arXiv subjects

Amaro Barreal

Publications and source records attributed to Amaro Barreal.

15 recordsLinked to original sources

arXiv2020

An Approximation of Theta Functions with Applications to Communications

Computing the theta series of an arbitrary lattice, and more specifically a related quantity known as the flatness factor, has been recently shown to be important for lattice code design in various wireless communication setups. However, the theta series is in general not known in closed form, excluding a small set of very special lattices. In this article, motivated by the practical applications as well as the mathematical problem itself, a simple approximation of the theta series of a lattice is derived. A rigorous analysis of its accuracy is provided. In relation to this, maximum-likelihood decoding in the context of compute-and-forward relaying is studied. Following previous work, it is shown that the related metric can exhibit a flat behavior, which can be characterized by the flatness factor of the decoding function. Contrary to common belief, we note that the decoding metric can be rewritten as a sum over a random lattice only when at most two sources are considered. Using a particular matrix decomposition, a link between the random lattice and the code lattice employed at the transmitter is established, which leads to an explicit criterion for code design, in contrast to implicit criteria derived previously. Finally, candidate lattices are examined with respect to the proposed criterion using the derived theta series approximation.

cs.IT↗

arXiv2017

On Fast-Decodable Algebraic Space--Time Codes

In the near future, the $5^{th}$ generation (5G) wireless systems will be established. They will consist of an integration of different techniques, including distributed antenna systems and massive multiple-input multiple-output systems, and the overall performance will highly depend on the channel coding techniques employed. Due to the nature of future wireless networks, space--time codes are no longer merely an object of choice, but will often appear naturally in the communications setting. However, as the involved communication devices often exhibit a modest computational power, the complexity of the codes to be utilised should be reasonably low for possible practical implementation. Fast-decodable codes enjoy reduced complexity of maximum-likelihood (ML) decoding due to a smart inner structure allowing for parallelisation in the ML search. The complexity reductions considered in this chapter are entirely owing to the algebraic structure of the considered codes, and could be further improved by employing non-ML decoding methods, however yielding suboptimal performance. The aim of this chapter is twofold. First, we provide a tutorial introduction to space--time coding and study powerful algebraic tools for their design and construction. Secondly, we revisit algebraic techniques used for reducing the worst-case decoding complexity of both single-user and multiuser space-time codes, alongside with general code families and illustrative examples.

cs.IT↗

arXiv2017

Natural orders for asymmetric space--time coding: minimizing the discriminant

Algebraic space--time coding --- a powerful technique developed in the context of multiple-input multiple-output (MIMO) wireless communications --- has profited tremendously from tools from Class Field Theory and, more concretely, the theory of central simple algebras and their orders. During the last decade, the study of space--time codes for practical applications, and more recently for future generation (5G+) wireless systems, has provided a practical motivation for the consideration of many interesting mathematical problems. One such problem is the explicit computation of orders of central simple algebras with small discriminants. In this article, we consider the most interesting asymmetric MIMO channel setups and, for each treated case, we provide explicit pairs of fields and a corresponding non-norm element giving rise to a cyclic division algebra whose natural order has the minimum possible discriminant.

math.NT↗

arXiv2017

Lattice Codes for Physical Layer Communications

Lattices are deceptively simple mathematical structures that have become indispensable for code design for physical layer communications. While lattice-related problems are interesting in their own right, the usefulness of these discrete structures in wireless communications provides additional motivation for their study and enables a multidisciplinary line of research. This thesis is devoted to the study of lattice code design for physical layer communications. Modern wireless communication networks are required to accommodate significantly varied types of mobile devices, differing in available computational power or number of equipped antennas. Additionally, the density of the networks increases rapidly, and many communication protocols diverge from the classical direct point-to-point transmission in favor of allowing for intermediate relays to process and forward data. An important consequence of this shift towards more sophisticated transmission protocols is that traditional well-performing codes become futile for modern communications, thus the study and development of novel codes is called for. Yet, however involved a transmission protocol may be, the characteristics of the physical medium, i.e., the wireless channel, stay unaffected. It is thus natural that an underlying lattice structure for code design remains crucial. This thesis consists of several articles considering lattice code design for four different communication settings relevant in modern wireless communications.

cs.IT↗

arXiv2016

Well-Rounded Lattices for Coset Coding in MIMO Wiretap Channels

The concept of well-rounded lattices has recently found important applications in the setting of a fading single-input single-output (SISO) wiretap channel. It has been shown that, under this setup, the property of being well-rounded is critical for minimizing the eavesdropper's probability of correct decoding in lower SNR regimes. The superior performance of coset codes constructed from well-rounded lattices has been illustrated in several simulations. In the present article, this work is extended to fading multiple-input multiple-output (MIMO) wiretap channels, and similar design criteria as in the SISO case are derived. Further, explicit coset codes for Rayleigh fading MIMO wiretap channels are designed. In particular, it is shown through extensive simulations that sublattices of the well-known Alamouti code and Golden code which meet our design criteria perform better than scalar multiples of the code lattice for the same parameters.

cs.IT↗

arXiv2016

Information Bounds and Flatness Factor Approximation for Fading Wiretap MIMO Channels

In this article, the design of secure lattice coset codes for general wireless channels with fading and Gaussian noise is studied. Recalling the eavesdropper's probability and information bounds, a variant of the latter is given from which it is explicitly seen that both quantities are upper bounded by (increasing functions of) the expected flatness factor of the faded lattice related to the eavesdropper. By making use of a recently developed approximation of the theta series of a lattice, it is further shown how the average flatness factor can be approximated numerically. In particular, based on the numerical computations, the average flatness factor not only bounds but also orders correctly the performance of different lattices.

cs.IT↗

arXiv2016

Coded Caching Clusters with Device-to-Device Communications

We consider a geographically constrained caching community where popular data files are cached on mobile terminals and distributed through Device-to-Device (D2D) communications. Further, to ensure availability, data files are protected against user mobility, or churn, with erasure coding. Communication and storage costs (in units of energy) are considered. We focus on finding the coding method that minimizes the overall cost in the network. Closed-form expressions for the expected energy consumption incurred by data delivery and redundancy maintenance are derived, and it is shown that coding significantly decreases the overall energy consumption -- by more than 90% in a realistic scenario. It is further shown that D2D caching can also yield notable economical savings for telecommunication operators. Our results are illustrated by numerical examples and verified by extensive computer simulations.

cs.NI↗

arXiv2016

Nested Lattice Codes for Vector Perturbation Systems

Vector perturbation is an encoding method for broadcast channels in which the transmitter solves a shortest vector problem in a lattice to create a perturbation vector, which is then added to the data before transmission. In this work, we introduce nested lattice codes into vector perturbation systems, resulting in a strategy which we deem matrix perturbation. We propose design criteria for the nested lattice codes, and show empirically that lattices satisfying these design criteria can improve the performance of vector perturbation systems. The resulting design criteria are the same as those recently proposed for the Compute-and-Forward protocol.

cs.IT↗

arXiv2015

Fast-Decodable Space-Time Codes for the $N$-Relay and Multiple-Access MIMO Channel

In this article, the first general constructions of fast-decodable, more specifically (conditionally) $g$-group decodable, space-time block codes for the Nonorthogonal Amplify and Forward (NAF) Multiple-Input Multiple-Output (MIMO) relay channel under the half-duplex constraint are proposed. In this scenario, the source and the intermediate relays used for data amplification are allowed to employ multiple antennas for data transmission and reception. The worst-case decoding complexity of the obtained codes is reduced by up to $75%$. In addition to being fast-decodable, the proposed codes achieve full-diversity and have nonvanishing determinants, which has been shown to be useful for achieving the optimal Diversity-Multiplexing Tradeoff (DMT) of the NAF channel. Further, it is shown that the same techniques as in the cooperative scenario can be utilized to achieve fast-decodability for $K$-user MIMO Multiple-Access Channel (MAC) space-time block codes. The resulting codes in addition exhibit the conditional nonvanishing determinant property which, for its part, has been shown to be useful for achieving the optimal MAC-DMT.

cs.IT↗

arXiv2015

A Low-Complexity Message Recovery Method for Compute-and-Forward Relaying

The Compute-and-Forward relaying strategy achieves high computation rates by decoding linear combinations of transmitted messages at intermediate relays. However, if the involved relays independently choose which combinations of the messages to decode, there is no guarantee that the overall system of linear equations is solvable at the destination. In this article it is shown that, for a Gaussian fading channel model with two transmitters and two relays, always choosing the combination that maximizes the computation rate often leads to a case where the original messages cannot be recovered. It is further shown that by limiting the relays to select from carefully designed sets of equations, a solvable system can be guaranteed while maintaining high computation rates. The proposed method has a constant computational complexity and requires no information exchange between the relays.

cs.IT↗

arXiv2015

Constructions of Fast-Decodable Distributed Space-Time Codes

Fast-decodable distributed space-time codes are constructed by adapting the iterative code construction introduced in [1] to the N -relay multiple-input multiple-output channel, leading to the first fast-decodable distributed space-time codes for more than one antenna per user. Explicit constructions are provided alongside with a performance comparison to non-iterated (non-) fast-decodable codes.

cs.IT↗

arXiv2015

Reduced Complexity Decoding of n x n Algebraic Space-Time Codes

Algebraic space-time coding allows for reliable data exchange across fading multiple-input multiple-output channels. A powerful technique for decoding space-time codes in Maximum-Likelihood (ML) decoding, but well-performing and widely-used codes such as the Golden code often suffer from high ML-decoding complexity. In this article, a recursive algorithm for decoding general algebraic space-time codes of arbitrary dimension is proposed, which reduces the worst-case decoding complexity from $O(|S|^{n^2})$ to $O(|S|^n)$.

cs.IT↗

arXiv2014

Node Repair for Distributed Storage Systems over Fading Channels

Distributed storage systems and associated storage codes can efficiently store a large amount of data while ensuring that data is retrievable in case of node failure. The study of such systems, particularly the design of storage codes over finite fields, assumes that the physical channel through which the nodes communicate is error-free. This is not always the case, for example, in a wireless storage system. We study the probability that a subpacket is repaired incorrectly during node repair in a distributed storage system, in which the nodes communicate over an AWGN or Rayleigh fading channels. The asymptotic probability (as SNR increases) that a node is repaired incorrectly is shown to be completely determined by the repair locality of the DSS and the symbol error rate of the wireless channel. Lastly, we propose some design criteria for physical layer coding in this scenario, and use it to compute optimally rotated QAM constellations for use in wireless distributed storage systems.

cs.IT↗

arXiv2014

Algebraic Codes and a New Physical Layer Transmission Protocol for Wireless Distributed Storage Systems

In a wireless storage system, having to communicate over a fading channel makes repair transmissions prone to physical layer errors. The first approach to combat fading is to utilize the existing optimal space-time codes. However, it was recently pointed out that such codes are in general too complex to decode when the number of helper nodes is bigger than the number of antennas at the newcomer or data collector. In this paper, a novel protocol for wireless storage transmissions based on algebraic space-time codes is presented in order to improve the system reliability while enabling feasible decoding. The diversity-multiplexing gain tradeoff (DMT) of the system together with sphere-decodability even with low number of antennas are used as the main design criteria, thus naturally establishing a DMT-complexity tradeoff. It is shown that the proposed protocol outperforms the simple time-division multiple access (TDMA) protocol, while still falling behind the optimal DMT.

cs.IT↗

arXiv2014

Space-Time Storage Codes for Wireless Distributed Storage Systems

Distributed storage systems (DSSs) have gained a lot of interest recently, thanks to their robustness and scalability compared to single-device storage. Majority of the related research has exclusively concerned the network layer. At the same time, the number of users of, e.g., peer-to-peer (p2p) and device-to-device (d2d) networks as well as proximity based services is growing rapidly, and the mobility of users is considered more and more important. This motivates, in contrast to the existing literature, the study of the physical layer functionality of wireless distributed storage systems. In this paper, we take the first step towards protecting the storage repair transmissions from physical layer errors when the transmission takes place over a fading channel. To this end, we introduce the notion of a space-time storage code, drawing together the aspects of network layer and physical layer functionality and resulting in cross-layer robustness. It is also pointed out that existing space-time codes are too complex to be utilized in storage networks when the number of helpers involved is larger than the number of receive antennas at the newcomer or data collector, hence creating a call for less complex transmission protocols.

cs.IT↗