Error Probability Analysis of Binary Asymmetric Channels

In his world-famous paper of 1948, Shannon defined channel capacity as the ultimate rate at which information can be transmitted over a communication channel with an error probability that will vanish if we allow the blocklength to get infinitely large. While this result is of tremendous theoretical importance, the reality of practical systems looks quite different: no communication system will tolerate an infinite delay caused by an extremely large blocklength. On the other hand, it is not necessary to have an error probability that is exactly zero either, a small, but finite value will suffice. Therefore, the question arises what can be done in a practical scheme. In particular, what is the maximal rate at which information can be transmitted over a communication channel for a given fixed maximum blocklength (i.e., a fixed maximum delay) if we allow a certain maximal probability of error? In this project, we have started to study these questions.