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Extrinsic LLR Computation by the SISO LMMSE Detector: Four Different Approaches

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Computer Aided Systems Theory – EUROCAST 2015 (EUROCAST 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9520))

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In this paper we present four different approaches for the computation of the extrinsic information by a soft-input soft-output LMMSE detector used in a turbo equalization system. Moreover, we show the equivalence of the four approaches. All methods apply a Gaussian approximation, but at different stages, e.g. Gaussian approximation on the LMMSE filter output. Each approach offers different strategies for reducing the computational complexity, where the factor graph approach is the most promising solution.

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  1. 1.

    Usually, data symbols are drawn from a discrete symbol alphabet (e.g., binary phase shift keying (BPSK)).

  2. 2.

    For more information on FGs and the sum-product algorithm please refer to [6].

  3. 3.

    Note that terms that are independent of \(x_n\) can be neglected.


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Correspondence to Werner Haselmayr .

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© 2015 Springer International Publishing Switzerland

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Haselmayr, W., Springer, A. (2015). Extrinsic LLR Computation by the SISO LMMSE Detector: Four Different Approaches. In: Moreno-Díaz, R., Pichler, F., Quesada-Arencibia, A. (eds) Computer Aided Systems Theory – EUROCAST 2015. EUROCAST 2015. Lecture Notes in Computer Science(), vol 9520. Springer, Cham.

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-27339-6

  • Online ISBN: 978-3-319-27340-2

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