Implements a discrete memoryless channel (DMC).

Notes

The inputs to the DMC are \(x_i \in \mathcal{X}\) and the outputs are \(y_i \in \mathcal{Y}\). The capacity of the DMC is

where \(I(X; Y)\) is the mutual information between the input \(X\) and output \(Y\) of the channel.

References

• John Proakis, Digital Communications, Chapter 6.5-1: Channel Models.

Examples

Define the binary symmetric channel (BSC) with transition probability \(p=0.25\).

In [1]: p = 0.25

In [2]: dmc = sdr.DiscreteMemorylessChannel([[1 - p, p], [p, 1 - p]], seed=1)

In [3]: dmc.P
Out[3]: 
array([[0.75, 0.25],
       [0.25, 0.75]])

In [4]: x = np.random.randint(0, 2, 20); x
Out[4]: array([0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1])

In [5]: y = dmc(x); y
Out[5]: array([0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1])

In [6]: np.count_nonzero(x != y)
Out[6]: 6

Define the binary erasure channel (BEC) with erasure probability \(p=0.25\).

In [7]: p = 0.25

In [8]: dmc = sdr.DiscreteMemorylessChannel([[1 - p, 0, p], [0, 1 - p, p]], Y=[0, 1, -1], seed=1)

In [9]: x = np.random.randint(0, 2, 20); x
Out[9]: array([0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1])

In [10]: y = dmc(x); y
Out[10]: 
array([ 0,  1, -1, -1,  1,  1, -1,  1,  1,  1,  1,  0, -1,  1,  0,  0, -1,
        0,  0,  1])

In [11]: np.count_nonzero(x != y)
Out[11]: 5

Constructors¶

DiscreteMemorylessChannel(P: ArrayLike, ...)

Creates a new discrete memoryless channel (DMC).

Special methods¶

__call__(x: ArrayLike) → NDArray[int_]

Passes the input sequence \(x\) through the channel.

Methods¶

reset(seed: int | None = None)

Resets the channel with a new seed.

static capacities() → NDArray

Computes the channel capacity given the channel configuration.

Properties¶

property X : NDArray[np.int_]

The input alphabet \(\mathcal{X}\) of the DMC channel.

property Y : NDArray[np.int_]

The output alphabet \(\mathcal{Y}\) of the DMC channel.

property P : NDArray[np.float64]

The transition probability matrix \(P\) of the DMC channel.

property capacity : float

The channel capacity \(C\) in bits/2D of the instantiated channel.