After some thinking I found the unicity distance formula weird, so I reread the article and sure enough I misunderstood what D is, it's not the information density it's the difference between the actual information density and the maximum information density given the source character set size.
Which probably means that for D we need to compute the difference between lb(9) ≈ 3.17 and the actual per character information of an English text after mapping 27 source tokens to 9 ciphertext tokens. But here we have a problem: I think this latter number depends on the actual mapping used. Intuitively this is easy to understand, when grouping letters into sets of 3, one can group each of popular letters with a pair of significantly more rare ones and make a code that would be almost readable by just replacing each number with the most common letter associated with this number, so the information density will be closer to plain English. Alternatively, one can group all frequent letters and all rare letters and get a code with so much information loss that it would be very hard or even impossible to break.
So, I'm not sure how to approach this. If we are talking about the unicity distance for an arbitrary grouping of source characters into triplets, then maybe some averaging should be done for D. And in a bad enough case this distance can be infinite (no information redundancy after mapping letters to digits).
Again, as I said in the very beginning, I have no idea what I'm doing and it could even be the first time I encounter this "unicity distance" metric at all.
Which probably means that for D we need to compute the difference between lb(9) ≈ 3.17 and the actual per character information of an English text after mapping 27 source tokens to 9 ciphertext tokens. But here we have a problem: I think this latter number depends on the actual mapping used. Intuitively this is easy to understand, when grouping letters into sets of 3, one can group each of popular letters with a pair of significantly more rare ones and make a code that would be almost readable by just replacing each number with the most common letter associated with this number, so the information density will be closer to plain English. Alternatively, one can group all frequent letters and all rare letters and get a code with so much information loss that it would be very hard or even impossible to break.
So, I'm not sure how to approach this. If we are talking about the unicity distance for an arbitrary grouping of source characters into triplets, then maybe some averaging should be done for D. And in a bad enough case this distance can be infinite (no information redundancy after mapping letters to digits).
Again, as I said in the very beginning, I have no idea what I'm doing and it could even be the first time I encounter this "unicity distance" metric at all.