Crisanquito <crisancost@hotmail.com> wrote:

>I guess it is one of the most basic topics, but I am not able to
>understand this topic, mainly because I have not found yet any reference
>explaining it:

>I am trying to understand the iterative turbo decoding, but I am still
>trying to understand the APP decoding part.

Let me try to state the appropriate expression.

The APP that a transmitted bit is a one is

P(1) = poss(1) / (poss(1) + poss(0)) where

poss(1) = sum over (constellations points p corresponding to 
            a transmitted 1) of poss(1,p)

where for additive white noise of variance v and received signal x

      poss(1,p) = exp(-(x-p)^2/(2*v))

Use a simlar formula for poss(0).  You compute P(1) for each
transmitted bit.  Obviously p, x, and v are computed using the
same units (based on the scale of the Cartestian coordinate
system upon which you have defined your constellation).

For BPSK there is only one constellation point for each
possible value of the transmitted bit and the log of this
expression reduces to the familiar distance metric used in
most Viterbi decoders.   For higher-order QAM, either use
the full expression, or just use the dominant term in which
case you are using the "nearest neighbor approximation" or
"slicing" which entails an implementation loss.

You are on the right track doing this computation in the probability
domain, rather than the log probability domain as the arithmetic
(both for this part and within the turbo decoder) is much simpler.

Hope this helps.

Steve

Hello

I guess it is one of the most basic topics, but I am not able to
understand this topic, mainly because I have not found yet any reference
explaining it:
I am trying to understand the iterative turbo decoding, but I am still
trying to understand the APP decoding part.
The computation of gamma implies to find gamma(s',s)=P(yk|xk), being yk
the received codeword and xk the transmitted codeword. Ok, my doubt is so
simple as: how yk is obtained? It is obtained by means of a soft
demodulation algorithm, but I am not acquainted with this topic, and I do
not understand the equations which give me the probability of receiving a
certain bit of the codeword yk having sent a certain bit of the transmitted
codeword xk:

gamma(s',s)=P(yk|xk)=Prod_l=1_to_l=n of P(ykl|xkl), being
yk=[yk1,yk2,..ykn]

and P(ykl|xkl)=1/(sqrt(2*pi)*sigma)*exp(-Eb/(2*sigma^2)*(ykl-a*xkl)^2)

being a the fading amplitude of a Gaussian channel. This modulation is
given for a BPSK modulation.

Well, may you give me any reference in which soft demodulation is
explained? Then I think I will be able to understand why these formulas.

Thank you