Lower Bound for Error Probability in Channels with Feedback

The greatest lower bound for the error probability is obtained in the case of discrete memoryless channels with feedback. In the case of channels with a matrix of transition probabilities and with a specific symmetry [R. G. Gallager, Information Theory and Reliable Communication, Wiley, New York (1968)], this lower bound is identical with the bound for packing of spheres. The decoding by lists is also considered.