Binary symmetric channel

A binary symmetric channel (or BSCp) is a common <a href="/facts/Communications_channel/MtlxEShV">communications channel</a> model used in <a href="/facts/Coding_theory/SBqStoGL">coding theory</a> and <a href="/facts/Information_theory/qNLH3U5P">information theory</a>. In this model, a transmitter wishes to send a <a href="/facts/Bit/RwfjaYSv">bit</a> (a zero or a one), and the receiver will receive a bit. The bit will be "flipped" with a "crossover <a href="/facts/Probability/fgYvMhwb">probability</a>" of p, and otherwise is received correctly. This model can be applied to varied communication channels such as telephone lines or <a href="/facts/Disk_drive/hnsXRb5X">disk drive</a> storage.
The <a href="/facts/Noisy-channel_coding_theorem/vvr8u4Gg">noisy-channel coding theorem</a> applies to BSCp, saying that information can be transmitted at any rate up to the <a href="/facts/Channel_capacity/55wJYsS6">channel capacity</a> with arbitrarily low error. The channel capacity is 
 
 
 
 1
 −
 
 H
 
 b
 
 
 ⁡
 (
 p
 )
 
 
 {\displaystyle 1-\operatorname {H} _{\text{b}}(p)}
 
 bits, where 
 
 
 
 
 H
 
 b
 
 
 
 
 {\displaystyle \operatorname {H} _{\text{b}}}
 
 is the <a href="/facts/Binary_entropy_function/s9cwzz4n">binary entropy function</a>. Codes including Forney's code have been designed to transmit information efficiently across the channel.

Binary symmetric channel open-in-new

Binary symmetric channel