The Experts below are selected from a list of 6330 Experts worldwide ranked by ideXlab platform

Rodrigo De Miguel - One of the best experts on this subject based on the ideXlab platform.

  • Vector precoding for Gaussian MIMO broadcast channels: Impact of replica symmetry breaking
    2012
    Co-Authors: Benjamin M. Zaidel, Ralf R. Müller, Aris L. Moustakas, Rodrigo De Miguel
    Abstract:

    The “replica method” of statistical physics is employed for the large-system analysis of vector precoding for the Gaussian multiple-Input multiple-output broadcast channel. The transmitter comprises a linear front-end combined with nonlinear precoding, minimizing transmit energy by means of Input Alphabet relaxation. For the common discrete lattice-based relaxation, the problem violates replica symmetry and a replica symmetry breaking (RSB) ansatz is taken. The limiting empirical distribution of the precoder's output and the limiting transmit energy are derived for one-step RSB. Particularizing to a “zero-forcing” (ZF) linear front-end, a decoupling result is derived. For discrete lattice-based relaxations, the impact of RSB is demonstrated for the transmit energy. The spectral efficiencies of the aforementioned precoding methods are compared to linear ZF and Tomlinson-Harashima precoding (THP). Focusing on quaternary phase shift-keying (QPSK), significant performance gains of both lattice and convex relaxations are revealed for medium to high signal-to-noise ratios (SNRs) when compared to linear ZF precoding. THP is shown to be outperformed as well. Comparing certain lattice-based relaxations for QPSK against a convex counterpart, the latter is found to be superior for low and high SNRs but slightly inferior for medium SNRs in terms of spectral efficiency.

  • vector precoding for gaussian mimo broadcast channels impact of replica symmetry breaking
    2010
    Co-Authors: Benjamin M. Zaidel, Aris L. Moustakas, Ralf R Mueller, Rodrigo De Miguel
    Abstract:

    The so-called "replica method" of statistical physics is employed for the large system analysis of vector precoding for the Gaussian multiple-Input multiple-output (MIMO) broadcast channel. The transmitter is assumed to comprise a linear front-end combined with nonlinear precoding, that minimizes the front-end imposed transmit energy penalty. Focusing on discrete complex Input Alphabets, the energy penalty is minimized by relaxing the Input Alphabet to a larger Alphabet set prior to precoding. For the common discrete lattice-based relaxation, the problem is found to violate the assumption of replica symmetry and a replica symmetry breaking ansatz is taken. The limiting empirical distribution of the precoder's output, as well as the limiting energy penalty, are derived for one-step replica symmetry breaking. For convex relaxations, replica symmetry is found to hold and corresponding results are obtained for comparison. Particularizing to a "zero-forcing" (ZF) linear front-end, and non-cooperative users, a decoupling result is derived according to which the channel observed by each of the individual receivers can be effectively characterized by the Markov chain u-x-y, where u, x, and y are the channel Input, the equivalent precoder output, and the channel output, respectively. For discrete lattice-based Alphabet relaxation, the impact of replica symmetry breaking is demonstrated for the energy penalty at the transmitter. An analysis of spectral efficiency is provided to compare discrete lattice-based relaxations against convex relaxations, as well as linear ZF and Tomlinson-Harashima precoding (THP). Focusing on quaternary phase shift-keying (QPSK), significant performance gains of both lattice and convex relaxations are revealed compared to linear ZF precoding, for medium to high signal-to-noise ratios (SNRs). THP is shown to be outperformed as well.

  • on spectral efficiency of vector precoding for gaussian mimo broadcast channels
    2008
    Co-Authors: Benjamin M. Zaidel, Rodrigo De Miguel, Ralf R. Müller, Aris L. Moustakas
    Abstract:

    The spectral efficiency of practically oriented vector precoding schemes for the Gaussian multiple-Input multiple- output (MIMO) broadcast channel is analyzed in the large system limit. Considering discrete complex Input Alphabets, the transmitter is assumed to comprise a linear front-end combined with nonlinear precoding, that minimizes the transmit energy penalty imposed by the linear front-end. The energy penalty is minimized by relaxing the Input Alphabet to a larger Alphabet set prior to precoding. The so-called "replica method" of statistical physics is employed to derive the limiting empirical distribution of the precoder's output, as well as the limiting energy penalty. Particularizing to a "zero-forcing" (ZF) linear front-end, and non- cooperative users, a decoupling result is derived according to which the channel observed by each of the individual receivers can be characterized by the Markov chain u-x-y ,w hereu is the channel Input, x is the equivalent precoder output, and y is the channel output. A comparative spectral efficiency analysis of two illustrative examples reveals significant performance gains com- pared to linear ZF precoding in the medium to high Eb/N0 region. In particular, we demonstrate that convex extended Alphabets, amenable to efficient energy minimization algorithms, provide an attractive alternative to Alphabets based on the discrete Gaussian integer lattice, for which the energy minimization problem is NP- hard.

  • on replica symmetry breaking in vector precoding for the gaussian mimo broadcast channel
    2008
    Co-Authors: Benjamin M. Zaidel, Rodrigo De Miguel, Ralf R. Müller, Aris L. Moustakas
    Abstract:

    The so-called ldquoreplica methodrdquo of statistical physics is employed for the large system analysis of vector precoding for the Gaussian multiple-Input multiple-output (MIMO) broadcast channel. Focusing on discrete complex Input Alphabets, the transmitter is assumed to comprise a linear front-end combined with nonlinear precoding, that minimizes the front-end imposed transmit energy penalty. The energy penalty is minimized by relaxing the Input Alphabet to a larger Alphabet set prior to precoding. The limiting empirical distribution of the precoder's output, as well as the limiting energy penalty, are derived while harnessing what is referred to as the first order replica symmetry breaking (1RSB) ansatz. Particularizing to a ldquozero-forcingrdquo (ZF) linear front-end, and non-cooperative users, a decoupling result is derived according to which the channel observed by each of the individual receivers can be effectively characterized by the Markov chain u-x-y, where u is the channel Input, x is the equivalent precoder output, and y is the channel output. An illustrative example is considered, based on discrete-lattice Alphabet relaxation, for which the impact of replica symmetry breaking is demonstrated. A comparative spectral efficiency analysis reveals significant performance gains compared to linear ZF precoding in the medium to high Eb/N0 region. The performance vs. complexity tradeoff of the nonlinear precoding scheme is also shortly discussed.

Aris L. Moustakas - One of the best experts on this subject based on the ideXlab platform.

  • Vector precoding for Gaussian MIMO broadcast channels: Impact of replica symmetry breaking
    2012
    Co-Authors: Benjamin M. Zaidel, Ralf R. Müller, Aris L. Moustakas, Rodrigo De Miguel
    Abstract:

    The “replica method” of statistical physics is employed for the large-system analysis of vector precoding for the Gaussian multiple-Input multiple-output broadcast channel. The transmitter comprises a linear front-end combined with nonlinear precoding, minimizing transmit energy by means of Input Alphabet relaxation. For the common discrete lattice-based relaxation, the problem violates replica symmetry and a replica symmetry breaking (RSB) ansatz is taken. The limiting empirical distribution of the precoder's output and the limiting transmit energy are derived for one-step RSB. Particularizing to a “zero-forcing” (ZF) linear front-end, a decoupling result is derived. For discrete lattice-based relaxations, the impact of RSB is demonstrated for the transmit energy. The spectral efficiencies of the aforementioned precoding methods are compared to linear ZF and Tomlinson-Harashima precoding (THP). Focusing on quaternary phase shift-keying (QPSK), significant performance gains of both lattice and convex relaxations are revealed for medium to high signal-to-noise ratios (SNRs) when compared to linear ZF precoding. THP is shown to be outperformed as well. Comparing certain lattice-based relaxations for QPSK against a convex counterpart, the latter is found to be superior for low and high SNRs but slightly inferior for medium SNRs in terms of spectral efficiency.

  • vector precoding for gaussian mimo broadcast channels impact of replica symmetry breaking
    2010
    Co-Authors: Benjamin M. Zaidel, Aris L. Moustakas, Ralf R Mueller, Rodrigo De Miguel
    Abstract:

    The so-called "replica method" of statistical physics is employed for the large system analysis of vector precoding for the Gaussian multiple-Input multiple-output (MIMO) broadcast channel. The transmitter is assumed to comprise a linear front-end combined with nonlinear precoding, that minimizes the front-end imposed transmit energy penalty. Focusing on discrete complex Input Alphabets, the energy penalty is minimized by relaxing the Input Alphabet to a larger Alphabet set prior to precoding. For the common discrete lattice-based relaxation, the problem is found to violate the assumption of replica symmetry and a replica symmetry breaking ansatz is taken. The limiting empirical distribution of the precoder's output, as well as the limiting energy penalty, are derived for one-step replica symmetry breaking. For convex relaxations, replica symmetry is found to hold and corresponding results are obtained for comparison. Particularizing to a "zero-forcing" (ZF) linear front-end, and non-cooperative users, a decoupling result is derived according to which the channel observed by each of the individual receivers can be effectively characterized by the Markov chain u-x-y, where u, x, and y are the channel Input, the equivalent precoder output, and the channel output, respectively. For discrete lattice-based Alphabet relaxation, the impact of replica symmetry breaking is demonstrated for the energy penalty at the transmitter. An analysis of spectral efficiency is provided to compare discrete lattice-based relaxations against convex relaxations, as well as linear ZF and Tomlinson-Harashima precoding (THP). Focusing on quaternary phase shift-keying (QPSK), significant performance gains of both lattice and convex relaxations are revealed compared to linear ZF precoding, for medium to high signal-to-noise ratios (SNRs). THP is shown to be outperformed as well.

  • on spectral efficiency of vector precoding for gaussian mimo broadcast channels
    2008
    Co-Authors: Benjamin M. Zaidel, Rodrigo De Miguel, Ralf R. Müller, Aris L. Moustakas
    Abstract:

    The spectral efficiency of practically oriented vector precoding schemes for the Gaussian multiple-Input multiple- output (MIMO) broadcast channel is analyzed in the large system limit. Considering discrete complex Input Alphabets, the transmitter is assumed to comprise a linear front-end combined with nonlinear precoding, that minimizes the transmit energy penalty imposed by the linear front-end. The energy penalty is minimized by relaxing the Input Alphabet to a larger Alphabet set prior to precoding. The so-called "replica method" of statistical physics is employed to derive the limiting empirical distribution of the precoder's output, as well as the limiting energy penalty. Particularizing to a "zero-forcing" (ZF) linear front-end, and non- cooperative users, a decoupling result is derived according to which the channel observed by each of the individual receivers can be characterized by the Markov chain u-x-y ,w hereu is the channel Input, x is the equivalent precoder output, and y is the channel output. A comparative spectral efficiency analysis of two illustrative examples reveals significant performance gains com- pared to linear ZF precoding in the medium to high Eb/N0 region. In particular, we demonstrate that convex extended Alphabets, amenable to efficient energy minimization algorithms, provide an attractive alternative to Alphabets based on the discrete Gaussian integer lattice, for which the energy minimization problem is NP- hard.

  • on replica symmetry breaking in vector precoding for the gaussian mimo broadcast channel
    2008
    Co-Authors: Benjamin M. Zaidel, Rodrigo De Miguel, Ralf R. Müller, Aris L. Moustakas
    Abstract:

    The so-called ldquoreplica methodrdquo of statistical physics is employed for the large system analysis of vector precoding for the Gaussian multiple-Input multiple-output (MIMO) broadcast channel. Focusing on discrete complex Input Alphabets, the transmitter is assumed to comprise a linear front-end combined with nonlinear precoding, that minimizes the front-end imposed transmit energy penalty. The energy penalty is minimized by relaxing the Input Alphabet to a larger Alphabet set prior to precoding. The limiting empirical distribution of the precoder's output, as well as the limiting energy penalty, are derived while harnessing what is referred to as the first order replica symmetry breaking (1RSB) ansatz. Particularizing to a ldquozero-forcingrdquo (ZF) linear front-end, and non-cooperative users, a decoupling result is derived according to which the channel observed by each of the individual receivers can be effectively characterized by the Markov chain u-x-y, where u is the channel Input, x is the equivalent precoder output, and y is the channel output. An illustrative example is considered, based on discrete-lattice Alphabet relaxation, for which the impact of replica symmetry breaking is demonstrated. A comparative spectral efficiency analysis reveals significant performance gains compared to linear ZF precoding in the medium to high Eb/N0 region. The performance vs. complexity tradeoff of the nonlinear precoding scheme is also shortly discussed.

Benjamin M. Zaidel - One of the best experts on this subject based on the ideXlab platform.

  • Vector precoding for Gaussian MIMO broadcast channels: Impact of replica symmetry breaking
    2012
    Co-Authors: Benjamin M. Zaidel, Ralf R. Müller, Aris L. Moustakas, Rodrigo De Miguel
    Abstract:

    The “replica method” of statistical physics is employed for the large-system analysis of vector precoding for the Gaussian multiple-Input multiple-output broadcast channel. The transmitter comprises a linear front-end combined with nonlinear precoding, minimizing transmit energy by means of Input Alphabet relaxation. For the common discrete lattice-based relaxation, the problem violates replica symmetry and a replica symmetry breaking (RSB) ansatz is taken. The limiting empirical distribution of the precoder's output and the limiting transmit energy are derived for one-step RSB. Particularizing to a “zero-forcing” (ZF) linear front-end, a decoupling result is derived. For discrete lattice-based relaxations, the impact of RSB is demonstrated for the transmit energy. The spectral efficiencies of the aforementioned precoding methods are compared to linear ZF and Tomlinson-Harashima precoding (THP). Focusing on quaternary phase shift-keying (QPSK), significant performance gains of both lattice and convex relaxations are revealed for medium to high signal-to-noise ratios (SNRs) when compared to linear ZF precoding. THP is shown to be outperformed as well. Comparing certain lattice-based relaxations for QPSK against a convex counterpart, the latter is found to be superior for low and high SNRs but slightly inferior for medium SNRs in terms of spectral efficiency.

  • vector precoding for gaussian mimo broadcast channels impact of replica symmetry breaking
    2010
    Co-Authors: Benjamin M. Zaidel, Aris L. Moustakas, Ralf R Mueller, Rodrigo De Miguel
    Abstract:

    The so-called "replica method" of statistical physics is employed for the large system analysis of vector precoding for the Gaussian multiple-Input multiple-output (MIMO) broadcast channel. The transmitter is assumed to comprise a linear front-end combined with nonlinear precoding, that minimizes the front-end imposed transmit energy penalty. Focusing on discrete complex Input Alphabets, the energy penalty is minimized by relaxing the Input Alphabet to a larger Alphabet set prior to precoding. For the common discrete lattice-based relaxation, the problem is found to violate the assumption of replica symmetry and a replica symmetry breaking ansatz is taken. The limiting empirical distribution of the precoder's output, as well as the limiting energy penalty, are derived for one-step replica symmetry breaking. For convex relaxations, replica symmetry is found to hold and corresponding results are obtained for comparison. Particularizing to a "zero-forcing" (ZF) linear front-end, and non-cooperative users, a decoupling result is derived according to which the channel observed by each of the individual receivers can be effectively characterized by the Markov chain u-x-y, where u, x, and y are the channel Input, the equivalent precoder output, and the channel output, respectively. For discrete lattice-based Alphabet relaxation, the impact of replica symmetry breaking is demonstrated for the energy penalty at the transmitter. An analysis of spectral efficiency is provided to compare discrete lattice-based relaxations against convex relaxations, as well as linear ZF and Tomlinson-Harashima precoding (THP). Focusing on quaternary phase shift-keying (QPSK), significant performance gains of both lattice and convex relaxations are revealed compared to linear ZF precoding, for medium to high signal-to-noise ratios (SNRs). THP is shown to be outperformed as well.

  • on spectral efficiency of vector precoding for gaussian mimo broadcast channels
    2008
    Co-Authors: Benjamin M. Zaidel, Rodrigo De Miguel, Ralf R. Müller, Aris L. Moustakas
    Abstract:

    The spectral efficiency of practically oriented vector precoding schemes for the Gaussian multiple-Input multiple- output (MIMO) broadcast channel is analyzed in the large system limit. Considering discrete complex Input Alphabets, the transmitter is assumed to comprise a linear front-end combined with nonlinear precoding, that minimizes the transmit energy penalty imposed by the linear front-end. The energy penalty is minimized by relaxing the Input Alphabet to a larger Alphabet set prior to precoding. The so-called "replica method" of statistical physics is employed to derive the limiting empirical distribution of the precoder's output, as well as the limiting energy penalty. Particularizing to a "zero-forcing" (ZF) linear front-end, and non- cooperative users, a decoupling result is derived according to which the channel observed by each of the individual receivers can be characterized by the Markov chain u-x-y ,w hereu is the channel Input, x is the equivalent precoder output, and y is the channel output. A comparative spectral efficiency analysis of two illustrative examples reveals significant performance gains com- pared to linear ZF precoding in the medium to high Eb/N0 region. In particular, we demonstrate that convex extended Alphabets, amenable to efficient energy minimization algorithms, provide an attractive alternative to Alphabets based on the discrete Gaussian integer lattice, for which the energy minimization problem is NP- hard.

  • on replica symmetry breaking in vector precoding for the gaussian mimo broadcast channel
    2008
    Co-Authors: Benjamin M. Zaidel, Rodrigo De Miguel, Ralf R. Müller, Aris L. Moustakas
    Abstract:

    The so-called ldquoreplica methodrdquo of statistical physics is employed for the large system analysis of vector precoding for the Gaussian multiple-Input multiple-output (MIMO) broadcast channel. Focusing on discrete complex Input Alphabets, the transmitter is assumed to comprise a linear front-end combined with nonlinear precoding, that minimizes the front-end imposed transmit energy penalty. The energy penalty is minimized by relaxing the Input Alphabet to a larger Alphabet set prior to precoding. The limiting empirical distribution of the precoder's output, as well as the limiting energy penalty, are derived while harnessing what is referred to as the first order replica symmetry breaking (1RSB) ansatz. Particularizing to a ldquozero-forcingrdquo (ZF) linear front-end, and non-cooperative users, a decoupling result is derived according to which the channel observed by each of the individual receivers can be effectively characterized by the Markov chain u-x-y, where u is the channel Input, x is the equivalent precoder output, and y is the channel output. An illustrative example is considered, based on discrete-lattice Alphabet relaxation, for which the impact of replica symmetry breaking is demonstrated. A comparative spectral efficiency analysis reveals significant performance gains compared to linear ZF precoding in the medium to high Eb/N0 region. The performance vs. complexity tradeoff of the nonlinear precoding scheme is also shortly discussed.

Ralf R. Müller - One of the best experts on this subject based on the ideXlab platform.

  • Vector precoding for Gaussian MIMO broadcast channels: Impact of replica symmetry breaking
    2012
    Co-Authors: Benjamin M. Zaidel, Ralf R. Müller, Aris L. Moustakas, Rodrigo De Miguel
    Abstract:

    The “replica method” of statistical physics is employed for the large-system analysis of vector precoding for the Gaussian multiple-Input multiple-output broadcast channel. The transmitter comprises a linear front-end combined with nonlinear precoding, minimizing transmit energy by means of Input Alphabet relaxation. For the common discrete lattice-based relaxation, the problem violates replica symmetry and a replica symmetry breaking (RSB) ansatz is taken. The limiting empirical distribution of the precoder's output and the limiting transmit energy are derived for one-step RSB. Particularizing to a “zero-forcing” (ZF) linear front-end, a decoupling result is derived. For discrete lattice-based relaxations, the impact of RSB is demonstrated for the transmit energy. The spectral efficiencies of the aforementioned precoding methods are compared to linear ZF and Tomlinson-Harashima precoding (THP). Focusing on quaternary phase shift-keying (QPSK), significant performance gains of both lattice and convex relaxations are revealed for medium to high signal-to-noise ratios (SNRs) when compared to linear ZF precoding. THP is shown to be outperformed as well. Comparing certain lattice-based relaxations for QPSK against a convex counterpart, the latter is found to be superior for low and high SNRs but slightly inferior for medium SNRs in terms of spectral efficiency.

  • on spectral efficiency of vector precoding for gaussian mimo broadcast channels
    2008
    Co-Authors: Benjamin M. Zaidel, Rodrigo De Miguel, Ralf R. Müller, Aris L. Moustakas
    Abstract:

    The spectral efficiency of practically oriented vector precoding schemes for the Gaussian multiple-Input multiple- output (MIMO) broadcast channel is analyzed in the large system limit. Considering discrete complex Input Alphabets, the transmitter is assumed to comprise a linear front-end combined with nonlinear precoding, that minimizes the transmit energy penalty imposed by the linear front-end. The energy penalty is minimized by relaxing the Input Alphabet to a larger Alphabet set prior to precoding. The so-called "replica method" of statistical physics is employed to derive the limiting empirical distribution of the precoder's output, as well as the limiting energy penalty. Particularizing to a "zero-forcing" (ZF) linear front-end, and non- cooperative users, a decoupling result is derived according to which the channel observed by each of the individual receivers can be characterized by the Markov chain u-x-y ,w hereu is the channel Input, x is the equivalent precoder output, and y is the channel output. A comparative spectral efficiency analysis of two illustrative examples reveals significant performance gains com- pared to linear ZF precoding in the medium to high Eb/N0 region. In particular, we demonstrate that convex extended Alphabets, amenable to efficient energy minimization algorithms, provide an attractive alternative to Alphabets based on the discrete Gaussian integer lattice, for which the energy minimization problem is NP- hard.

  • on replica symmetry breaking in vector precoding for the gaussian mimo broadcast channel
    2008
    Co-Authors: Benjamin M. Zaidel, Rodrigo De Miguel, Ralf R. Müller, Aris L. Moustakas
    Abstract:

    The so-called ldquoreplica methodrdquo of statistical physics is employed for the large system analysis of vector precoding for the Gaussian multiple-Input multiple-output (MIMO) broadcast channel. Focusing on discrete complex Input Alphabets, the transmitter is assumed to comprise a linear front-end combined with nonlinear precoding, that minimizes the front-end imposed transmit energy penalty. The energy penalty is minimized by relaxing the Input Alphabet to a larger Alphabet set prior to precoding. The limiting empirical distribution of the precoder's output, as well as the limiting energy penalty, are derived while harnessing what is referred to as the first order replica symmetry breaking (1RSB) ansatz. Particularizing to a ldquozero-forcingrdquo (ZF) linear front-end, and non-cooperative users, a decoupling result is derived according to which the channel observed by each of the individual receivers can be effectively characterized by the Markov chain u-x-y, where u is the channel Input, x is the equivalent precoder output, and y is the channel output. An illustrative example is considered, based on discrete-lattice Alphabet relaxation, for which the impact of replica symmetry breaking is demonstrated. A comparative spectral efficiency analysis reveals significant performance gains compared to linear ZF precoding in the medium to high Eb/N0 region. The performance vs. complexity tradeoff of the nonlinear precoding scheme is also shortly discussed.

  • on the capacity loss due to separation of detection and decoding
    2004
    Co-Authors: Ralf R. Müller, Wolfgang H Gerstacker
    Abstract:

    The performance loss due to separation of detection and decoding on the binary-Input additive white Gaussian noise (AWGN) channel is quantified in terms of mutual information. Results are reported for both the code-division multiple-access (CDMA) channel in the large system limit and the intersymbol interference (ISI) channel. The results for CDMA rely on the replica method developed in statistical mechanics. It is shown that a previous result of Shamai and Verdu found for Gaussian Input Alphabet holds also for binary Input Alphabets. For the ISI channel, the performance loss is calculated via the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm. Comparisons are made to the capacity of separate detection and decoding using suboptimum detectors such as a decision-feedback equalizer.

Ido Tal - One of the best experts on this subject based on the ideXlab platform.

  • On the Construction of Polar Codes for Channels With Moderate Input Alphabet Sizes
    2017
    Co-Authors: Ido Tal
    Abstract:

    Current deterministic algorithms for the construction of polar codes can only be argued to be practical for channels with small Input Alphabet sizes. In this paper, we show that any construction algorithm for channels with moderate Input Alphabet size, which follows the paradigm of “degrading after each polarization step,” will inherently be impractical with respect to a certain “hard” underlying channel. This result also sheds light on why the construction of low-density parity-check codes using density evolution is impractical for channels with moderate-sized Input Alphabets.

  • On the Construction of Polar Codes for Channels with Moderate Input Alphabet Sizes
    2015
    Co-Authors: Ido Tal
    Abstract:

    Current deterministic algorithms for the construction of polar codes can only be argued to be practical for channels with small Input Alphabet sizes. In this paper, we show that any construction algorithm for channels with moderate Input Alphabet size which follows the paradigm of "degrading after each polarization step" will inherently be impractical with respect to a certain "hard" underlying channel. This result also sheds light on why the construction of LDPC codes using density evolution is impractical for channels with moderate sized Input Alphabets.

  • on the construction of polar codes for channels with moderate Input Alphabet sizes
    2015
    Co-Authors: Ido Tal
    Abstract:

    Current deterministic algorithms for the construction of polar codes cannot be argued to be practical for channels with Input Alphabets of moderate size. In this paper, we show that any construction algorithm which follows the paradigm of “degrading after each polarization step” will inherently be impractical with respect to a certain “hard” underlying channel having an Input Alphabet of moderate size. This result also sheds light on why the construction of LDPC codes using density evolution is impractical for channels with moderate sized Input Alphabets.