Browsing by Author "Vehkalahti, Roope"

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An algebraic look into MAC-DMT of lattice space-time codes
(2011)
Vehkalahti, Roope
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Lu, Hsiao-Feng (Francis)
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電機工程學系
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Department of Electrical and Computer Engineering
In this paper we are concentrating on the diversity-multiplexing gain trade-off (DMT) of some space-time lattice codes. First we give a DMT bound for lattice codes having restricted dimension. We then recover the well known results of the DMT of algebraic number field codes and the Alamouti code by using the union bound and see that these codes do achieve the previously mentioned bound. During our analysis interesting connections to the Dedekind\'s zeta-function and to Dirichlet\'s unit theorem are revealed. Finally we prove that both the number field codes and Alamouti code are in some sense optimal codes in the multiple access channel (MAC).
An Algebraic Tool for Obtaining Conditional Non-Vanishing Determinants
(2009)
Hollanti, Camilla
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Lu, Hsiao-Feng (Francis)
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Vehkalahti, Roope
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電信工程研究所
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Institute of Communications Engineering
An algebraic tool from the theory of central simple algebras is proposed to obtain families of complex matrices satisfying the conditional non-vanishing determinant (CNVD) property. Such property is of great use in e.g. the design of multiuser space-time (ST) codes, in which context it is not always crucial for the transmission matrix to be invertible. On the other hand, whenever it is invertible, it is important that it has a non-vanishing determinant. Also any submatrix of any subset of users multiplied with its transpose conjugate should preferably have a non-vanishing determinant, provided it is non-zero. In recent submissions by Lu et al. it has been shown that, with suitable multiplexing, such property yields a construction of space-time codes that achieve the optimal diversity-multiplexing tradeoff (DMT) of the multiple-input multiple-output (MIMO) multiple access channel (MAC) and outperform the previously known ST codes.
An Error Event Sensitive Tradeoff Between Rate and Coding Gain in MIMO MAC
(2015-11-01)
Ernvall, Toni
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Lahtonen, Jyrki
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Lu, Hsiao-feng (Francis)
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Vehkalahti, Roope
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電機資訊學士班
This paper investigates the design of codes for multiple-input multiple-output (MIMO) multiple access channel (MAC). If a joint maximum-likelihood decoding is to be performed at the receiver, then every MIMO-MAC code can be regarded as a single-user code, where the minimum determinant criterion proposed by Tarokh et al. is useful for designing such codes and for upper bounding the maximum pairwise error probability (PEP), whenever the codes are of finite rate and operate in finite signal-to-noise ratio range. Unlike the case of single-user codes where the minimum determinant can be lower bounded by a fixed constant as code-rate grows, it was proved by Lahtonen et al. that the minimum determinant of MIMO-MAC codes decays as a function of the rates. This decay phenomenon is further investigated in this paper, and upper bounds for the decays of minimum determinant corresponding to each error event are provided. Lower bounds for the optimal decay are established and are based on an explicit construction of codes using algebraic number theory and Diophantine approximation. For some error profiles, the constructed codes are shown to meet the aforementioned upper bounds, hence they are optimal finite-rate codes in terms of PEPs associated with such error events. An asymptotic diversity-multiplexing gain tradeoff (DMT) analysis of the proposed codes is also given. It is shown that these codes are DMT optimal when the values of multiplexing gains are small.
Diversity-multiplexing Gain Tradeoff: a Tool in Algebra?
(2011)
Vehkalahti, Roope
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Lu, Hsiao-feng (Francis)
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電機工程學系
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Department of Electrical and Computer Engineering
Since the invention of space-time coding numerous algebraic methods have been applied in code design. In particular algebraic number theory and central simple algebras have been on the forefront of the research. In this paper we are turning the table and asking whether information theory can be used as a tool in algebra. We first show how diversity-multiplexing gain tradeoff (DMT) bounds of Zheng and Tse will give us information of the spread of determinants in matrix lattices and then apply these results to analyze unit groups of orders of division algebras. The results considering unit groups are not new or the best possible but we do find that this interesting relation between algebra and information theory is quite surprising and worth pointing out.
Inverse Determinant Sums and Connections Between Fading Channel Information Theory and Algebra
(2013-09-01)
Vehkalahti, Roope
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Lu, Hsiao-Feng (Francis)
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Luzzi, Laura
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電機工程學系
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Department of Electrical and Computer Engineering
This work considers inverse determinant sums, which arise from the union bound on the error probability, as a tool for designing and analyzing algebraic space-time block codes. A general framework to study these sums is established, and the connection between asymptotic growth of inverse determinant sums and the diversity-multiplexing gain tradeoff is investigated. It is proven that the growth of the inverse determinant sum of a division algebra-based space-time code is completely determined by the growth of the unit group. This reduces the inverse determinant sum analysis to studying certain asymptotic integrals in Lie groups. Using recent methods from ergodic theory, a complete classification of the inverse determinant sums of the most well-known algebraic space-time codes is provided. The approach reveals an interesting and tight relation between diversity-multiplexing gain tradeoff and point counting in Lie groups.
New Space-Time Code Constructions for Two-User Multiple Access Channels
(2009-12-01)
Lu, Hsiao-feng (Francis)
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Vehkalahti, Roope
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Hollanti, Camilla
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Lahtonen, Jyrki
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Hong, Yi
This paper addresses the problem of constructing multiuser multiple-input multiple-output (MU-MIMO) codes for two users. The users are assumed to be equipped with n(t) transmit antennas, and there are n(r) antennas available at the receiving end. A general scheme is proposed and shown to achieve the optimal diversity-multiplexing gain tradeoff (DMT). Moreover, an explicit construction for the special case of n(t) = 2 and n(r) = 2 is given, based on the optimization of the code shape and density. All the proposed constructions are based on cyclic division algebras and their orders and take advantage of the multi-block structure. Computer simulations show that both the proposed schemes yield codes with excellent performance improving upon the best previously known codes. Finally, it is shown that the previously proposed design criteria for DMT optimal MU-MIMO codes are sufficient but in general too strict and impossible to fulfill. Relaxed alternative design criteria are then proposed and shown to be still sufficient for achieving the multiple-access channel diversity-multiplexing tradeoff.