Hi.
I think the residual redundancy due to (2) can be abtained by computing the
entropy rate conditioned by the same parameter value in successive frames.
Let x denote the particular parameter in question, and let time index
n=0 specify the present time index, accordingly n = -1, -2, .... are time
indices of previous frames or subframes, and n = +1, +2, ... are future time
indices. Then the conditional entropy rate is H( x0 | ..., x-2, x-1, x+1,
x+2, ....). If the symbol consists of M bits, the residual redundancy is M
- H (x0 | ..., x-2, x-1, x+1, x+2, ....).
However, it is very difficult is compute H( x0 | ..., x-2, x-1, x+1, x+2,
....). For simplicity, we can model the parameter as a Markov process of Nth
order, and N is always restricted to 0, 1 or 2. Then the conditional entropy
rate can be easily computed.
Plus, I don't think the sum of the redundancy due to (1) and (2) is
simply
the total residual redundancy. In fact, the redundancy due to (1) is
presented in (2) in a much more delicate way. What do you think?
2008/12/10
> Hi everyone!
>
> Residual redundancies that are extracted from the parameters of a
> particular source encoder output is said to be the result of (1) the
> nonuniform distribution of values (quantized levels) and (2) the actual
> temporal correlation that exists (memory) between successive frames. Based
> on formula, I am able to compute for the entropy rate of any particular
> parameter in question. The residual redundancy then could easily be
computed
> by subtracting the number of bits per symbol used for the parameter to the
> entropy rate calculated earlier.
>
> The question now is, how do you actually quantify the separate values of
> the residual redundancy due to (1) and (2)? I've seen from the paper
by
> Fazel and Fuja that they were able to separate these values.
>
> I attempted to compute for it by getting the distribution of each possible
> bit vector values for a particular parameter. Then I counted the total
> number of occurrences (for each value) and solved for their relative
> frequencies leading me to solve for the entropy rate. Then I subtract the
> entropy from the number of bits per symbol. I'm guessing that the value
I
> got is the residual redundancy due to (1) but how about (2)? Is there a
> clear cut way of getting (1) and (2) separately without using the fact that
> the sum of the two is simply the total residual redundancy? If anyone
> understands what I'm saying please feel free to help me out.
Thanks!