in this paper, we consider a class of column-weight two quasi-cyclic low-density paritycheck codes in which the girth can be large enough, as an arbitrary multiple of 8. then we devote a convolutional form to these codes, such that their generator matrix can be obtained by elementary row and column operations on the parity-check matrix. finally, we show that the free distance of the convolution...

Third generation mobile radio systems will employ TD-CDMA in their TDD mode. To increase the capacity and performance of this system, the receiver will contain a joint detector. Joint detection is equivalent to solving a least squares problem, which represents a significant computational effort because of the amount of data that is involved. Therefore, algorithms and implementations must be dev...

This paper analyzes circulant Johnson-Lindenstrauss (JL) embeddings which, as an important class of structured random JL embeddings, are formed by randomizing the column signs of a circulant matrix generated by a random vector. With the help of recent decoupling techniques and matrix-valued Bernstein inequalities, we obtain a new bound k = O(ǫ log(n)) for Gaussian circulant JL embeddings. Moreo...

In many situations related to acoustics and data communications we are confronted with multiple signals received from a multipath mixture, e.g., the famous cocktail-party problem. A multipath mixture can be described by a mixing matrix, whose elements are the individual transfer functions between a source and a sensor. The mixing matrix is usually unknown, and so are sometimes also the source s...

The energy of a graph was introduced by Gutman in 1978 as the sum of the absolute values of the eigenvalues of its adjacency matrix. We study the energy of integral circulant graphs, also called gcd graphs. These are Cayley graphs on cyclic groups (i.e. there adjacency matrix is circulant) each of whose eigenvalues is an integer. Given an arbitrary prime power p, we determine all integral circu...

For a given nonnegative integer g , a matrix An of size n is called g-Toeplitz if its entries obey the rule An =  ar−gs n−1 r,s=0. Analogously, a matrix An again of size n is called g-circulant if An =  a(r−gs) mod n n−1 r,s=0. In a recent work we studied the asymptotic properties, in terms of spectral distribution, of both g-circulant and g-Toeplitz sequences in the case where {ak} can be ...

Simulation of multiple-input multiple-output (MIMO) fading channels, with crosscorrelated subchannels, is of paramount importance in performance evaluation of space-time techniques in multiantenna systems. This paper focuses on four methods to simulate several spatio-temporally crosscorrelated stationary complex Gaussian processes: the spectral representation method, the sampling theorem method...

The main result is the “black dot algorithm” and its fast version for the construction of a new circulant preconditioner for Toeplitz matrices. This new preconditioner C is sought directly as a solution to one of possible settings of the approximation problem A ≈ C + R, where A is a given matrix and R should be a “low-rank” matrix. This very problem is a key to the analysis of superlinear conve...

Circulant matrices can be effective preconditioners for linear systems of equations with a Toeplitz matrix. Several approaches to construct such preconditioners have been described in the literature. This paper focuses on the superoptimal circulant preconditioners proposed by Tyrtyshnikov, and investigates a generalization obtained by allowing generalized circulant matrices. Numerical examples ...

An important aspect of cryptography with matrices is that given N ×N matrix P over a field F find a class of matrices G over F such that the associated doubly circulant matrix Gc is singular in order that the equation AGB = P in circulant matrices A,B has infinitely many solutions. The aim of this note is to present such a class of matrices G. We also present a direct method of finding the inve...