What does it mean to determine the savings over the most efficient fixed length code?

Question

I have some information coding theory questions but I'm asked to determine the savings over the most efficient fixed length code, and I don't know what this means. What is the "savings?" that the question is asking for? Thank you for any help!
exercises

Answer 1

You are supposed to look up and understand the definitions. If you have $k$ different messages you might want to send, a fixed length code needs $\lceil \log_2 k\rceil$ bits. Compression techniques will send frequent messages with fewer bits. You should compare the average number of bits sent for a compressed message with the number of bits of a fixed length code. The difference is the savings. The result depends on the compression used and the probability distribution of the messages.