Computing the entropy
Mathematica, 48 68 bytes

Edit: Preprocess is added for accepting string as the parameter.

With the help of Tuples and Entropy, the implementation is both concise and readable.

Entropy[2,{-1,1}~Tuples~Length@#.#]&amp;@Thread@ImportString[#,"Table"]&amp;


where Tuples[{-1,1},n] gives all possible n-tuples from {-1,1}, and Entropy[2,list] gives the base-2 information entropy.

One of the cool things is that Mathematica will actually return an accurate expression: 

%["-1 -1 \n -1 -1"]
(* 3/2 *)


Approximate result can be achieved with an extra . added (Entropy[2., ...).