If one were to transmit sequences comprising the 4 characters 'A', 'B', 'C', and 'D', a transmitted message might be 'ABADDCAB'. The entropy of a message per bit multiplied by the length of that message is a measure of how much total information the message contains. Shannon's source coding theorem states a lossless compression scheme cannot compress messages, on average, to have more than one bit of information per bit of message, but that any value less than one bit of information per bit of message can be attained by employing a suitable coding scheme. A compressed message has less redundancy.

It has more information (higher entropy) per character. If a compression scheme is lossless вЂ“ one in which you can always recover the entire original message by decompression вЂ“ then a compressed message has the same quantity of information as the original but communicated in fewer characters. English text has between 0.6 and 1.3 bits of entropy per character of the message. After the first few letters one can often guess the rest of the word. If we do not know exactly what is going to come next, we can be fairly certain that, for example, 'e' will be far more common than 'z', that the combination 'qu' will be much more common than any other combination with a 'q' in it, and that the combination 'th' will be more common than 'z', 'q', or 'qu'. Given a discrete random variable X (about 1.58496) bits of information because it can have one of three values.Д®nglish text, treated as a string of characters, has fairly low entropy, i.e., is fairly predictable. Other values of p give different entropies between zero and one bits. When the entropy is zero bits, this is sometimes referred to as unity, where there is no uncertainty at all - no freedom of choice - no information. The minimum surprise is for p = 0 or p = 1, when the event is known and the entropy is zero bits. In this case a coin flip has an entropy of one bit. The maximum surprise is for p = 1/2, when there is no reason to expect one outcome over another. As an example, consider a biased coin with probability p of landing on heads and probability 1 в€’ p of landing on tails. The concept of information entropy was introduced by Claude Shannon in his 1948 paper ' A Mathematical Theory of Communication', and is also referred to as Shannon entropy. In information theory, the entropy of a random variable is the average level of 'information', 'surprise', or 'uncertainty' inherent in the variable's possible outcomes.

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