On Exact Block $\varepsilon$-Approximation of Equiprobable Messages

It is shown that for sources of equiprobable discrete symbols and a symmetrical error function there exist block codes in which exact $\varepsilon$-approximation of each message is attained. With increasing block length $n$, the rate of these codes tends to the $\varepsilon$-entropy at a rate $n^{-1}\ln n$, i.e., at the same rate as in the customary estimation of $\varepsilon$-error on average with respect to all messages. An estimate is obtained for the block length beginning with which exact $\varepsilon$-approximation is attained.