I want to encode the messages to a sequence of 1s and 0s (subsequently called "bits"). This is called "source coding". Shannon's source coding theory states that the entropy of a source that emits a sequence of N symbols that are independent and identically distributed (iid) is N·H bits (per message of N symbols) where H is the source entropy.
Question 1: Does $N$ mean the length of the message or number of distinct symbols? For examp,e if message $m = 1001$, then $N = 4$ or $N = 2$?
Question 2: I want to apply the source coding similar to Arithmetic Coding using nonlinear dynamical system (chaos map). I had asked Help in understanding a coding technique based on inverse mapping of a dynamical system
for a detailed explanation on how this coding works. Using the inverse iterations of Skew Tent Map and the symbol representation of the message, we can get the initial condition from backward iterations of the map. In this way we can embed the message into the symbolic dynamics of the Skew Tent Map.
Now, my problem is that I have a database consisting of a collection of $N$ different messages of same length $D$. For each $N$, I apply the coding technique. Thus, I am using $N$ number of Skew Tent Maps each initialized with different initial condition. I then iterate the Skew Tent Map $d < D$ times and perform symbolization (or binarization) using the mean of the real valued time series as the cut-off (threshold) point. Please correct me if this way of applying $N$ maps is wrong. I now wonder how I can apply Shannon's source coding here - I want to transmit $N$ messages but what will be the length $d$ in bits? The entropy of the Tent Map = H = 1 bits/symbol.