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Error exponents for multi-keyhole MIMO channels

  • Information Theory
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Abstract

Along with the channel capacity, the error exponent is one of the most important information-theoretic measures of reliability, because it sets ultimate bounds on the performance of communication systems employing codes of finite complexity. In this paper, we derive closed-form expressions for the Gallager random coding and expurgated error exponents for multi-keyhole multiple-input multiple-output (MIMO) channels, which provide insights into a fundamental tradeoff between the communication reliability and information rate. We investigate the effect of keyholes on the error exponents and cutoff rate. Moreover, without an extensive Monte-Carlo simulation we can easily compute the codeword length necessary to achieve a predefined error probability at a given rate, which quantifies the effects of the number of antennas, channel coherence time, and the number of keyholes. In addition, we derive exact closed-form expressions for the ergodic capacity and cutoff rate based on the easily computable Meijer G-function. Finally, we extend our study to Rayleigh-product MIMO channels and keyhole MIMO channels.

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Authors and Affiliations

  1. Institute for Digital Communications, School of Engineering, The University of Edinburgh, Edinburgh, UK

    J. Xue & T. Ratnarajah

  2. Institute of Information and Communication Engineering, Zhejiang University, Zhejiang, China

    C. Zhong

  3. National Mobile Communications Research Laboratory, Southeast University, Nanjing, China

    C. Zhong

Authors
  1. J. Xue
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  2. T. Ratnarajah
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  3. C. Zhong
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Correspondence to J. Xue.

Additional information

Original Russian Text © J. Xue, T. Ratnarajah, C. Zhong, 2015, published in Problemy Peredachi Informatsii, 2015, Vol. 51, No. 1, pp. 3–22.

Supported in part by the UK Engineering and Physical Sciences Research Council (EPSRC), grant no. EP/I037156/2, funded by the UK government.

Supported in part by the National High-Tech. R&D Program of China under grant 2014AA01A705, the National Natural Science Foundation of China (61201229), the Zhejiang Science and Technology Department Public Project (2014C31051), the Fundamental Research Funds for Central Universities (2014QNA5019), and the open research fund of National Mobile Communications Research Laboratory, Southeast University (no. 2013D06).

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Xue, J., Ratnarajah, T. & Zhong, C. Error exponents for multi-keyhole MIMO channels. Probl Inf Transm 51, 1–19 (2015). https://doi.org/10.1134/S0032946015010019

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  • DOI: https://doi.org/10.1134/S0032946015010019

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