d v=2-n8 into Eq. (13.30) and take the limit of large n to obtain: (13.31) 2 1-v=1-2-ne. In the limit n 8, we, thus, have p 1, which means that any output message yi corresponds exclusively to an input message Xi. The error probability, Pe=1 - p, Channel capacity and coding theorem becomes identically zero as the sequence length n becomes large, which means that, under the above prerequisites, any original message can be transmitted through a noisy channel with asymptotically 100% accuracy or zero error. Concerning binary channels, the above conclusion can be readily reformulated in terms of the "block code" concept introduced in Chapter 11, according to the following: Given a noisy binary communication channel with capacity C, there exists a block code (n,k) of 2k codewords of length n, and code rate R = k/n < C, for which message codewords can be transmitted through the channel with an arbitrary small error E. The above constitutes the formal demonstration of the CCT, as in accordance with the original Shannon paper. Having gone through this preliminary, but somewhat math- ematically abstract, exercise, we can now revisit the CCT through simpler approaches, which are more immediately intuitive or concrete. The following, which includes three different approaches is inspired from reference.14 Approach 1 Recall the example of the "noisy typewriter" channel described in Chapter 12 and illustrated in Fig. 12.4. The noisy typewriter is a channel translating single-character messages from keyboard to paper. But any input character Xi (say, J) from the keyboard results in a printed character Yj, which has equal chances of being one of three possible characters (say, I, J, K). As we have seen earlier (Section 13.1, Example 3), it is possible to extract a subset of triplets from all the 26 possible output messages. If we add the space as a 27th character, there exist exactly 27/3 9 such triplets. Such triplets are called nonconfusable outputs, because they correspond to a unique input, which we call distinguishable. The