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komm.TerminatedConvolutionalCode

Terminated convolutional code. It is a linear block code obtained by terminating a $(n_0, k_0)$ convolutional code. A total of $h$ information blocks (each containing $k_0$ information bits) is encoded. The dimension of the resulting block code is thus $k = h k_0$; its length depends on the termination mode employed. There are three possible termination modes:

  • Direct truncation. The encoder always starts at state $0$, and its output ends immediately after the last information block. The encoder may not necessarily end in state $0$. The resulting block code will have length $n = h n_0$.

  • Zero termination. The encoder always starts and ends at state $0$. To achieve this, a sequence of $k \mu$ tail bits is appended to the information bits, where $\mu$ is the memory order of the convolutional code. The resulting block code will have length $n = (h + \mu) n_0$.

  • Tail-biting. The encoder always starts and ends at the same state. To achieve this, the initial state of the encoder is chosen as a function of the information bits. The resulting block code will have length $n = h n_0$.

For more details, see LC04, Sec. 12.7 and WBR01.

Attributes:

  • convolutional_code (ConvolutionalCode) –

    The convolutional code to be terminated.

  • num_blocks (int) –

    The number $h$ of information blocks.

  • mode (TerminationMode) –

    The termination mode. It must be one of 'direct-truncation' | 'zero-termination' | 'tail-biting'. The default value is 'zero-termination'.

Examples:

>>> convolutional_code = komm.ConvolutionalCode([[0b1, 0b11]])

>>> code = komm.TerminatedConvolutionalCode(convolutional_code, num_blocks=3, mode='direct-truncation')
>>> (code.length, code.dimension, code.redundancy)
(6, 3, 3)
>>> code.generator_matrix
array([[1, 1, 0, 1, 0, 0],
       [0, 0, 1, 1, 0, 1],
       [0, 0, 0, 0, 1, 1]])
>>> code.minimum_distance()
2

>>> code = komm.TerminatedConvolutionalCode(convolutional_code, num_blocks=3, mode='zero-termination')
>>> (code.length, code.dimension, code.redundancy)
(8, 3, 5)
>>> code.generator_matrix
array([[1, 1, 0, 1, 0, 0, 0, 0],
       [0, 0, 1, 1, 0, 1, 0, 0],
       [0, 0, 0, 0, 1, 1, 0, 1]])
>>> code.minimum_distance()
3

>>> code = komm.TerminatedConvolutionalCode(convolutional_code, num_blocks=3, mode='tail-biting')
>>> (code.length, code.dimension, code.redundancy)
(6, 3, 3)
>>> code.generator_matrix
array([[1, 1, 0, 1, 0, 0],
       [0, 0, 1, 1, 0, 1],
       [0, 1, 0, 0, 1, 1]])
>>> code.minimum_distance()
3