Good codes (those with positive rate $r=k/n$ and positive relative distance $\delta=d/n$) will achieve capacity on $BSC$ (binary symmetric channel) if the codes have lower rates than capacity where positive relative distance is seen. However this requires very long codes to drive the error to reasonably low value.


To achieve an error rate of $e$ if capacity is $C$ then what is the shortest good code that is possible over $BSC$ as a function of $e$? I am just looking for an upper bound and a lower bound.



Shortest possible good codes?
Upper and lower bounds as well as approximations are given in "Channel Coding Rate in the Finite Blocklength Regime" by Yury Polyanskiy, H. Vincent Poor, and Sergio Verdu.


