Statistical Pruning for Near-Maximum Likelihood Decoding

In many communications problems, maximum-likelihood (ML) decoding reduces to finding the closest (skewed) lattice point in N-dimensions to a given point xisin CN. In its full generality, this problem is known to be NP-complete. Recently, the expected complexity of the sphere decoder, a particular algorithm that solves the ML problem exactly, has been computed. An asymptotic analysis of this complexity has also been done where it is shown that the required computations grow exponentially in N for any fixed SNR. At the same time, numerical computations of the expected complexity show that there are certain ranges of rates, SNRs and dimensions N for which the expected computation (counted as the number of scalar multiplications) involves no more than N3 computations. However, when the dimension of the problem grows too large, the required computations become prohibitively large, as expected from the asymptotic exponential complexity. In this paper, we propose an algorithm that, for large N, offers substantial computational savings over the sphere decoder, while maintaining performance arbitrarily close to ML. We statistically prune the search space to a subset that, with high probability, contains the optimal solution, thereby reducing the complexity of the search. Bounds on the error performance of the new method are proposed. The complexity of the new algorithm is analyzed through an upper bound. The asymptotic behavior of the upper bound for large N is also analyzed which shows that the upper bound is also exponential but much lower than the sphere decoder. Simulation results show that the algorithm is much more efficient than the original sphere decoder for smaller dimensions as well, and does not sacrifice much in terms of performance

Faster Projection in Sphere Decoding

Most of the calculations in standard sphere decoders are redundant, in the sense that they either calculate quantities that are never used or calculate some quantities more than once. A new method, which is applicable to lattices as well as finite constellations, is proposed to avoid these redundant calculations while still returning the same result. Pseudocode is given to facilitate immediate implementation. Simulations show that the speed gain with the proposed method increases linearly with the lattice dimension. At dimension 60, the new algorithms avoid about 75% of all floating-point operations

Improved Maximum Likelihood Detection through Sphere Decoding combined with Box Optimization

this is the author’s version of a work that was accepted for publication in Signal Processing. Changes resulting from the publishing process, such as peer review, editing, corrections, structural, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Signal Processing, [VOL 98, may 14] DOI 10.1016/j.sigpro.2013.11.041Sphere Decoding is a popular Maximum Likelihood algorithm that can be used to detect signals coming from multiple-input, multiple-output digital communication systems. It is well known that the complexity required to detect each signal with the Sphere Decoding algorithm may become unacceptable, especially for low signal-to-noise ratios. In this paper, we describe an auxiliary technique that drastically decreases the computation required to decode a signal. This technique was proposed by Stojnic, Hassibi and Vikalo in 2008, and is based on using continuous box-bounded minimization in combination with Sphere Decoding. Their implementation is, however, not competitive due to the box minimization algorithm selected. In this paper we prove that by judiciously selecting the box minimization algorithm and tailoring it to the Sphere Decoding environment, the computational complexity of the resulting algorithm for low signal-to-noise ratios is better (by orders of magnitude) than standard Sphere Decoding implementations. & 2013 Elsevier B.V. All rights reserved.This work has been partially funded by Universitat Politecnica de Valencia through Programa de Apoyo a la Investigacion y Desarrollo de la UPV (PAID-06-11) and (PAID-05-12), by Generalitat Valenciana through projects PROMETEO/2009/013 and Ayudas para la realizacion de proyectos de I+D para grupos de investigacion emergentes GV/2012/039, and by Ministerio Espanol de Economia y Competitividad through project TEC2012-38142-C04.García Mollá, VM.; Vidal Maciá, AM.; González Salvador, A.; Roger Varea, S. (2014). Improved Maximum Likelihood Detection through Sphere Decoding combined with Box Optimization. Signal Processing. 98:284-294. https://doi.org/10.1016/j.sigpro.2013.11.041S2842949

Maximum likelihood soft-output detection through Sphere Decoding combined with box optimization

This is the author’s version of a work that was accepted for publication in Signal Processing. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Signal Processing 125 (2016) 249–260. DOI 10.1016/j.sigpro.2016.02.006.This paper focuses on the improvement of known algorithms for maximum likelihood soft-output detection. These algorithms usually have large computational complexity, that can be reduced by using clipping. Taking two well-known soft-output maximum likelihood algorithms (Repeated Tree Search and Single Tree Search) as a starting point, a number of modifications (based mainly on box optimization techniques) are proposed to improve the efficiency of the search. As a result, two new algorithms are proposed for soft-output maximum likelihood detection. One of them is based on Repeated Tree Search (which can be applied with and without clipping). The other one is based on Single Tree Search, which can only be applied to the case with clipping. The proposed algorithms are compared with the Single Tree Search algorithm, and their efficiency is evaluated in standard detection problems (4 4 16-QAM and 4 4 64-QAM) with and without clipping. The results show that the efficiency of the proposed algorithms is similar to that of the Single Tree Search algorithm in the case 4 4 16-QAM; however, in the case 4 4 64- QAM, the new algorithms are far more efficient than the Single Tree Search algorithm. & 2016 Elsevier B.V. All rights reserved.This work has been partially funded by Generalitat Valenciana through the projects ISIC/2012/006 and PROMETEO II/2014/003, and by Ministerio Espanol de Economia y Competitividad through the project TEC2012-38142-C04 and through the Grant RACHEL TEC2013-47141-C4-4-R.García Mollá, VM.; Simarro Haro, MDLA.; Martínez Zaldívar, FJ.; González Salvador, A.; Vidal Maciá, AM. (2016). Maximum likelihood soft-output detection through Sphere Decoding combined with box optimization. Signal Processing. 125:249-260. https://doi.org/10.1016/j.sigpro.2016.02.006S24926012

Symbol-Level Noise-Guessing Decoding with Antenna Sorting for URLLC Massive MIMO

Supporting ultra-reliable and low-latency communication (URLLC) is a challenge in current wireless systems. Channel codes that generate large codewords improve reliability but necessitate the use of interleavers, which introduce undesirable latency. Only short codewords can eliminate the requirement for interleaving and reduce decoding latency. This paper suggests a coding and decoding method which, when combined with the high spectral efficiency of spatial multiplexing, can provide URLLC over a fading channel. Random linear coding and high-order modulation are used to transmit information over a massive multiple-input multiple-output (mMIMO) channel, followed by zero-forcing detection and guessing random additive noise decoding (GRAND) at a receiver. A variant of GRAND, called symbol-level GRAND, originally proposed for single-antenna systems that employ high-order modulation schemes, is generalized to spatial multiplexing. The paper studies the impact of the orthogonality defect of the underlying mMIMO lattice on symbol-level GRAND, and proposes to leverage side-information that comes from the mMIMO channel-state information and relates to the reliability of each receive antenna. This induces an antenna sorting step, which further reduces decoding complexity by over 80\% when compared to bit-level GRAND

Simulación computacional y paralelización de un sistema de comunicaciones inalámbrico MIMO: Estimación del Canal y Decodificación de Señales

En la presente tesis se realiza un estudio de todo el proceso de una comunicación en un sistema MIMO, desde la estimación de las condiciones del canal, hasta la decodificación de la señal, utilizando algoritmos de ramificación y poda (ASD), y paralelizando los algoritmos sobre Unidades Gráficas de Proceso (GPU).Puig Borrás, V. (2011). Simulación computacional y paralelización de un sistema de comunicaciones inalámbrico MIMO: Estimación del Canal y Decodificación de Señales. http://hdl.handle.net/10251/1136