Abstract This paper addresses the generation of binary 2-separating codes and the study of the code rates that can be achieved in practice. In the case of binary 2-separating codes, there exist lower and upper theoretical bounds in the rates that can be achieved. The generation of 2-separating codes has been studied from a theoretical point of view, but, as far as we know, it has not been tackled from a practical point of view. In this paper, we consider and analyze two different generation algorithms. Both algorithms were implemented in CUDA and executed in GPUs, for the sake of efficiency. The first algorithm is inspired by the Moser–Tardos algorithm, which is based on the Local Lovász Lemma. This algorithm has a strong theoretical appeal; codes obtained through this first algorithm can be shown to match the best known lower bound. To generate codes with rates as large as possible, a second algorithm has been implemented. The rates achieved are larger than those achieved with the first algorithm, but they still are very far from the theoretical upper bound. The results obtained suggest that the theoretical upper bound can probably be improved.

This paper addresses the assessment of the stability of distributed active noise control (ANC) systems, which are designed to cancel acoustic noise at given points in space. These systems distribute the control task across several simple acoustic nodes that generate the control signals by filtering a noise reference signal. The coefficients of each node filter are iteratively calculated by the filtered-X LMS algorithm. The nodes remain stable when the adaptive filters computed in each node converge to finite values. However, the acoustic coupling among nodes can cause instability (i.e., divergence). Collaboration among nodes is required to avoid this phenomenon. It is shown that the properties of the system are summarized in a system matrix and that the system remains stable when the real parts of all of the eigenvalues of this system matrix are positive. However, computation of all of the eigenvalues is computationally expensive. In this paper, we propose a fast method for checking the positiveness of the real parts of the system matrix eigenvalues. It is shown that the proposed method is faster than the direct calculation of eigenvalues and it assesses the stability/instability of the ANC systems without any false stability outcomes and more accurately than existing alternatives.

The choice of a suitable convergence step that allows the fast convergence of the filtered-x LMS algorithm in practical scenarios is usually carried out by trial and error, since the theoretical developments provide only indicative values. The particularity of the filtered-x structure, which adds a delay between the output of the adaptive filter and the error signal and colors the reference signal, increases the inaccuracy of the theoretical models. Furthermore, the use of band-limited reference signals is beyond the scope of most theoretical studies, which focus on the cases of full-band reference signals, making it difficult to extrapolate these models to band-limited signals. In this paper, we propose a low-cost and meaningful method for selecting the convergence step that is well tuned in most practical cases. It can be used regardless of the type of the reference signal, the system delays, and the nature of the filter required in the filtered-x structure. Numerical simulations are performed to validate the effectiveness of the proposed approach.

Abstract Border tracking in binary images is an important operation in many computer vision applications. The problem consists in finding borders in a 2D binary image (where all of the pixels are either 0 or 1). There are several algorithms available for this problem, but most of them are sequential. In a former paper, a parallel border tracking algorithm was proposed. This algorithm was designed to run in Graphics Processing units, and it was based on the sequential algorithm known as the Suzuki algorithm. In this paper, we adapt the previously proposed GPU algorithm so that it can be executed in multicore computers. The resulting algorithm is evaluated against its GPU counterpart. The results show that the performance of the GPU algorithm worsens (or even fails) for very large images or images with many borders. On the other hand, the proposed multicore algorithm can efficiently cope with large images.

Generalized Spatial Modulation (GSM) is a recent Multiple-Input Multiple-Output (MIMO) scheme, which achieves high spectral and energy efficiencies. Specifically, soft-output detectors have a key role in achieving the highest coding gain when an error-correcting code (ECC) is used. Nowadays, soft-output Maximum Likelihood (ML) detection in MIMO-GSM systems leads to a computational complexity that is unfeasible for real applications; however, it is important to develop low-complexity decoding algorithms that provide a reasonable computational simulation time in order to make a performance benchmark available in MIMO-GSM systems. This paper presents three algorithms that achieve ML performance. In the first algorithm, different strategies are implemented, such as a preprocessing sorting step in order to avoid an exhaustive search. In addition, clipping of the extrinsic log-likelihood ratios (LLRs) can be incorporating to this algorithm to give a lower cost version. The other two proposed algorithms can only be used with clipping and the results show a significant saving in computational cost. Furthermore clipping allows a wide-trade-off between performance and complexity by only adjusting the clipping parameter.

Abstract Border tracking in binary images is an important kernel for many applications. There are very efficient sequential algorithms, most notably, the algorithm proposed by Suzuki et al., which has been implemented for CPUs in well-known libraries. However, under some circumstances, it would be advantageous to perform the border tracking in GPUs as efficiently as possible. In this paper, we propose a parallel version of the Suzuki algorithm that is designed to be executed in GPUs and implemented in CUDA. The proposed algorithm is based on splitting the image into small rectangles. Then, a thread is launched for each rectangle, which tracks the borders in its associated rectangle. The final step is to perform the connection of the borders belonging to several rectangles. The parallel algorithm has been compared with a state-of-the-art sequential CPU version, using two different CPUs and two different GPUs for the evaluation. The computing times obtained show that in these experiments with the GPUs and CPUs that we had available, the proposed parallel algorithm running in the fastest GPU is more than 10 times faster than the sequential CPU routine running in the fastest CPU.

Abstract Generalized Spatial Modulation is a recently developed technique that is designed to enhance the efficiency of transmissions in MIMO Systems. However, the procedure for correctly retrieving the sent signal at the receiving end is quite demanding. Specifically, the computation of the maximum likelihood solution is computationally very expensive. In this paper, we propose a parallel method for the computation of the maximum likelihood solution using the parallel computing library OpenMP. The proposed parallel algorithm computes the maximum likelihood solution faster than the sequential version, and substantially reduces the worst-case computing times.

Generalized Spatial Modulation (GSM) is a trans-mission technique used in wireless communications in which only part of the transmitter antennas are activated during each time signaling period. A low complexity Sphere Decoding (SD) algorithm to achieve maximum likelihood (ML) detection has recently been proposed by using subproblem partitions, sorting preprocessing and radius updating. However, the ordering method has a serious limitation when the number of activated antennas is equal to the number of received antennas. Therefore, alternative sorting methods are studied in the present paper. In addition, the computational cost of the ML algorithm can be high when the system sizes increases. In this paper a suboptimal version is proposed where only the first L SD subproblems are carried out. The results show that the proposed algorithm achieves near optimal performance at lower computational cost than ML algorithms.

A new algorithm called SUMIS-BO is proposed for soft-output MIMO detection. This method is a meaningful improvement of the "Subspace Marginalization with Interference Suppression" (SUMIS) algorithm. It exhibits good performance with reduced complexity and has been evaluated and compared in terms of performance and efficiency with the SUMIS algorithm using different system parameters. Results show that the performance of the SUMIS-BO is similar to the SUMIS algorithm, however its efficiency is improved. The new algorithm is far more efficient than SUMIS, especially with large systems.

In Multiple-Input Multiple-Output (MIMO) schemes, the high computational complexity of soft optimal detection algorithms can make these algorithms impractical for real systems, especially when the number of antennas and modulation orders increase. In this paper, we present a modification on Repeated Tree Search (RTS) strategy, reducing the complexity by using Box- Optimization (BO) method combined with the Zero Forcing (ZF) algorithm. The proposed soft input soft output algorithm presents lower complexity than already proposed optimal algorithms, however it loses the optimal behavior. The proposed suboptimal soft detector exhibits a scalable tradeoff between complexity and performance.

This paper describes a parallel implementation of a Lanczos-based method to solve generalised eigenvalue problems related to the modal computation of arbitrarily shaped waveguides. This efficient implementation is intended for execution in moderate-low cost workstations (2 to 4 processors). The problem under study has several features: the involved matrices are sparse with a certain structure, and all the eigenvalues needed are contained in a given interval. The novel parallel algorithms proposed show excellent speed-up for small number of processors