMO Detection

Recently, lattice-reduction-aided detectors have been proposed for multiinput multioutput (MIMO) systems to achieve performance with full diversity like the maximum likelihood receiver. However, these lattice-reduction-aided detectors are based on the traditional Lenstra-Lenstra-Lovasz (LLL) reduction algorithm that was originally introduced for reducing real lattice bases, in spite of the fact that the channel matrices are inherently complex-valued. In this paper, we introduce the complex LLL algorithm for direct application to reducing the basis of a complex lattice which is naturally defined by a complex-valued channel matrix. We derive an upper bound on proximity factors, which not only show the full diversity of complex LLL reduction-aided detectors, but also characterize the performance gap relative to the lattice decoder. Our analysis reveals that the complex LLL algorithm can reduce the complexity by nearly 50% compared to the traditional LLL algorithm, and this is confirmed by simulation. Interestingly, our simulation results suggest that the complex LLL algorithm has practically the same bit-error-rate performance as the traditional LLL algorithm, in spite of its lower complexity.

Semantically Secure Lattice Codes for the Gaussian Wiretap Channel

We propose a new scheme of wiretap lattice coding that achieves semantic security and strong secrecy over the Gaussian wiretap channel. The key tool in our security proof is the flatness factor, which characterizes the convergence of the conditional output distributions corresponding to different messages and leads to an upper bound on the information leakage. We not only introduce the notion of secrecy-good lattices, but also propose the flatness factor as a design criterion of such lattices. Both the modulo-lattice Gaussian channel and genuine Gaussian channel are considered. In the latter case, we propose a novel secrecy coding scheme based on the discrete Gaussian distribution over a lattice, which achieves the secrecy capacity to within a half nat under mild conditions. No a priori distribution of the message is assumed, and no dither is used in our proposed schemes.

Effective LLL Reduction for Lattice Decoding

The use of Lenstra-Lenstra-Lovasz (LLL) lattice reduction significantly improves the performance of zero-forcing (ZF) and successive interference cancellation (SIC) decoders in multi-input multi-output (MIMO) communications. Capitalizing on the observation that the decision region of SIC is determined by the Gram-Schmidt vectors rather than the basis itself, we propose the use of effective LLL reduction in SIC decoding, where size reduction is only performed for pairs of consecutive basis vectors. We establish the theoretic upper bound O(n3 log n) on the average complexity of effective LLL reduction for the i.i.d. Gaussian model of MIMO fading channels, which is an order lower than previously thought. Moreover, an effectively LLL-reduced basis can easily be transformed into the standard LLL-reduced basis for the purpose of ZF decoding.

On the Proximity Factors of Lattice Reduction-Aided Decoding

Lattice reduction-aided decoding (LRAD) features reduced decoding complexity and near-optimum performance in multiinput multioutput communications. In this paper, a quantitative error-rate analysis of LRAD is presented. To this aim, the proximity factors are defined to measure the worst-case losses in decoding distances associated with the decision region relative to infinite lattice decoding (ILD), namely, closest point search in an infinite lattice. Upper bounds on the proximity factors are derived, which are functions of the dimension n of the lattice alone. The study is then extended to the dual-basis reduction. It is found that the bounds for dual basis reduction may be smaller. Reasonably good bounds are derived in many cases. Proximity factors not only imply the same diversity order in fading channels, but also relate the error probabilities of ILD and LRAD.

Feasibility Condition for Interference Alignment With Diversity

This paper studies the diversity benefit of different interference alignment solutions. While most research about interference alignment was aiming at deriving or realizing the maximum achievable multiplexing gain, the symbol error rate performance, which can be characterized by the diversity gain is of equal importance. Different interference alignment solutions are classified into two categories called diversity interference alignment and zero-forcing interference alignment. Although these two types of solutions are not distinguishable in terms of the multiplexing gain, this paper will show their difference lies in the fact that they have different diversity gains. In this paper, a K-user (M × N) interference channel is used, with each user sending 1 degree of freedom of information by using interference alignment precoding and receiving filters but without space-time codes. The feasibility conditions for diversity interference alignment to be achieved are analyzed and the diversity orders different solutions can provide are compared. The results imply that diversity interference alignment solutions offer both multiplexing and diversity gains simultaneously. It also tells us two important rules about the interference alignment precoding filters design: an optimal design has to take both desired and interference channel matrices into consideration and the separation of interference alignment precoding filters design and space-time codes design may not be optimal in general.

Achieving AWGN Channel Capacity With Lattice Gaussian Coding

We propose a new coding scheme using only one lattice that achieves the 1/2 log(1 + SNR) capacity of the additive white Gaussian noise (AWGN) channel with lattice decoding, which is provable for signal-to-noise ratio SNR > e at present. The scheme applies a discrete Gaussian distribution over an AWGN-good lattice, but otherwise does not require a shaping lattice or dither. Thus, it significantly simplifies the default lattice coding scheme of Erez and Zamir which involves a quantization good lattice as well as an AWGN-good lattice. Using the flatness factor, we show that the error probability of the proposed scheme under minimum mean-square error lattice decoding is almost the same as that of Erez and Zamir, for any rate up to the AWGN channel capacity. We introduce the notion of good constellations, which carry almost the same mutual information as that of continuous Gaussian inputs. We also address the implementation of Gaussian shaping for the proposed lattice Gaussian coding scheme.

Polar lattices: Where Arıkan meets Forney

In this paper, we propose the explicit construction of a new class of lattices based on polar codes, which are provably good for the additive white Gaussian noise (AWGN) channel. We follow the multilevel construction of Forney et al. (i.e., Construction D), where the code on each level is a capacity-achieving polar code for that level. The proposed polar lattices are efficiently decodable by using multistage decoding. Performance bounds are derived to measure the gap to the generalized capacity at given error probability. A design example is presented to demonstrate the performance of polar lattices.

Decoding by Sampling: A Randomized Lattice Algorithm for Bounded Distance Decoding

Despite its reduced complexity, lattice reduction-aided decoding exhibits a widening gap to maximum-likelihood (ML) performance as the dimension increases. To improve its performance, this paper presents randomized lattice decoding based on Kleins sampling technique, which is a randomized version of Babais nearest plane algorithm [i.e., successive interference cancelation (SIC)] and samples lattice points from a Gaussian-like distribution over the lattice. To find the closest lattice point, Kleins algorithm is used to sample some lattice points and the closest among those samples is chosen. Lattice reduction increases the probability of finding the closest lattice point, and only needs to be run once during preprocessing. Further, the sampling can operate very efficiently in parallel. The technical contribution of this paper is twofold: we analyze and optimize the decoding radius of sampling decoding resulting in better error performance than Kleins original algorithm, and propose a very efficient implementation of random rounding. Of particular interest is that a fixed gain in the decoding radius compared to Babais decoding can be achieved at polynomial complexity. The proposed decoder is useful for moderate dimensions where sphere decoding becomes computationally intensive, while lattice reduction-aided decoding starts to suffer considerable loss. Simulation results demonstrate near-ML performance is achieved by a moderate number of samples, even if the dimension is as high as 32.

Convolutional Compressed Sensing Using Deterministic Sequences

In this paper, a new class of orthogonal circulant matrices built from deterministic sequences is proposed for convolution-based compressed sensing (CS). In contrast to random convolution, the coefficients of the underlying filter are given by the discrete Fourier transform of a deterministic sequence with good autocorrelation. Both uniform recovery and non-uniform recovery of sparse signals are investigated, based on the coherence parameter of the proposed sensing matrices. Many examples of the sequences are investigated, particularly the Frank-Zadoff-Chu (FZC) sequence, the m-sequence and the Golay sequence. A salient feature of the proposed sensing matrices is that they can not only handle sparse signals in the time domain, but also those in the frequency and/or or discrete-cosine transform (DCT) domain.

Noncoherent sequence detection of differential space-time modulation

Approximate maximum-likelihood noncoherent sequence detection (NSD) for differential space-time modulation (DSTM) in time-selective fading channels is proposed. The starting point is the optimum multiple-symbol differential detection for DSTM that is characterized by exponential complexity. By truncating the memory of the incremental metric, a finite-state trellis is obtained so that a Viterbi algorithm can be implemented to perform sequence detection. Compared to existing linear predictive receivers, a distinguished feature of NSD is that it can accommodate nondiagonal constellations in continuous fading. Error analysis demonstrates that significant improvement in performance is achievable over linear prediction receivers. By incorporating the reduced-state sequence detection techniques, performance and complexity tradeoffs can be controlled by the branch memory and trellis size. Numerical results show that most of the performance gain can be achieved by using an L-state trellis, where L is the size of the DSTM constellation.