Let us assume a file based on a character set where each character has equal probability of occurance. This will result in the maximum entropy for that character set. On calculating the entropy, let us say that the entropy is just above an integral value. Usually, in such cases, the number is rounded up(which makes sense when it comes to storage).
Using standard techniques, when a single character in the string changes, the entire binary representation changes along with it. So is there any efficient coding technique where the representation doesn't change much with small changes in the original string?