comnum.theory_bicm_cutoff_rate#

comnum.theory_bicm_cutoff_rate(constellation, snr_db, *, fading='awgn', points=Ellipsis)#

The BICM cutoff rate (bits per channel use) of a labelled constellation, m(1 - log2(1 + B)) with the Bhattacharyya factor B (Caire, Taricco & Biglieri 1998, eqs. (19), (21)).

Parameters:

  • constellation (Constellation) – the labelled points.

  • snr_db (float | array_like) – E_s/σ² (dB).

  • fading (str) – "awgn" or "rayleigh".

  • points (int) – quadrature nodes per dimension.

Returns:

the cutoff rate at every SNR.

Return type:

float | numpy.ndarray

Raises:

ValueError – for an invalid parameter or input (the message names it).