A binary symmetric channel is a random transformation of a binary symbol that reverses its value with a fixed probability 
and leaves it unchanged with probability 
.
Here 
is the crossover probability. A vector
of signs 
produces 
, where the signs 
are independent
of 
and one another and satisfy 
(Courtade and Kumar 2014, p. 4516).
At 
the input is preserved, while at 
the output contains no mutual
information about the input. The corresponding Boolean
noise operator has parameter 
.
