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Algebraic Basis

The Experts below are selected from a list of 204 Experts worldwide ranked by ideXlab platform

Dong Fang – 1st expert on this subject based on the ideXlab platform

  • EUSIPCO – Linear physical layer network coding for multihop wireless networks
    , 2014
    Co-Authors: Alister G. Burr, Dong Fang

    Abstract:

    We consider linear network coding functions that can be employed at the relays in wireless physical layer network coding, applied to a general multi-hop network topology. We introduce a general model of such a network, and discuss the Algebraic Basis of linear functions, deriving conditions for unambiguous decodability of the source data at the destination. We consider the use of integer rings, integer fields, binary extension fields and the ring of binary matrices as potential Algebraic constructs, and show that the ring constructs provide more flexibility. We use the two-way relay channel and a network containing two sources and two relays to illustrate the concept and to demonstrate the effect of fading of the wireless channels. We show the capacity benefits of the more flexible rings.

  • Linear physical layer network coding for multihop wireless networks
    2014 22nd European Signal Processing Conference (EUSIPCO), 2014
    Co-Authors: Alister Burr, Dong Fang

    Abstract:

    We consider linear network coding functions that can be employed at the relays in wireless physical layer network coding, applied to a general multi-hop network topology. We introduce a general model of such a network, and discuss the Algebraic Basis of linear functions, deriving conditions for unambiguous decodability of the source data at the destination. We consider the use of integer rings, integer fields, binary extension fields and the ring of binary matrices as potential Algebraic constructs, and show that the ring constructs provide more flexibility. We use the two-way relay channel and a network containing two sources and two relays to illustrate the concept and to demonstrate the effect of fading of the wireless channels. We show the capacity benefits of the more flexible rings.

Alister Burr – 2nd expert on this subject based on the ideXlab platform

  • Linear physical layer network coding for multihop wireless networks
    2014 22nd European Signal Processing Conference (EUSIPCO), 2014
    Co-Authors: Alister Burr, Dong Fang

    Abstract:

    We consider linear network coding functions that can be employed at the relays in wireless physical layer network coding, applied to a general multi-hop network topology. We introduce a general model of such a network, and discuss the Algebraic Basis of linear functions, deriving conditions for unambiguous decodability of the source data at the destination. We consider the use of integer rings, integer fields, binary extension fields and the ring of binary matrices as potential Algebraic constructs, and show that the ring constructs provide more flexibility. We use the two-way relay channel and a network containing two sources and two relays to illustrate the concept and to demonstrate the effect of fading of the wireless channels. We show the capacity benefits of the more flexible rings.

Senhadji Lotfi – 3rd expert on this subject based on the ideXlab platform

  • Semi-nonnegative joint diagonalization by congruence and semi-nonnegative ICA
    Signal Processing, 2016
    Co-Authors: Coloigner Julie, Albera Laurent, Kachenoura Amar, Noury Fanny, Senhadji Lotfi

    Abstract:

    In this paper, we focus on the Joint Diagonalization by Congruence (JDC) decomposition of a set of matrices, while imposing nonnegative constraints on the joint diagonalizer. The latter will be referred to the semi-nonnegative JDC fitting problem. This problem appears in semi-nonnegative Independent Component Analysis (ICA), say ICA involving nonnegative static mixtures, such as those encountered for instance in image processing and in magnetic resonance spectroscopy. In order to achieve the semi-nonnegative JDC decomposition, we propose two novel algorithms called ELS-ALSexp and CGexp, which optimize an unconstrained problem obtained by means of an exponential change of variable. The proposed methods are based on the line search strategy for which an analytic global plane search procedure has been considered. All derivatives have been jointly calculated in matrix form using the Algebraic Basis for matrix calculus and product operator properties. Our algorithms have been tested on synthetic arrays and the semi-nonnegative ICA problem is illustrated through simulations in magnetic resonance spectroscopy and in image processing. The numerical results show the benefit of using a priori information, such as nonnegativity.