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komm.GaussianEliminationDecoder

Gaussian elimination decoder for general block codes over the binary erasure channel. This decoder performs bit-wise MAP decoding: it solves the linear system relating the erased positions to the received ones, and returns the bits shared by all its solutions. For more details, see RU08, Sec. 3.2.

Parameters:

  • code (BlockCode) –

    The block code to be used for decoding.

Notes
  • Input type: erasure (bits, with 2 denoting an erasure).
  • Output type: erasure (bits, with 2 denoting an undetermined position).

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.HammingCode(3)
>>> decoder = komm.GaussianEliminationDecoder(code)
>>> decoder.decode_to_codeword([2, 1, 0, 2, 2, 1, 1])
array([1, 1, 0, 0, 0, 1, 1])
>>> decoder.decode_to_codeword([2, 2, 0, 2, 0, 1, 1])  # Stopping set, but still recoverable
array([1, 1, 0, 0, 0, 1, 1])
>>> decoder.decode_to_codeword([1, 0, 2, 1, 2, 2, 2])
array([1, 0, 2, 1, 0, 2, 2])

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]) –

    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.HammingCode(3)
>>> decoder = komm.GaussianEliminationDecoder(code)
>>> decoder.decode([2, 1, 0, 2, 2, 1, 1])
array([1, 1, 0, 0])
>>> decoder.decode([2, 2, 0, 2, 0, 1, 1])  # Stopping set, but still recoverable
array([1, 1, 0, 0])
>>> decoder.decode([1, 0, 2, 1, 2, 2, 2])
array([1, 0, 2, 1])