make_systematic

sionna.phy.fec.utils.make_systematic(mat: numpy.ndarray, is_pcm: bool = False) → Tuple[numpy.ndarray, List[List[int]]]

Converts a binary matrix to its systematic form.

This function transforms a binary matrix into systematic form, where the first k columns (or last k columns if is_pcm is True) form an identity matrix.

Parameters:

• mat (numpy.ndarray) – Binary matrix of shape [k, n] to be transformed to systematic form.

• is_pcm (bool) – If True, mat is treated as a parity-check matrix, and the identity part will be placed in the last k columns.

Outputs:

• mat_sys – The systematic matrix.

• column_swaps – A list of column swap operations performed.

Notes

This function may swap columns of the input matrix to achieve systematic form. As a result, the output matrix represents a permuted version of the code, defined by the column_swaps list. To revert to the original column order, apply the inverse permutation in reverse order of the swaps. If is_pcm is True, indicating a parity-check matrix, the identity matrix portion will be arranged in the last k columns.