QR Decomposition Scheme Research Articles

Fingerprint image encryption using phase retrieval algorithm in gyrator wavelet transform domain using QR decomposition

In this paper, we propose a novel optical asymmetric fingerprint image encryption technique that uses QR decomposition in gyrator wavelet transform domain. A fingerprint image is bonded with a phase mask generated with Gerchberg–Saxton phase retrieval algorithm, which is gyrator wavelet transformed. This output is further applied to QR decomposition scheme and different keys are generated through it. The process is iterated to enhance the level of security. A Haar wavelet has been used in the study. Different phase images, gyrator transform orders and the parameters of the wavelet help achieve imperceptibility and robustness. The asymmetric keys make the system attack free like Brute force attack, known plain text attack, and special attack. Numerical simulations carried out on a MATLAB platform demonstrate the security, privacy, and validity of the proposed encryption scheme.

Capacity Bounds and High-SNR Capacity of MIMO Intensity-Modulation Optical Channels

The capacity of the intensity modulation direct detection multiple-input-multiple-output channel is studied. Therein, the nonnegativity constraint of the transmit signal limits the applicability of classical schemes, including precoding. Thus, new ways are required for deriving capacity bounds for this channel. To this end, capacity lower bounds are developed in this paper by deriving the achievable rates of two precoding-free schemes: channel inversion and orthogonal-upper triangular matrix product decomposition. The achievable rate of a dc-offset singular-value decomposition-based scheme is also derived as a benchmark. Then, capacity upper bounds are derived and compared against the lower bounds. As a result, the capacity at high signal-to-noise ratio (SNR) is characterized for the case where the number of transmit apertures is not larger than the number of receive apertures, and is shown to be achievable by the QR decomposition scheme. This is shown for a channel with average intensity or peak intensity constraints. Under both constraints, the high-SNR capacity is approximated within a small gap. Extensions to a channel with more transmit apertures than receive apertures are discussed, and capacity bounds for this case are derived.

Efficient Implementation of QR Decomposition for Gigabit MIMO-OFDM Systems

This paper presents a VLSI architecture of QR decomposition for 4×4 MIMO-OFDM systems. A real-value decomposed MIMO system model is handled and thus the channel matrix to be processed is extended to the size of 8×8. Instead of direct factorization, a QR decomposition scheme by cascading one complex-value and one real-value Givens rotation stages is proposed, which can save 44% hardware complexity. Besides, the requirement of skewed inputs in the conventional QR-decomposition systolic array is eliminated and 36% of delay elements are removed. The real-value Givens rotation stage is also constructed in a form of a stacked triangular systolic array to match with the throughput of the complex-value one. Hardware sharing is considered to enhance the utilization. The proposed design is implemented in 0.18-μm CMOS technology with 152K gates. From measurement, the maximum operating frequency is 100 MHz. It generates QR decomposition results every four clock cycles and accomplishes continuous projection every clock cycle to support MIMO detection up to 2.4 Gb/s. The measured power consumption is 318.6 mW and 219.6 mW for QR decomposition and projection, respectively, at the highest operating frequency. From the comparison, our proposed design achieves the highest throughput with high efficiency.

New fast QR decomposition least squares adaptive algorithms

This paper presents two new, closely related adaptive algorithms for LS system identification. The starting point for the derivation of the algorithms is the inverse Cholesky factor of the data correlation matrix, obtained via a QR decomposition (QRD). Both algorithms are of O(p) computational complexity, with p being the order of the system. The first algorithm is a fixed order QRD scheme with enhanced parallelism. The second is an order recursive lattice type algorithm based exclusively on orthogonal Givens rotations, with lower complexity compared to previously derived ones. Both algorithms are derived following a new approach, which exploits efficient the and order updates of a specific state vector quantity.

Algorithm 686: FORTRAN subroutines for updating the QR decomposition

Let the matrix A E R”““, m 2 n, have a QR decomposition A = QR, where Q E R”“” has orthonormal columns, and R E R”“” is upper triangular. Assume that Q and R are explicitly known. We present FORTRAN subroutines that update the QR decomposition in a numerically stable manner when A is modified by a matrix of rank one, or when a row or a column is inserted or deleted. These subroutines are modifications of the Algol procedures in Daniel et al. [5]. We also present a subroutine that permutes the columns of A and updates the QR decomposition so that the elements in the lower right corner of R will generally be small if the columns of A are nearly linearly dependent. This subroutine is an implementation of the rank-revealing QR decomposition scheme recently proposed by Chan [3].