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komm.BerlekampDecoder

Berlekamp decoder for BCH codes and Reed–Solomon codes. For more details, see LC04, Sec. 6.3 and LC04, Sec. 7.4.

Parameters:

  • code (BCHCode | ReedSolomonCode) –

    The BCH or Reed–Solomon code to be used for decoding.

Notes
  • Input type: hard (bits).
  • Output type: hard (bits).

decode_to_codeword()

Decode received words to codewords. This method takes one or more sequences of received words and returns their corresponding estimated codeword sequences.

Parameters:

  • input (ArrayLike) –

    The input sequence(s). Can be either a single sequence whose length is a multiple of $n$, or a multidimensional array where the last dimension is a multiple of $n$.

Returns:

  • output (NDArray[integer]) –

    The output sequence(s). Has the same shape as the input.

Examples:

>>> code = komm.BCHCode(4, 7)
>>> decoder = komm.BerlekampDecoder(code)
>>> decoder.decode_to_codeword(
...     [0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0],
... )
array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])

>>> code = komm.ReedSolomonCode(3, 5)
>>> decoder = komm.BerlekampDecoder(code)
>>> decoder.decode_to_codeword(
...     [1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0],
... )
array([1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0])

decode()

Decode received words. This method takes one or more sequences of received words and returns their corresponding estimated message sequences.

Parameters:

  • input (ArrayLike) –

    The input sequence(s). Can be either a single sequence whose length is a multiple of $n$, or a multidimensional array where the last dimension is a multiple of $n$.

Returns:

  • output (NDArray[integer | floating]) –

    The output sequence(s). Has the same shape as the input, with the last dimension contracted from $bn$ to $bk$, where $b$ is a positive integer.

Examples:

>>> code = komm.BCHCode(4, 7)
>>> decoder = komm.BerlekampDecoder(code)
>>> decoder.decode(
...     [0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0],
... )
array([0, 0, 0, 0, 0])

>>> code = komm.ReedSolomonCode(3, 5)
>>> decoder = komm.BerlekampDecoder(code)
>>> decoder.decode(
...     [1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0],
... )
array([0, 0, 0, 1, 1, 0, 1, 0, 0])