Calculates the capacity of a binary erasure channel (BEC).

Parameters:¶

p: ArrayLike¶

The erasure probability \(p\) of the BEC channel.

Returns:¶

The capacity \(C\) of the channel in bits/channel use.

Notes

The inputs to the BEC are \(x_i \in \{0, 1\}\) and the outputs are \(y_i \in \{0, 1, e\}\). Erasures \(e\) are represented by -1. The capacity of the BEC is

Examples

When the probability \(p\) of erasure is 0, the capacity of the channel is 1 bit/channel use. However, as the probability of erasure approaches 1, the capacity of the channel approaches 0.

In [1]: p = np.linspace(0, 1, 100); \
   ...: C = sdr.bec_capacity(p)
   ...: 

In [2]: plt.figure(); \
   ...: plt.plot(p, C); \
   ...: plt.xlabel("Erasure probability, $p$"); \
   ...: plt.ylabel("Capacity (bits/channel use), $C$"); \
   ...: plt.title("Capacity of the Binary Erasure Channel");
   ...: