The question with proper formatting (http://stats.stackexchange.com/questions/244969/log-likelihhood-ratio-with-soft-information)
The log likelihood ratio of two binary random variables $x$ and $y$ (only taking values $0$ or $1$) can be defined as
$LLR_x=\frac{P(x=0|y)}{P(x=1|y)}$
The above definition is OK if $y=0$ or $1$.
Now if $y$ is in the form of log likelihood ratio (soft information output from another system), how can it be incorporated in the above equation i.e.
$LLR_y=\frac{P(y=0|z)}{P(y=1|z)}$
so that,
$LLR_xnew=\frac{P(x=0|LLR_{y})}{P(x=1|LLR_{y})}$
Obviously, I don't want to take the hard decisions on the value of $y$ (it is straight forward for the hard decisions).
In other words, if $P(x=0|y)$ is already known but some how $y$ is the output from a system and is in the form of log likelihood ratio. So, is it possible to redefine $P(x=0|y)$?
I posted answer on
(http://stats.stackexchange.com/questions/244969/log-likelihhood-ratio-with-soft-information)
You ca also look to
http://ptgmedia.pearsoncmg.com/images/art_sklar3_turbocodes/elementLinks/art_sklar3_turbocodes.pdf
under Log-likelihood ratio
Thank you for your suggestions. Please have another look on the question as I have further elaborated it. Hope you will guide me in the right direction.
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