  For the information transmission a binary symmetric channel is used. There is
also another noisy binary symmetric channel (feedback channel), and the
transmitter observes without delay all the outputs of the forward channel via
that feedback channel. The transmission of a nonexponential number of messages
(i.e. the transmission rate equals zero) is considered. The achievable decoding
error exponent for such a combination of channels is investigated. It is shown
that if the crossover probability of the feedback channel is less than a
certain positive value, then the achievable error exponent is better than the
similar error exponent of the no-feedback channel.
  The transmission method described and the corresponding lower bound for the
error exponent can be strengthened, and also extended to the positive
transmission rates.
