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Communications in Interference Limited Networks pp 31–52Cite as

Modulo-Type Precoding for Networks

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Part of the book series: Signals and Communication Technology ((SCT))

Abstract

In this chapter, we address scenarios where the tasks of (modulo-type) precoding for the multiple-input/multiple-output (MIMO) broadcast channel, network coding with its associated finite-field matrix channel, and channel coding meet or complement each other. By enlightening dualities, similarities, and differences between the areas and corresponding schemes, a deeper understanding of their mutual interaction is gained. Moreover, this allows for a transfer of schemes and strategies from one field to another one. Exemplarily, schemes operating at the intersection of complex-valued and finite-field/modulo processing are addressed. First, an overview on modulo-type precoding and its latest version via finite-field preprocessing is given; the connections and specific restrictions of the different approaches are illustrated. The advantages of modulo-type precoding are addressed when additional requirements, such as per-antenna power constraints and a reduced degree of coordination in a network MIMO scenario, are imposed. Finally, the application of precoding to finite-field channels is discussed, either as differential network coding or as selection precoding.

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Notes

  1. 1.

    If, in addition to the multi-user interference, intersymbol interference (ISI) occurs, the usual way is to apply orthogonal frequency-division multiplexing (OFDM) to deal with the ISI. The MIMO model is then valid per subcarrier.

  2. 2.

    In terms of RLNC, one channel usage, i.e., the transmission of one transmit and the reception of one receive matrix, is called one generation. In terms of the BC, this is a transmission burst.

  3. 3.

    All results in this section are displayed over the ratio of transmitted energy per information bit \(E_\mathrm {b}\) and one-sided noise power spectral density \(N_0'\), where the average channel attenuation is eliminated. For details on the normalization, see [6].

  4. 4.

    Again, we assume the network channel matrix to be a full rank matrix. However, it is known from the conventional setting that non-linear schemes (e.g., THP) can even be used on singular channels where linear schemes fail. This stabilization due to the multiple representation of symbols and the degree of freedom to choose from them is an additional advantage of the present scheme.

  5. 5.

    Both cost functions have the same distribution for the cost and, thus, lead to the same performance.

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Acknowledgments

The work of Robert Fischer and Johannes Huber was supported by the German Research Foundation (DFG) under Grants FI 982/4-1, FI 982/4-2, FI 982/4-3, and HU 634/11-3, respectively.

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Authors and Affiliations

  1. Ulm University, Albert-Einstein-Allee 43, 89081, Ulm, Germany

    Robert F. H. Fischer & Sebastian Stern

  2. FAU Erlangen-Nürnberg, Cauerstrasse 7, 91058, Erlangen, Germany

    Michael Cyran & Johannes B. Huber

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  1. Robert F. H. Fischer
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  2. Michael Cyran
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  4. Johannes B. Huber
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Correspondence to Robert F. H. Fischer .

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  1. Technische Universität München, Muenchen, Germany

    Wolfgang Utschick

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Fischer, R.F.H., Cyran, M., Stern, S., Huber, J.B. (2016). Modulo-Type Precoding for Networks. In: Utschick, W. (eds) Communications in Interference Limited Networks. Signals and Communication Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-22440-4_2

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  • DOI: https://doi.org/10.1007/978-3-319-22440-4_2

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