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komm.DiscreteMemorylessSource

Discrete memoryless source. It is defined by a finite source alphabet $\mathcal{X}$ and a pmf $p$ over $\mathcal{X}$. The value of $p(x)$ gives the probability of the source emitting symbol $x \in \mathcal{X}$, with the probability of emitting a symbol being independent of all previously emitted symbols. Here, for simplicity, the alphabet is taken as $\mathcal{X} = [0 : |\mathcal{X}|)$, where $|\mathcal{X}|$ is called the source cardinality.

Parameters:

  • pmf (ArrayLike | int) –

    Either a one-dimensional array of floats representing the source pmf $p$, or a positive integer $M$, in which case a uniform pmf over $[0 : M)$ is assumed.

Note

The cardinality $|\mathcal{X}|$ is inferred from the length of the pmf array.

pmf Array1D[floating] cached property

The source pmf $p$ over $\mathcal{X}$.

Examples:

>>> source = komm.DiscreteMemorylessSource([1/2, 1/4, 1/8, 1/8])
>>> source.pmf
array([0.5  , 0.25 , 0.125, 0.125])

>>> source = komm.DiscreteMemorylessSource(4)
>>> source.pmf
array([0.25, 0.25, 0.25, 0.25])

cardinality int cached property

The source cardinality $|\mathcal{X}|$.

Examples:

>>> source = komm.DiscreteMemorylessSource([1/2, 1/4, 1/8, 1/8])
>>> source.cardinality
4

>>> source = komm.DiscreteMemorylessSource(4)
>>> source.cardinality
4

entropy_rate()

Computes the source entropy rate. For a discrete memoryless source, this is simply the entropy of the pmf $p$.

Parameters:

  • base (float | Literal['e']) –

    See komm.entropy. The default value is 2.0.

Returns:

  • entropy_rate (floating) –

    The source entropy rate.

Examples:

>>> source = komm.DiscreteMemorylessSource([1/2, 1/4, 1/8, 1/8])
>>> source.entropy_rate()
np.float64(1.75)
>>> source.entropy_rate(base=4)
np.float64(0.875)

>>> source = komm.DiscreteMemorylessSource(4)
>>> source.entropy_rate()
np.float64(2.0)
>>> source.entropy_rate(base=4)
np.float64(1.0)

emit()

Returns random symbols from the source.

Parameters:

  • shape (tuple[int, ...] | int | None) –

    The shape of the output array. The default value corresponds to a single symbol.

Returns:

  • symbols (NDArray[integer]) –

    The emitted symbols from the source. It is an array with elements in $\mathcal{X}$ and the given shape.

Examples:

>>> source = komm.DiscreteMemorylessSource([1/2, 1/4, 1/8, 1/8])
>>> source.emit()
array([2])
>>> source.emit(10)
array([0, 2, 1, 0, 3, 2, 2, 0, 0, 0])
>>> source.emit((2, 5))
array([[3, 1, 2, 0, 0],
       [1, 0, 2, 1, 2]])