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SC-LDPC Code Design for Half-Duplex Relay Channels

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Abstract

This paper studies code design for the half-duplex relay channel when the transmissions take place over binary input additive white Gaussian noise (BIAWGN) channels. Using the decode-forward relay protocol, we design the relay code based on a spatially coupled low-density parity-check (SC-LDPC) code. We show a low complexity density evolution analysis for the proposed relay code. From the density evolution results, we observe that the proposed spatially coupled relay code achieves a capacity approaching performance. We also observe that the proposed code outperforms existing optimized LDPC relay codes. Through simulation results, we evaluate the finite-length performance of the proposed code.

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Notes

  1. Due to the actual density evolution of SC-LDPC codes over BIAWGN channel, the analysis in [10] requires tracking multiple pdfs of messages traveling over multiple edge types (see [18] for more details).

  2. Note that other existing works related to the design of relay code based on SC-LDPC codes including [11] and [12] do not fit with the code design scheme mentioned in [8].

  3. Two extremes can be considered for relay coding strategy. In one extreme, s and r simultaneously transmit completely independent information. In the other extreme, s and r simultaneously transmit identical information. In [13], it has been shown that the latter strategy performs better than first extreme for low SNRs. Moreover, the latter strategy reduces the complexity at the destination [8].

  4. Similar to [8], we define the capacity bound as the lowest total power required in (1) to achieve a given rate.

  5. For a given total power P and rate R, we calculate \(\frac{E_b}{N_0}\) by \(\frac{E_b}{N_0} = 10\log _{10}\frac{P}{2R}\) dB.

  6. For a given total power P and rate R, we calculate \(\frac{E_b}{N_0}\) by \(\frac{E_b}{N_0} = 10\log _{10}\frac{P}{2R}\) dB.

  7. Similar to [8], we define the capacity bound as the lowest total power required in (1) to achieve a given rate.

  8. Note that there exists a slight difference (about 0.04 dB) in capacity bound results between [8] and our paper. Since [8] showed capacity bound considering AWGN channel, while we calculate the capacity bound considering BIAWGN channel.

References

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Acknowledgments

This work was supported by the Australian Research Council Grant DE12010016.

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Authors and Affiliations

  1. Centre for Infocomm Technology (INFINITUS), Nanyang Technological University, Nanyang Avenue, Singapore

    Md. Noor-A-Rahim

  2. Institute for Telecommunications Research, University of South Australia, Adelaide, Australia

    Khoa D. Nguyen & Gottfried Lechner

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  1. Md. Noor-A-Rahim
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  2. Khoa D. Nguyen
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  3. Gottfried Lechner
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Correspondence to Md. Noor-A-Rahim.

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Noor-A-Rahim, M., Nguyen, K.D. & Lechner, G. SC-LDPC Code Design for Half-Duplex Relay Channels. Wireless Pers Commun 92, 771–783 (2017). https://doi.org/10.1007/s11277-016-3576-2

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