算数暗号の続き

まだ算数のコードの理論を考えています。
The probability-based method is more clear cut than the frequency based method. I believe I covered this in a previous journal article, but it is worth reviewing. If each symbol's probability is known, we begin with interval [0,1), then update the interval based on the symbol chosen and its probability. Say the first symbol chosen is the third in our list, where the first two have probabilities 1/4 and 1/2. Then the new interval must begin at 3/4. If our symbol has probability 1/8, the new interval is [3/4,7/8). If the first symbol is encoded next, the new interval is [3/4,25/32) (as 1/4 of 1/8 is 1/32).
Using this method to solve for the earlier DABDDB string's encoding, I obtained an interval containing the LOW value as its upper bound, but I still did not obtain the [LOW,HIGH) interval presented in Wikipedia.