.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/systems/plot_03_dvbs.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_auto_examples_systems_plot_03_dvbs.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_systems_plot_03_dvbs.py:


DVB-S: the error rate after the Viterbi decoder against Table 3
===============================================================

:class:`comnum.Dvbs` implements the DVB-S transmitter of ETSI EN 300 421 V1.1.2 and a
receiver aligned on the burst: the energy dispersal of the MPEG-2 transport stream (the
PRBS :math:`1 + X^{14} + X^{15}` reset every 8 packets), the outer code RS(204, 188), the
convolutional interleaver of 12 branches (depths :math:`17 j`), the inner code of
constraint length 7 (:math:`X` from :math:`171_8`, :math:`Y` from :math:`133_8`) punctured
to 2/3, 3/4, 5/6 or 7/8 by Table 2, and the Gray QPSK of Figure 5.

**Table 3** gives the :math:`E_b/N_0` per useful bit (before the outer code) at which the
BER after the Viterbi decoder is :math:`2 \cdot 10^{-4}`, the input of the outer decoder
for a quasi-error-free output: 4.5, 5.0, 5.5, 6.0 and 6.4 dB from 1/2 to 7/8, a modem
implementation margin of 0.8 dB included. An ideal modem should reach the BER at Table 3
minus 0.8 dB. The card ``dvbs_table3`` measures it with :math:`10^6` bits per point at
3.60, 4.04, 4.50, 5.00 and 5.38 dB, 0.10 to 0.22 dB below. This script draws the
waterfalls with fewer bits.

**The bits on I and Q.** The punctured bits leave in time order, :math:`X` before
:math:`Y` at every step, and alternate between I and Q: at rate 3/4, I carries
:math:`X_1 Y_2` and Q carries :math:`Y_1 X_3`, the rows of Table 2.

.. GENERATED FROM PYTHON SOURCE LINES 24-31

.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    import comnum
    from comnum.plot import BACKGROUND, BLUE, GREY, INK, PURPLE, RULE, RUST, TEAL








.. GENERATED FROM PYTHON SOURCE LINES 32-34

The BER after the Viterbi decoder: twelve bursts of 100 packets per point through the
whole chain, the errors counted on the bytes entering the inner coder.

.. GENERATED FROM PYTHON SOURCE LINES 34-66

.. code-block:: Python

    rng, noise = comnum.Rng(421), np.random.default_rng(421)
    table3 = {"1/2": 4.5, "2/3": 5.0, "3/4": 5.5, "5/6": 6.0, "7/8": 6.4}
    colors = [BLUE, RUST, TEAL, PURPLE, GREY]
    fig, ax = plt.subplots()
    for (rate, required), color in zip(table3.items(), colors, strict=True):
        link = comnum.Dvbs(rate)
        ebn0 = np.arange(required - 1.6, required - 0.39, 0.2)
        ber = []
        for e in ebn0:
            noise_var = 1 / comnum.db2lin(link.esn0_db(e))
            errors = bits = 0
            for _ in range(12):  # about 2.2e6 bits per point
                tx = link.outer(comnum.dvb_packets(100, rng))
                x = link.inner(tx)
                w = (noise.normal(size=len(x)) + 1j * noise.normal(size=len(x))) * np.sqrt(
                    noise_var / 2
                )
                rx = link.inner_decode(x + w, noise_var)
                errors += int(np.unpackbits(tx ^ rx).sum())
                bits += 8 * len(tx)
            ber.append(errors / bits if errors else np.nan)
        ax.semilogy(
            ebn0, ber, marker="o", color=color, markeredgecolor=BACKGROUND, label=f"rate {rate}"
        )
        ax.plot(required - 0.8, 2e-4, marker="*", markersize=12, color=color, markeredgecolor=INK)
    ax.axhline(2e-4, color=RULE, linewidth=0.8)
    ax.annotate("Table 3 − 0.8 dB (★)", (3.0, 2.6e-4), color=INK, fontsize=8)
    ax.set(xlabel="Eb/N0 per useful bit (dB)", ylabel="BER after the Viterbi decoder", ylim=(1e-6, 1e-2),
           title="DVB-S, AWGN, soft Viterbi decoding")  # fmt: skip
    ax.legend(loc="lower left")
    fig.tight_layout()




.. image-sg:: /auto_examples/systems/images/sphx_glr_plot_03_dvbs_001.png
   :alt: DVB-S, AWGN, soft Viterbi decoding
   :srcset: /auto_examples/systems/images/sphx_glr_plot_03_dvbs_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 67-68

The Gray QPSK of Figure 5, label :math:`b_I b_Q`.

.. GENERATED FROM PYTHON SOURCE LINES 68-80

.. code-block:: Python

    c = comnum.Dvbs("1/2").constellation
    p = np.asarray(c.points)
    fig, ax = plt.subplots(figsize=(4.5, 4.5))
    ax.plot(p.real, p.imag, "o", color=BLUE, markeredgecolor=BACKGROUND)
    for label, z in enumerate(p):
        ax.annotate(format(label, "02b"), (z.real, z.imag), textcoords="offset points", xytext=(0, 8),
                    ha="center", color=INK)  # fmt: skip
    ax.axhline(0, color=RULE, linewidth=0.6)
    ax.axvline(0, color=RULE, linewidth=0.6)
    ax.set(aspect="equal", xlim=(-1.2, 1.2), ylim=(-1.2, 1.2), xlabel="I", ylabel="Q",
           title="DVB-S QPSK (Figure 5)")  # fmt: skip
    fig.tight_layout()



.. image-sg:: /auto_examples/systems/images/sphx_glr_plot_03_dvbs_002.png
   :alt: DVB-S QPSK (Figure 5)
   :srcset: /auto_examples/systems/images/sphx_glr_plot_03_dvbs_002.png
   :class: sphx-glr-single-img






.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 42.650 seconds)


.. _sphx_glr_download_auto_examples_systems_plot_03_dvbs.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_03_dvbs.ipynb <plot_03_dvbs.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_03_dvbs.py <plot_03_dvbs.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_03_dvbs.zip <plot_03_dvbs.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

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