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komm.ExhaustiveBitwiseDecoder

Exhaustive bitwise decoder for general block codes. This decoder computes the a posteriori L-value of each bit by summing over all possible codewords, assuming equiprobable messages. Its hard decisions, the signs of the L-values, are the bitwise maximum a posteriori (MAP) decisions, and may not form a codeword. For more details, see MacK03, Sec. 25.1.

Parameters:

  • code (BlockCode) –

    The block code to be used for decoding.

  • output_type (Literal['hard', 'soft']) –

    The type of the output. Either 'hard' or 'soft'. Default is 'soft'.

Notes
  • Input type: soft (L-values).
  • Output type: hard (bits) or soft (L-values).

decode_to_codeword()

Decode received words to estimates of the $n$ code bits. This method takes one or more sequences of received words and returns their corresponding estimated sequences. Depending on the decoder, the estimates may be bits, erasure-marked bits, or L-values, and need not form a valid codeword.

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.

Examples:

>>> code = komm.HammingCode(3)

>>> decoder = komm.ExhaustiveBitwiseDecoder(code)
>>> decoder.decode_to_codeword([-1.3, -0.8, +1.1, -0.8, +1.2, -0.2, -1.4])
array([-1.4867878 , -0.47876436,  1.30351111, -0.2634431 ,  1.38090385,
       -0.20271875, -1.57367212])

>>> decoder = komm.ExhaustiveBitwiseDecoder(code, output_type="hard")
>>> decoder.decode_to_codeword([-1.3, -0.8, +1.1, -0.8, +1.2, -0.2, -1.4])
array([1, 1, 0, 1, 0, 1, 1])

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.HammingCode(3)

>>> decoder = komm.ExhaustiveBitwiseDecoder(code)
>>> decoder.decode([-1.3, -0.8, +1.1, -0.8, +1.2, -0.2, -1.4])
array([-1.4867878 , -0.47876436,  1.30351111, -0.2634431 ])

>>> decoder = komm.ExhaustiveBitwiseDecoder(code, output_type="hard")
>>> decoder.decode([-1.3, -0.8, +1.1, -0.8, +1.2, -0.2, -1.4])
array([1, 1, 0, 1])