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Hideki Yagi - One of the best experts on this subject based on the ideXlab platform.

  • single bit quantization of Binary Input continuous output channels
    International Symposium on Information Theory, 2017
    Co-Authors: Brian M. Kurkoski, Hideki Yagi
    Abstract:

    A Binary-Input, memoryless channel with a continuous-valued output quantized to one bit is considered. For arbitrary noise models, conditions on an optimal quantizer, in the sense of maximizing mutual information between the channel Input and the quantizer output, are given. This result is obtained by considering the “backward” channel and applying Burshtein et al.'s theorem on optimal classification. In this backward channel, there exists an optimal quantizer for which the quantizer preimage is convex. It is possible no optimal forward quantizer is convex, but by working with the backward channel, the optimal quantizer may be found. However, if the channel satisfies a certain condition, then a convex optimal forward quantizer exists.

  • ISIT - Single-bit quantization of Binary-Input, continuous-output channels
    2017 IEEE International Symposium on Information Theory (ISIT), 2017
    Co-Authors: Brian M. Kurkoski, Hideki Yagi
    Abstract:

    A Binary-Input, memoryless channel with a continuous-valued output quantized to one bit is considered. For arbitrary noise models, conditions on an optimal quantizer, in the sense of maximizing mutual information between the channel Input and the quantizer output, are given. This result is obtained by considering the “backward” channel and applying Burshtein et al.'s theorem on optimal classification. In this backward channel, there exists an optimal quantizer for which the quantizer preimage is convex. It is possible no optimal forward quantizer is convex, but by working with the backward channel, the optimal quantizer may be found. However, if the channel satisfies a certain condition, then a convex optimal forward quantizer exists.

  • Quantization of Binary-Input Discrete Memoryless Channels
    IEEE Transactions on Information Theory, 2014
    Co-Authors: Brian M. Kurkoski, Hideki Yagi
    Abstract:

    The quantization of the output of a Binary-Input discrete memoryless channel to a smaller number of levels is considered. An algorithm, which finds an optimal quantizer, in the sense of maximizing mutual information between the channel Input and quantizer output is given. This result holds for arbitrary channels, in contrast to previous results for restricted channels or a restricted number of quantizer outputs. In the worst case, the algorithm complexity is cubic M 3 in the number of channel outputs M. Optimality is proved using the theorem of Burshtein, Della Pietra, Kanevsky, and Nadas for mappings, which minimize average impurity for classification and regression trees.

  • finding the capacity of a quantized Binary Input dmc
    International Symposium on Information Theory, 2012
    Co-Authors: Brian M. Kurkoski, Hideki Yagi
    Abstract:

    Consider a Binary-Input, M-output discrete memoryless channel (DMC) where the outputs are quantized to K levels, with K < M. The subject of this paper is the maximization of mutual information between the Input and quantizer output, over both the Input distribution and channel quantizer. This can be regarded as finding the capacity of a quantized DMC. An algorithm is given, which either finds the optimal Input distribution and corresponding quantizer, or declares a failure.

  • channel quantizers that maximize random coding exponents for Binary Input memoryless channels
    International Conference on Communications, 2012
    Co-Authors: Hideki Yagi, Brian M. Kurkoski
    Abstract:

    The problem of finding the optimum output quantizer for a given discrete memoryless channel is investigated, where the quantizer output has fewer values than the channel output. While mutual information has received attention as an objective function for optimization, the focus of this paper is use of the random coding exponent, which was originally derived by Gallager, as criteria. Two problems are addressed, where one problem is a partial problem of the other. The main result is a quantizer design algorithm, and a proof that it finds the optimum quantizer in the partial problem. The quantizer design algorithm is based on a dynamic programming approach, and is an extension of a mutual-information maximization method. For the Binary-Input case, it is shown that the optimum quantizer can be found with complexity that is polynomial in the number of channel outputs.

Saygun Onay - One of the best experts on this subject based on the ideXlab platform.

Brian M. Kurkoski - One of the best experts on this subject based on the ideXlab platform.

  • single bit quantization of Binary Input continuous output channels
    International Symposium on Information Theory, 2017
    Co-Authors: Brian M. Kurkoski, Hideki Yagi
    Abstract:

    A Binary-Input, memoryless channel with a continuous-valued output quantized to one bit is considered. For arbitrary noise models, conditions on an optimal quantizer, in the sense of maximizing mutual information between the channel Input and the quantizer output, are given. This result is obtained by considering the “backward” channel and applying Burshtein et al.'s theorem on optimal classification. In this backward channel, there exists an optimal quantizer for which the quantizer preimage is convex. It is possible no optimal forward quantizer is convex, but by working with the backward channel, the optimal quantizer may be found. However, if the channel satisfies a certain condition, then a convex optimal forward quantizer exists.

  • ISIT - Single-bit quantization of Binary-Input, continuous-output channels
    2017 IEEE International Symposium on Information Theory (ISIT), 2017
    Co-Authors: Brian M. Kurkoski, Hideki Yagi
    Abstract:

    A Binary-Input, memoryless channel with a continuous-valued output quantized to one bit is considered. For arbitrary noise models, conditions on an optimal quantizer, in the sense of maximizing mutual information between the channel Input and the quantizer output, are given. This result is obtained by considering the “backward” channel and applying Burshtein et al.'s theorem on optimal classification. In this backward channel, there exists an optimal quantizer for which the quantizer preimage is convex. It is possible no optimal forward quantizer is convex, but by working with the backward channel, the optimal quantizer may be found. However, if the channel satisfies a certain condition, then a convex optimal forward quantizer exists.

  • Quantization of Binary-Input Discrete Memoryless Channels
    IEEE Transactions on Information Theory, 2014
    Co-Authors: Brian M. Kurkoski, Hideki Yagi
    Abstract:

    The quantization of the output of a Binary-Input discrete memoryless channel to a smaller number of levels is considered. An algorithm, which finds an optimal quantizer, in the sense of maximizing mutual information between the channel Input and quantizer output is given. This result holds for arbitrary channels, in contrast to previous results for restricted channels or a restricted number of quantizer outputs. In the worst case, the algorithm complexity is cubic M 3 in the number of channel outputs M. Optimality is proved using the theorem of Burshtein, Della Pietra, Kanevsky, and Nadas for mappings, which minimize average impurity for classification and regression trees.

  • finding the capacity of a quantized Binary Input dmc
    International Symposium on Information Theory, 2012
    Co-Authors: Brian M. Kurkoski, Hideki Yagi
    Abstract:

    Consider a Binary-Input, M-output discrete memoryless channel (DMC) where the outputs are quantized to K levels, with K < M. The subject of this paper is the maximization of mutual information between the Input and quantizer output, over both the Input distribution and channel quantizer. This can be regarded as finding the capacity of a quantized DMC. An algorithm is given, which either finds the optimal Input distribution and corresponding quantizer, or declares a failure.

  • channel quantizers that maximize random coding exponents for Binary Input memoryless channels
    International Conference on Communications, 2012
    Co-Authors: Hideki Yagi, Brian M. Kurkoski
    Abstract:

    The problem of finding the optimum output quantizer for a given discrete memoryless channel is investigated, where the quantizer output has fewer values than the channel output. While mutual information has received attention as an objective function for optimization, the focus of this paper is use of the random coding exponent, which was originally derived by Gallager, as criteria. Two problems are addressed, where one problem is a partial problem of the other. The main result is a quantizer design algorithm, and a proof that it finds the optimum quantizer in the partial problem. The quantizer design algorithm is based on a dynamic programming approach, and is an extension of a mutual-information maximization method. For the Binary-Input case, it is shown that the optimum quantizer can be found with complexity that is polynomial in the number of channel outputs.

Toshiyuki Tanaka - One of the best experts on this subject based on the ideXlab platform.

  • performance and construction of polar codes on symmetric Binary Input memoryless channels
    International Symposium on Information Theory, 2009
    Co-Authors: Ryuhei Mori, Toshiyuki Tanaka
    Abstract:

    Channel polarization is a method of constructing capacity achieving codes for symmetric Binary-Input discrete memoryless channels (B-DMCs) [1]. In the original paper, the construction complexity is exponential in the blocklength. In this paper, a new construction method for arbitrary symmetric Binary memoryless channel (B-MC) with linear complexity in the blocklength is proposed. Furthermore, new upper bound and lower bound of the block error probability of polar codes are derived for the BEC and arbitrary symmetric B-MC, respectively.

  • Performance and Construction of Polar Codes on Symmetric Binary-Input Memoryless Channels
    arXiv: Information Theory, 2009
    Co-Authors: Ryuhei Mori, Toshiyuki Tanaka
    Abstract:

    Channel polarization is a method of constructing capacity achieving codes for symmetric Binary-Input discrete memoryless channels (B-DMCs) [1]. In the original paper, the construction complexity is exponential in the blocklength. In this paper, a new construction method for arbitrary symmetric Binary memoryless channel (B-MC) with linear complexity in the blocklength is proposed. Furthermore, new upper and lower bounds of the block error probability of polar codes are derived for the BEC and the arbitrary symmetric B-MC, respectively.

  • ISIT - Performance and construction of polar codes on symmetric Binary-Input memoryless channels
    2009 IEEE International Symposium on Information Theory, 2009
    Co-Authors: Ryuhei Mori, Toshiyuki Tanaka
    Abstract:

    Channel polarization is a method of constructing capacity achieving codes for symmetric Binary-Input discrete memoryless channels (B-DMCs) [1]. In the original paper, the construction complexity is exponential in the blocklength. In this paper, a new construction method for arbitrary symmetric Binary memoryless channel (B-MC) with linear complexity in the blocklength is proposed. Furthermore, new upper bound and lower bound of the block error probability of polar codes are derived for the BEC and arbitrary symmetric B-MC, respectively.

Satish Babu Korada - One of the best experts on this subject based on the ideXlab platform.

  • Tight Bounds on the Capacity of Binary Input Random CDMA Systems
    IEEE Transactions on Information Theory, 2010
    Co-Authors: Satish Babu Korada, Nicolas Macris
    Abstract:

    In this paper, we consider code-division multiple-access (CDMA) communication over a Binary Input additive white Gaussian noise (AWGN) channel using random spreading. For a general class of symmetric distributions for spreading sequences, in the limit of a large number of users, we prove an upper bound to the capacity. The bound matches the formula obtained by Tanaka using the replica method. We also show concentration of various relevant quantities including mutual information and free energy. The mathematical methods are quite general and allow us to discuss extensions to other multiuser scenarios.

  • a class of transformations that polarize Binary Input memoryless channels
    International Symposium on Information Theory, 2009
    Co-Authors: Satish Babu Korada, Eren Sasoglu
    Abstract:

    A generalization of Arikan's polar code construction using transformations of the form G⊗n where G is an l × l matrix is considered. Necessary and sufficient conditions are given for these transformations to ensure channel polarization. It is shown that a large class of such transformations polarize Binary-Input memoryless channels.

  • ISIT - A class of transformations that polarize Binary-Input memoryless channels
    2009 IEEE International Symposium on Information Theory, 2009
    Co-Authors: Satish Babu Korada, Eren Sasoglu
    Abstract:

    A generalization of Arikan's polar code construction using transformations of the form G⊗n where G is an l × l matrix is considered. Necessary and sufficient conditions are given for these transformations to ensure channel polarization. It is shown that a large class of such transformations polarize Binary-Input memoryless channels.

  • A Class of Transformations that Polarize Symmetric Binary-Input Memoryless Channels
    arXiv: Information Theory, 2008
    Co-Authors: Satish Babu Korada, Eren Sasoglu
    Abstract:

    A generalization of Ar\i kan's polar code construction using transformations of the form $G^{\otimes n}$ where $G$ is an $\ell \times \ell$ matrix is considered. Necessary and sufficient conditions are given for these transformations to ensure channel polarization. It is shown that a large class of such transformations polarize symmetric Binary-Input memoryless channels.

  • Tight Bounds on the Capacity of Binary Input random CDMA Systems
    arXiv: Information Theory, 2008
    Co-Authors: Satish Babu Korada, Nicolas Macris
    Abstract:

    We consider multiple access communication on a Binary Input additive white Gaussian noise channel using randomly spread code division. For a general class of symmetric distributions for spreading coefficients, in the limit of a large number of users, we prove an upper bound on the capacity, which matches a formula that Tanaka obtained by using the replica method. We also show concentration of various relevant quantities including mutual information, capacity and free energy. The mathematical methods are quite general and allow us to discuss extensions to other multiuser scenarios.