12 · Beat the channel with longer words

The noisy five-symbol channel: each symbol can be heard as either neighbour. Pick any two of the five two-letter codewords.

Try this. Check every pair: some position always distinguishes them safely. Five safe words of length two beats the two safe words that single letters allow, and that surplus is what capacity measures.

This is Shannon's 1956 example. The 2026 result plays the same trick with safe tables as the codebooks: because their rate climbs forever, there are channels where any three symbols contain a confusable pair and yet the capacity is as large as you like.