What is the "single-letter characterization of the secrecy capacity"? I'm reading a paper [1] in which secrecy capacity are being discussed under the following terms:


  A single-letter characterization of the secrecy capacity that holds for the general case remains unknown until now (if it exists at all). Only a multi-letter description of the secrecy capacity has been established so far.


What do the terms marked in bold mean, either in plain English or expressed in terms of entropy/mutual information/etc ?



[1]: Secure Communication under Channel Uncertainty and Adversarial Attacks - Rafael F. Schaefer, Holger Boche, and H. Vincent Poor
Secrecy capacity is defined as the maximum bit rate that can be sent securely through a channel. Single-letter means that the corresponding capacity expression does not depend on the block length $n$.

For example in a degraded wiretap channel, we have the following single-letter characterization of the capacity $C$:

$$C = I(X;Y) - I(X;Z)$$

But in more complex models like the compound wiretap channel, it's hard to find an expression that doesn't depends on $n$:

$$C = \lim_{n\to\infty} \frac{1}{n} \max_{U} ( \min_{s\in S}I(U,Y_s^n) - \max_{s\in S}I(U,Z_s^n))$$

Single-letter characterization is a desirable property, since it is simpler to express and compute.



Adapted from a mail explanation from R. F. Schaefer