Rate-reliability-complexity tradeoff for ML and lattice decoding of full-rate codes
07 Jul 2013-pp 1267-1271
TL;DR: The current work proves the fact that ML and (MMSE-preprocessed) lattice decoding share the same complexity exponent for a very broad setting, which now includes almost any DMT optimal code and all decoding order policies.
Abstract: Recent work in [1]-[3] quantified, in the form of a complexity exponent, the computational resources required for ML and lattice sphere decoding to achieve a certain diversity-multiplexing performance. For a specific family of layered lattice designs, and a specific set of decoding orderings, this complexity was shown to be an exponential function in the number of codeword bits, and was shown to meet a universal upper bound on complexity exponents. The same results raised the question of whether complexity reductions away from the universal upper bound are feasible, for example, with a proper choice of decoder (ML vs lattice), or with a proper choice of lattice codes and decoding ordering policies. The current work addresses this question by first showing that for almost any full-rate DMT optimal lattice code, there exists no decoding ordering policy that can reduce the complexity exponent of ML or lattice based sphere decoding away from the universal upper bound, i.e., that a randomly picked lattice code (randomly and uniformly drawn from an ensemble of DMT optimal lattice designs) will almost surely be such that no decoding ordering policy can provide exponential complexity reductions away from the universal upper bound. As a byproduct of this, the current work proves the fact that ML and (MMSE-preprocessed) lattice decoding share the same complexity exponent for a very broad setting, which now includes almost any DMT optimal code (again randomly drawn) and all decoding order policies. Under a basic richness of codes assumption, this is in fact further extended to hold, with probability one, over all full-rate codes. Under the same assumption, the result allows for a meaningful rate-reliability-complexity tradeoff that holds, almost surely in the random choice of the full-rate lattice design, and which holds irrespective of the decoding ordering policy. This tradeoff can be used to, for example, describe the optimal achievable diversity gain of ML or lattice sphere decoding in the presence of limited computational resources.
Citations
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TL;DR: The rate-reliability-complexity limits of a quasi-static K-user multiple access channel (MAC), with or without feedback, are explored, revealing the interesting finding that a proper calibration of user selection can allow for near-optimal ML-based decoding, with complexity that need not scale exponentially in the total number of codeword bits.
Abstract: The rate-reliability-complexity limits of a quasi-static $K$ -user multiple access channel (MAC), with or without feedback, are explored in this paper. Using high-SNR asymptotics, bounds on the computational resources required to achieve near-optimal (ML-based) decoding performance are first derived. They, in turn, yield bounds on the (reduced) complexity needed to achieve any (including suboptimal) diversity-multiplexing tradeoff (DMT) performance. Similar complexity-bounds in the presence of feedback-aided user selection are also given. This latter effort reveals the ability of a few bits of feedback not only to improve performance, but also to reduce complexity. In this context, our analysis reveals the interesting finding that a proper calibration of user selection can allow for near-optimal ML-based decoding, with complexity that need not scale exponentially in the total number of codeword bits. The derived bounds constitute the best known performance-versus-complexity behavior to date for ML-based MAC decoding, as well as a first exploration of the complexity-feedback-performance interdependencies in multiuser settings.
2 citations
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TL;DR: In this paper, the rate-reliability-complexity limits of the quasi-static K-user multiple access channel (MAC) with or without feedback were explored, and the authors showed that proper calibration of user selection can allow for near-optimal decoding, with complexity that need not scale exponentially in the total number of codeword bits.
Abstract: This work explores the rate-reliability-complexity limits of the quasi-static K-user multiple access channel (MAC), with or without feedback. Using high-SNR asymptotics, the work first derives bounds on the computational resources required to achieve near-optimal (ML-based) decoding performance. It then bounds the (reduced) complexity needed to achieve any (including suboptimal) diversity-multiplexing performance tradeoff (DMT) performance, and finally bounds the same complexity, in the presence of feedback-aided user selection. This latter effort reveals the ability of a few bits of feedback not only to improve performance, but also to reduce complexity. In this context, the analysis reveals the interesting finding that proper calibration of user selection can allow for near-optimal ML-based decoding, with complexity that need not scale exponentially in the total number of codeword bits. The derived bounds constitute the best known performance-vs-complexity behavior to date for ML-based MAC decoding, as well as a first exploration of the complexity-feedback-performance interdependencies in multiuser settings.
2 citations
01 Jan 2015
TL;DR: A Variable Radius Sphere Decoding (VR-SD) algorithm based on ZF algorithm is proposed in order to simplify the complex searching steps and the advantages of this algorithm are proved by analyzing from the derivation of mathematical formulas and the simulation of the BER performance between SD and VR-SD algorithm.
Abstract: Sphere Decoding (SD) algorithm is an implement decoding algorithm based on Zero Forcing (ZF) algorithm in the real number field. The classical SD algorithm is famous for its outstanding Bit Error Rate (BER) performance and decoding strategy. The algorithm gets its maximum likelihood solution by recursive shrinking the searching radius gradually. However, it is too complicated to use the method of shrinking the searching radius in ground communication system. This paper proposed a Variable Radius Sphere Decoding (VR-SD) algorithm based on ZF algorithm in order to simplify the complex searching steps. We prove the advantages of VR-SD algorithm by analyzing from the derivation of mathematical formulas and the simulation of the BER performance between SD and VR-SD algorithm.
References
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TL;DR: A simple characterization of the optimal tradeoff curve is given and used to evaluate the performance of existing multiple antenna schemes for the richly scattered Rayleigh-fading channel.
Abstract: Multiple antennas can be used for increasing the amount of diversity or the number of degrees of freedom in wireless communication systems. We propose the point of view that both types of gains can be simultaneously obtained for a given multiple-antenna channel, but there is a fundamental tradeoff between how much of each any coding scheme can get. For the richly scattered Rayleigh-fading channel, we give a simple characterization of the optimal tradeoff curve and use it to evaluate the performance of existing multiple antenna schemes.
4,422 citations
"Rate-reliability-complexity tradeof..." refers background in this paper
...I. INTRODUCTION In MIMO systems, the prohibitively large computational costs of maximum likelihood (ML) decoding serve as motivation to consider different branch-and-bound algorithms [4]–[6] which can provide computational savings at the expense of a relatively small error-performance degradation....
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...Combining (3) and (4) yields the equivalent system model y =Ms + w, (5a) where M,ρ 1 2− rT κ HG ∈ R2nRT×κ. (5b)...
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Book•
28 Jun 2004TL;DR: A tutorial on random matrices is provided which provides an overview of the theory and brings together in one source the most significant results recently obtained.
Abstract: Random matrix theory has found many applications in physics, statistics and engineering since its inception. Although early developments were motivated by practical experimental problems, random matrices are now used in fields as diverse as Riemann hypothesis, stochastic differential equations, condensed matter physics, statistical physics, chaotic systems, numerical linear algebra, neural networks, multivariate statistics, information theory, signal processing and small-world networks. This article provides a tutorial on random matrices which provides an overview of the theory and brings together in one source the most significant results recently obtained. Furthermore, the application of random matrix theory to the fundamental limits of wireless communication channels is described in depth.
2,308 citations
TL;DR: By judicious choice of the decoding radius, it is shown that this maximum-likelihood decoding algorithm can be practically used to decode lattice codes of dimension up to 32 in a fading environment.
Abstract: We present a maximum-likelihood decoding algorithm for an arbitrary lattice code when used over an independent fading channel with perfect channel state information at the receiver. The decoder is based on a bounded distance search among the lattice points falling inside a sphere centered at the received point. By judicious choice of the decoding radius we show that this decoder can be practically used to decode lattice codes of dimension up to 32 in a fading environment.
1,760 citations
"Rate-reliability-complexity tradeof..." refers background in this paper
...…this question by first showing that for almost any full-rate DMT optimal lattice code, there exists no decoding ordering policy that can reduce the complexity exponent of ML or lattice based sphere decoding away from the universal upper bound, i.e., that a randomly picked lattice code…...
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TL;DR: A novel algorithm is developed that is inspired by the Pohst enumeration strategy and is shown to offer a significant reduction in complexity compared to the Viterbo-Boutros sphere decoder and is supported by intuitive arguments and simulation results in many relevant scenarios.
Abstract: Maximum-likelihood (ML) decoding algorithms for Gaussian multiple-input multiple-output (MIMO) linear channels are considered. Linearity over the field of real numbers facilitates the design of ML decoders using number-theoretic tools for searching the closest lattice point. These decoders are collectively referred to as sphere decoders in the literature. In this paper, a fresh look at this class of decoding algorithms is taken. In particular, two novel algorithms are developed. The first algorithm is inspired by the Pohst enumeration strategy and is shown to offer a significant reduction in complexity compared to the Viterbo-Boutros sphere decoder. The connection between the proposed algorithm and the stack sequential decoding algorithm is then established. This connection is utilized to construct the second algorithm which can also be viewed as an application of the Schnorr-Euchner strategy to ML decoding. Aided with a detailed study of preprocessing algorithms, a variant of the second algorithm is developed and shown to offer significant reductions in the computational complexity compared to all previously proposed sphere decoders with a near-ML detection performance. This claim is supported by intuitive arguments and simulation results in many relevant scenarios.
1,410 citations