.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/foundations/plot_01_constellations.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_foundations_plot_01_constellations.py>`
        to download the full example code.

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

.. _sphx_glr_auto_examples_foundations_plot_01_constellations.py:


Constellations and Gray labels
==============================

The constellations of ``comnum`` carry the Gray labels of OptiCommPy: point ``i`` of
``c.points`` carries the bits of ``i``, most significant bit first, and two nearest
neighbours differ by a single bit. A symbol error to a neighbour therefore costs one
bit error, which is what makes the approximation :math:`P_b \approx P_s / \log_2 M`
of the bit error rate accurate at high SNR.

.. GENERATED FROM PYTHON SOURCE LINES 11-40

.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    import comnum
    from comnum.plot import BACKGROUND, BLUE, MUTED

    fig, axes = plt.subplots(1, 3, figsize=(9.5, 3.6))
    for ax, (kind, m) in zip(axes, [("qam", 16), ("psk", 8), ("pam", 4)], strict=True):
        c = comnum.Constellation(kind, m).normalized()
        p = c.points
        k = c.bits_per_symbol
        ax.scatter(p.real, p.imag, s=46, color=BLUE, zorder=3, edgecolor=BACKGROUND, linewidth=1.5)
        for i, z in enumerate(p):
            ax.annotate(
                format(i, f"0{k}b"),
                (z.real, z.imag),
                textcoords="offset points",
                xytext=(0, 7),
                ha="center",
                fontsize=8,
                color=MUTED,
            )
        lim = 1.35 * np.abs(p).max()
        ax.set(xlim=(-lim, lim), ylim=(-lim, lim), aspect="equal", title=f"{m}-{kind.upper()}")
        ax.set_xlabel("in phase")
    axes[0].set_ylabel("quadrature")
    fig.tight_layout()




.. image-sg:: /auto_examples/foundations/images/sphx_glr_plot_01_constellations_001.png
   :alt: 16-QAM, 8-PSK, 4-PAM
   :srcset: /auto_examples/foundations/images/sphx_glr_plot_01_constellations_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 41-42

Neighbours differ by one bit: check it on 64-QAM.

.. GENERATED FROM PYTHON SOURCE LINES 42-49

.. code-block:: Python

    c = comnum.Constellation("qam", 64).normalized()
    p = c.points
    d = np.abs(p[:, None] - p[None, :])
    dmin = d[d > 0].min()
    pairs = np.argwhere(np.isclose(d, dmin))
    print("nearest-neighbour pairs:", len(pairs) // 2)
    print("bits that differ:", {bin(i ^ j).count("1") for i, j in pairs})




.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    nearest-neighbour pairs: 112
    bits that differ: {1}





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

   **Total running time of the script:** (0 minutes 0.163 seconds)


.. _sphx_glr_download_auto_examples_foundations_plot_01_constellations.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_01_constellations.ipynb <plot_01_constellations.ipynb>`

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

      :download:`Download Python source code: plot_01_constellations.py <plot_01_constellations.py>`

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

      :download:`Download zipped: plot_01_constellations.zip <plot_01_constellations.zip>`


.. only:: html

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

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_