verify_gm_pcm

sionna.phy.fec.utils.verify_gm_pcm(gm: numpy.ndarray, pcm: numpy.ndarray) → bool

Verifies that the generator matrix and parity-check matrix are orthogonal in GF(2).

For a valid code with an all-zero syndrome, the following condition must hold:

\[\mathbf{H} \mathbf{c}^T = \mathbf{H} * (\mathbf{u} * \mathbf{G})^T = \mathbf{H} * \mathbf{G}^T * \mathbf{u}^T = \mathbf{0},\]

where \(\mathbf{c}\) represents an arbitrary codeword and \(\mathbf{u}\) the corresponding information bits.

Since \(\mathbf{u}\) can be arbitrary, this leads to the condition:

\[\mathbf{H} * \mathbf{G}^T = \mathbf{0}.\]

Parameters:

• gm (numpy.ndarray) – Binary generator matrix of shape [k, n].

• pcm (numpy.ndarray) – Binary parity-check matrix of shape [n - k, n].

Outputs:

is_valid – True if gm and pcm define a valid pair of orthogonal parity-check and generator matrices in GF(2).