If you are only sending one word, and the recipient already needs to know the word, then you only need 1 bit, essentially just signaling that you are saying that specific word
If you want a richer vocabulary, you could create an index of about 300k words (from the English dictionary), shared between the parties
Then to send any word you only need to send one number, and in binary it would have between 1 and at most 19 bits, for any word in the index (2^19 is around 500k)
That’s without even sorting the index by frequency of appearance/usage
Where did you get that you need 27 bits for one word?
> Then to send any word you only need to send one number, and in binary it would have between 1 and at most 19 bits
Yep! By sorting by frequency, you are able to make it so the majority of words have shorter bit strings. By my calculations, common words such as "the", "of", and "and" will have ~4-6 bits associated with them. That means you can encode a large number of words (googling says those words make up ~1/7 of words based on frequency) with only 4-6 bits each. That's far from the 27 bits you calculated
> Fano’s balancing approach starts by assigning the O and one other letter to the left branch, with the five total uses of those letters balancing out the five appearances of the remaining letters.
> The resulting message requires 27 bits.
I didn’t calculate it, the author of the article did
If you are only sending one word, and the recipient already needs to know the word, then you only need 1 bit, essentially just signaling that you are saying that specific word
If you want a richer vocabulary, you could create an index of about 300k words (from the English dictionary), shared between the parties
Then to send any word you only need to send one number, and in binary it would have between 1 and at most 19 bits, for any word in the index (2^19 is around 500k)
That’s without even sorting the index by frequency of appearance/usage
27 bits for just one word seems wasteful