In coding theory and information theory, a binary erasure channel (BEC) is a communications channel model. A transmitter sends a bit receives a message that the bit was not received ("erased") .

Definition

be the transmitted random variable is the erasure symbol. Then, the channel is characterized by the conditional probabilities:

Capacity

The channel capacity (i.e. half of the inputs should be 0 and half should be 1).

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!Proof. The channel capacity is:

Observe that, for the binary entropy function),

.

, so

1. .

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. However, by the noisy-channel coding theorem can be obtained even without such feedback.

Related channels

If bits are flipped rather than erased, the channel is a binary symmetric channel (for the binary entropy function.) then the channel is a deletion channel, and its capacity is an open problem.

History

The BEC was introduced by Peter Elias of MIT in 1955 as a toy example.

See also

• Erasure code

• Packet erasure channel

Notes

References