Sub-Intervals

After the initial encoding, any further symbol will not relate to the basic intervall [0; 1). The sub-interval identified by the first symbol has to be used for the next step. In the case of an 'a' the new interval would be [0; 0.4), for 'b' [0.4; 0.6).

Providing a constant probability distribution and the first symbol 'a', the new sub-intervals would be:

Divide interval after encoding of 'a'

    total: [0.0; 1.0)       total: [0.0; 0.4)

Sym. P(x)  Intervals              Sub-Intervals
 a   0.4   [0.0; 0.4) ----- 0.16   [0.00; 0.16)
 b   0.2   [0.4; 0.6)   |   0.08   [0.16; 0.24)
 c   0.2   [0.6; 0.8)   |   0.08   [0.24; 0.32)
 d   0.1   [0.8; 0.9)   |   0.04   [0.32; 0.36)
 e   0.1   [0.9; 1.0)    -- 0.04   [0.36; 0.40)
    -----                  ------
Sum  1.0                    0.40

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