Multiplexing Gain

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Roope Vehkalahti - One of the best experts on this subject based on the ideXlab platform.

  • the dmt of real and quaternionic lattice codes and dmt classification of division algebra codes
    arXiv: Information Theory, 2021
    Co-Authors: Roope Vehkalahti, Laura Luzzi
    Abstract:

    In this paper we consider the diversity-Multiplexing Gain tradeoff (DMT) of so-called minimum delay asymmetric space-time codes. Such codes are less than full dimensional lattices in their natural ambient space. Apart from the multiple input single output (MISO) channel there exist very few methods to analyze the DMT of such codes. Further, apart from the MISO case, no DMT optimal asymmetric codes are known. We first discuss previous criteria used to analyze the DMT of space-time codes and comment on why these methods fail when applied to asymmetric codes. We then consider two special classes of asymmetric codes where the code-words are restricted to either real or quaternion matrices. We prove two separate diversity-Multiplexing Gain trade-off (DMT) upper bounds for such codes and provide a criterion for a lattice code to achieve these upper bounds. We also show that lattice codes based on Q-central division algebras satisfy this optimality criterion. As a corollary this result provides a DMT classification for all Q-central division algebra codes that are based on standard embeddings. While the Q-central division algebra based codes achieve the largest possible DMT of a code restricted to either real or quaternion space, they still fall short of the optimal DMT apart from the MISO case.

  • towards a complete dmt classification of division algebra codes
    International Symposium on Information Theory, 2016
    Co-Authors: Laura Luzzi, Roope Vehkalahti, Alexander Gorodnik
    Abstract:

    This work aims at providing new lower bounds for the diversity-Multiplexing Gain trade-off of a general class of lattice codes based on division algebras.

  • towards a complete dmt classification of division algebra codes
    arXiv: Information Theory, 2015
    Co-Authors: Laura Luzzi, Roope Vehkalahti, Alexander Gorodnik
    Abstract:

    This work aims at providing new bounds for the diversity Multiplexing Gain trade-off of a general class of division algebra based lattice codes. In the low Multiplexing Gain regime, some bounds were previously obtained from the high signal-to-noise ratio estimate of the union bound for the pairwise error probabilities. Here these results are extended to cover a larger range of Multiplexing Gains. The improvement is achieved by using ergodic theory in Lie groups to estimate the behavior of the sum arising from the union bound. In particular, the new bounds for lattice codes derived from Q-central division algebras suggest that these codes can be divided into two subclasses based on their Hasse invariants at the infinite places. Algebras with ramification at the infinite place seem to provide better diversity-Multiplexing Gain tradeoff.

  • A new design criterion for spherically-shaped division algebra-based space-time codes
    2013
    Co-Authors: Laura Luzzi, Roope Vehkalahti
    Abstract:

    This work considers normalized inverse determinant sums as a tool for analyzing the performance of division algebra based space-time codes for multiple antenna wireless systems. A general union bound based code design criterion is obtained as a main result. In our previous work, the behavior of inverse determinant sums was analyzed using point counting techniques for Lie groups; it was shown that the asymptotic growth exponents of these sums correctly describe the diversity-Multiplexing Gain trade-off of the space-time code for some Multiplexing Gain ranges. This paper focuses on the constant terms of the inverse determinant sums, which capture the coding Gain behavior. Pursuing the Lie group approach, a tighter asymptotic bound is derived, allowing to compute the constant terms for several classes of space-time codes appearing in the literature. The resulting design criterion suggests that the performance of division algebra based codes depends on several fundamental algebraic invariants of the underlying algebra.

  • inverse determinant sums and connections between fading channel information theory and algebra
    IEEE Transactions on Information Theory, 2013
    Co-Authors: Roope Vehkalahti, Hsiaofeng Lu, Laura Luzzi
    Abstract:

    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.

Laura Luzzi - One of the best experts on this subject based on the ideXlab platform.

  • the dmt of real and quaternionic lattice codes and dmt classification of division algebra codes
    arXiv: Information Theory, 2021
    Co-Authors: Roope Vehkalahti, Laura Luzzi
    Abstract:

    In this paper we consider the diversity-Multiplexing Gain tradeoff (DMT) of so-called minimum delay asymmetric space-time codes. Such codes are less than full dimensional lattices in their natural ambient space. Apart from the multiple input single output (MISO) channel there exist very few methods to analyze the DMT of such codes. Further, apart from the MISO case, no DMT optimal asymmetric codes are known. We first discuss previous criteria used to analyze the DMT of space-time codes and comment on why these methods fail when applied to asymmetric codes. We then consider two special classes of asymmetric codes where the code-words are restricted to either real or quaternion matrices. We prove two separate diversity-Multiplexing Gain trade-off (DMT) upper bounds for such codes and provide a criterion for a lattice code to achieve these upper bounds. We also show that lattice codes based on Q-central division algebras satisfy this optimality criterion. As a corollary this result provides a DMT classification for all Q-central division algebra codes that are based on standard embeddings. While the Q-central division algebra based codes achieve the largest possible DMT of a code restricted to either real or quaternion space, they still fall short of the optimal DMT apart from the MISO case.

  • towards a complete dmt classification of division algebra codes
    International Symposium on Information Theory, 2016
    Co-Authors: Laura Luzzi, Roope Vehkalahti, Alexander Gorodnik
    Abstract:

    This work aims at providing new lower bounds for the diversity-Multiplexing Gain trade-off of a general class of lattice codes based on division algebras.

  • towards a complete dmt classification of division algebra codes
    arXiv: Information Theory, 2015
    Co-Authors: Laura Luzzi, Roope Vehkalahti, Alexander Gorodnik
    Abstract:

    This work aims at providing new bounds for the diversity Multiplexing Gain trade-off of a general class of division algebra based lattice codes. In the low Multiplexing Gain regime, some bounds were previously obtained from the high signal-to-noise ratio estimate of the union bound for the pairwise error probabilities. Here these results are extended to cover a larger range of Multiplexing Gains. The improvement is achieved by using ergodic theory in Lie groups to estimate the behavior of the sum arising from the union bound. In particular, the new bounds for lattice codes derived from Q-central division algebras suggest that these codes can be divided into two subclasses based on their Hasse invariants at the infinite places. Algebras with ramification at the infinite place seem to provide better diversity-Multiplexing Gain tradeoff.

  • A new design criterion for spherically-shaped division algebra-based space-time codes
    2013
    Co-Authors: Laura Luzzi, Roope Vehkalahti
    Abstract:

    This work considers normalized inverse determinant sums as a tool for analyzing the performance of division algebra based space-time codes for multiple antenna wireless systems. A general union bound based code design criterion is obtained as a main result. In our previous work, the behavior of inverse determinant sums was analyzed using point counting techniques for Lie groups; it was shown that the asymptotic growth exponents of these sums correctly describe the diversity-Multiplexing Gain trade-off of the space-time code for some Multiplexing Gain ranges. This paper focuses on the constant terms of the inverse determinant sums, which capture the coding Gain behavior. Pursuing the Lie group approach, a tighter asymptotic bound is derived, allowing to compute the constant terms for several classes of space-time codes appearing in the literature. The resulting design criterion suggests that the performance of division algebra based codes depends on several fundamental algebraic invariants of the underlying algebra.

  • inverse determinant sums and connections between fading channel information theory and algebra
    IEEE Transactions on Information Theory, 2013
    Co-Authors: Roope Vehkalahti, Hsiaofeng Lu, Laura Luzzi
    Abstract:

    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.

P V Kumar - One of the best experts on this subject based on the ideXlab platform.

  • d mg tradeoff and optimal codes for a class of af and df cooperative communication protocols
    IEEE Transactions on Information Theory, 2009
    Co-Authors: Petros Elia, K Vinodh, Madhukar Anand, P V Kumar
    Abstract:

    Cooperative relay communication in a fading channel environment under the orthogonal amplify-and-forward (OAF), nonorthogonal and orthogonal selection decode-and-forward (NSDF and OSDF) protocols is considered here. The diversity-Multiplexing Gain tradeoff (DMT) of the three protocols is determined and DMT-optimal distributed space-time (ST) code constructions are provided. The codes constructed are sphere decodable and in some instances incur minimum possible delay.

  • explicit space time codes achieving the diversity Multiplexing Gain tradeoff
    IEEE Transactions on Information Theory, 2006
    Co-Authors: Petros Elia, K R Kumar, Sameer Pawar, P V Kumar, Hsiaofeng Lu
    Abstract:

    A recent result of Zheng and Tse states that over a quasi-static channel, there exists a fundamental tradeoff, referred to as the diversity-Multiplexing Gain (D-MG) tradeoff, between the spatial Multiplexing Gain and the diversity Gain that can be simultaneously achieved by a space-time (ST) code. This tradeoff is precisely known in the case of independent and identically distributed (i.i.d.) Rayleigh fading, for Tgesnt+nr-1 where T is the number of time slots over which coding takes place and nt,nr are the number of transmit and receive antennas, respectively. For T nt case, we present two general techniques for building D-MG-optimal rectangular ST codes from their square counterparts. A byproduct of our results establishes that the D-MG tradeoff for all Tgesnt is the same as that previously known to hold for Tgesnt+n r-1

  • explicit space time codes that achieve the diversity Multiplexing Gain tradeoff
    International Symposium on Information Theory, 2005
    Co-Authors: Petros Elia, K R Kumar, Sameer Pawar, P V Kumar
    Abstract:

    In the recent landmark paper of Zheng and Tse it is shown for the quasi-static, Rayleigh-fading MIMO channel with nt transmit and nr receive antennas, that there exists a fundamental tradeoff between diversity Gain and Multiplexing Gain, referred to as the diversity-Multiplexing Gain (D-MG) tradeoff. This paper presents the first explicit construction of space-time (ST) codes for an arbitrary number of transmit and/or receive antennas that achieve the D-MG tradeoff. It is shown here that ST codes constructed from cyclic-division-algebras (CDA) and satisfying a certain non-vanishing determinant (NVD) property, are optimal under the D-MG tradeoff for any nt,nr. Furthermore, this optimality is achieved with minimum possible value of the delay or block-length parameter T = n t. CDA-based ST codes with NVD have previously been constructed for restricted values of nt. A unified construction of D-MG optimal CDA-based ST codes with NVD is given here, for any number nt of transmit antennas. The CDA-based constructions are also extended to provide D-MG optimal codes for all T ges nt, aGain for any number nt of transmit antennas. This extension thus presents rectangular D-MG optimal space-time codes that achieve the D-MG tradeoff. Taken together, the above constructions also extend the region of T for which the D-MG tradeoff is precisely known from T ges nt + nr - 1 to T ges nt

Mohamed Oussama Damen - One of the best experts on this subject based on the ideXlab platform.

  • the mimo arq channel diversity Multiplexing delay tradeoff
    IEEE Transactions on Information Theory, 2006
    Co-Authors: Hesham El Gamal, Giuseppe Caire, Mohamed Oussama Damen
    Abstract:

    In this paper, the fundamental performance tradeoff of the delay-limited multiple-input multiple-output (MIMO) automatic retransmission request (ARQ) channel is explored. In particular, we extend the diversity-Multiplexing tradeoff investigated by Zheng and Tse in standard delay-limited MIMO channels with coherent detection to the ARQ scenario. We establish the three-dimensional tradeoff between reliability (i.e., diversity), throughput (i.e., Multiplexing Gain), and delay (i.e., maximum number of retransmissions). This tradeoff quantifies the ARQ diversity Gain obtained by leveraging the retransmission delay to enhance the reliability for a given Multiplexing Gain. Interestingly, ARQ diversity appears even in long-term static channels where all the retransmissions take place in the same channel state. Furthermore, by relaxing the input power constraint allowing variable power levels in different retransmissions, we show that power control can be used to dramatically increase the diversity advantage. Our analysis reveals some important insights on the benefits of ARQ in slow-fading MIMO channels. In particular, we show that 1) allowing for a sufficiently large retransmission delay results in an almost flat diversity-Multiplexing tradeoff, and hence, renders operating at high Multiplexing Gain more advantageous; 2) MIMO ARQ channels quickly approach the ergodic limit when power control is employed. Finally, we complement our information-theoretic analysis with an incremental redundancy lattice space-time (IR-LAST) coding scheme which is shown, through a random coding argument, to achieve the optimal tradeoff(s). An integral component of the optimal IR-LAST coding scheme is a list decoder, based on the minimum mean-square error (MMSE) lattice decoding principle, for joint error detection and correction. Throughout the paper, our theoretical claims are validated by numerical results

  • the diversity Multiplexing delay tradeoff in mimo arq channels
    International Symposium on Information Theory, 2005
    Co-Authors: Hesham El Gamal, Giuseppe Caire, Mohamed Oussama Damen
    Abstract:

    In this paper, we explore the fundamental performance tradeoff of the delay-limited multi-input-multi-output (MIMO) automatic retransmission request (ARQ) channel. In particular, we extend the diversity-Multiplexing tradeoff investigated by Zheng and Tse in standard delay-limited MIMO channels with coherent detection to the ARQ scenario. We establish the three-dimensional tradeoff between reliability (i.e. diversity), throughput (i.e., Multiplexing Gain), and delay (i.e., maximum number of retransmissions). This tradeoff quantifies the ARQ diversity Gain obtained by leveraging the retransmission delay to enhance the reliability for a given Multiplexing Gain. Interestingly, ARQ diversity appears even in long-term static channels where all the retransmissions take place in the same channel state. Furthermore, by relaxing the input power constraint allowing variable power levels in different retransmissions, we show that power control can be used to dramatically increase the diversity advantage. Our analysis reveals some important insights on the benefits of ARQ in slow fading MIMO channels. In particular, we show that: 1) allowing for a sufficiently large retransmission delay results in an almost flat diversity-Multiplexing tradeoff, and hence, renders operating at high Multiplexing Gain more advantageous; 2) MIMO ARQ channels quickly approach the ergodic limit when power control is employed

Petros Elia - One of the best experts on this subject based on the ideXlab platform.

  • d mg tradeoff and optimal codes for a class of af and df cooperative communication protocols
    IEEE Transactions on Information Theory, 2009
    Co-Authors: Petros Elia, K Vinodh, Madhukar Anand, P V Kumar
    Abstract:

    Cooperative relay communication in a fading channel environment under the orthogonal amplify-and-forward (OAF), nonorthogonal and orthogonal selection decode-and-forward (NSDF and OSDF) protocols is considered here. The diversity-Multiplexing Gain tradeoff (DMT) of the three protocols is determined and DMT-optimal distributed space-time (ST) code constructions are provided. The codes constructed are sphere decodable and in some instances incur minimum possible delay.

  • explicit space time codes achieving the diversity Multiplexing Gain tradeoff
    IEEE Transactions on Information Theory, 2006
    Co-Authors: Petros Elia, K R Kumar, Sameer Pawar, P V Kumar, Hsiaofeng Lu
    Abstract:

    A recent result of Zheng and Tse states that over a quasi-static channel, there exists a fundamental tradeoff, referred to as the diversity-Multiplexing Gain (D-MG) tradeoff, between the spatial Multiplexing Gain and the diversity Gain that can be simultaneously achieved by a space-time (ST) code. This tradeoff is precisely known in the case of independent and identically distributed (i.i.d.) Rayleigh fading, for Tgesnt+nr-1 where T is the number of time slots over which coding takes place and nt,nr are the number of transmit and receive antennas, respectively. For T nt case, we present two general techniques for building D-MG-optimal rectangular ST codes from their square counterparts. A byproduct of our results establishes that the D-MG tradeoff for all Tgesnt is the same as that previously known to hold for Tgesnt+n r-1

  • explicit space time codes that achieve the diversity Multiplexing Gain tradeoff
    International Symposium on Information Theory, 2005
    Co-Authors: Petros Elia, K R Kumar, Sameer Pawar, P V Kumar
    Abstract:

    In the recent landmark paper of Zheng and Tse it is shown for the quasi-static, Rayleigh-fading MIMO channel with nt transmit and nr receive antennas, that there exists a fundamental tradeoff between diversity Gain and Multiplexing Gain, referred to as the diversity-Multiplexing Gain (D-MG) tradeoff. This paper presents the first explicit construction of space-time (ST) codes for an arbitrary number of transmit and/or receive antennas that achieve the D-MG tradeoff. It is shown here that ST codes constructed from cyclic-division-algebras (CDA) and satisfying a certain non-vanishing determinant (NVD) property, are optimal under the D-MG tradeoff for any nt,nr. Furthermore, this optimality is achieved with minimum possible value of the delay or block-length parameter T = n t. CDA-based ST codes with NVD have previously been constructed for restricted values of nt. A unified construction of D-MG optimal CDA-based ST codes with NVD is given here, for any number nt of transmit antennas. The CDA-based constructions are also extended to provide D-MG optimal codes for all T ges nt, aGain for any number nt of transmit antennas. This extension thus presents rectangular D-MG optimal space-time codes that achieve the D-MG tradeoff. Taken together, the above constructions also extend the region of T for which the D-MG tradeoff is precisely known from T ges nt + nr - 1 to T ges nt

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