BCJR algorithm for M-ary modulations

Hello

Anybody who knows the BCJR algorithm may tell me how to compute the metric
gamma(s',s) when 16QAM or in general M-QAM, with M>4, is used?

Thanks in advance

>Hello
>
>Anybody who knows the BCJR algorithm may tell me how to compute the
metric
>gamma(s',s) when 16QAM or in general M-QAM, with M>4, is used?
>
>Thanks in advance

%%%%%

I am assuming that u want to design soft demapper to get soft estimate of
coded bits.

check this paper, 'Optimized symbol mappings for bit-interleaved coded
modulation with iterative decoding' the link is:

http://www.lnt.ei.tum.de/mitarbeiter/goertz/globecom03.pdf

Just try to read section II.

IHTH.

Chintan

>>Hello
>>
>>Anybody who knows the BCJR algorithm may tell me how to compute the
>metric
>>gamma(s',s) when 16QAM or in general M-QAM, with M>4, is used?
>>
>>Thanks in advance
>
>%%%%%
>
>I am assuming that u want to design soft demapper to get soft estimate
of
>coded bits.
>
>check this paper, 'Optimized symbol mappings for bit-interleaved coded
>modulation with iterative decoding' the link is:
>
>http://www.lnt.ei.tum.de/mitarbeiter/goertz/globecom03.pdf
>
>Just try to read section II.
>
>IHTH.
>
>Chintan
>

Thank you, but I dont understand it yet. I mean, how the extrinsic
information provided by equation (1) of that article is used to compute
gamma(s',s)? 
All I have read everywhere is that to compute gamma(s',s) I need to
calculate P(receivedcodeword|transmittedcodeword)=product j=1 to n of P(bit
j of the receivedcodeword|bit j of the transmittedcodeword)

Maybe it is very evident, but I do not see it. All the literature I have
found explain for the BPSK case and then the expression for
P(bit j of the receivedcodeword|bit j of the transmittedcodeword) can be
easily found for an AWGN channel, but I can not see it for M-QAM, M>4. For
M=4 must be quite similar to BPSK separating the bits for inphase component
and quadrature component, but what about M>4?

Thanks

Well, I guess u r trying to implement BCJR channel decoder? If the ans is
yes, then I am not sure how to help you, as I just know the theory but I
have not implemented the BCJR channel decoder. And I guess because for
channel decoder, u need just 1's and 0's (in terms of soft processing, -ve
and +ve values).

I have implemented soft demapper from the above paper, it is working
fine.


Chintan

>Well, I guess u r trying to implement BCJR channel decoder? If the ans is
>yes, then I am not sure how to help you, as I just know the theory but I
>have not implemented the BCJR channel decoder. And I guess because for
>channel decoder, u need just 1's and 0's (in terms of soft processing,
-ve
>and +ve values).
>
>I have implemented soft demapper from the above paper, it is working
>fine.
>
>
>Chintan
>

Yes, exactly, and I do not find any reference explaining how to compute
gamma(s',s) when log likelihood ratios are the input to the decoder and the
modulation employed is M-QAM, with M>4. That makes me think it must be very
easy, evident, but I just do not see how to calculate the conditional
distribution P(received codeword|transmitted codeword)

Crisanquito <crisancost@hotmail.com> wrote:

>Thank you, but I dont understand it yet. I mean, how the extrinsic
>information provided by equation (1) of that article is used to compute
>gamma(s',s)? 
>All I have read everywhere is that to compute gamma(s',s) I need to
>calculate P(receivedcodeword|transmittedcodeword)=product j=1 to n of P(bit
>j of the receivedcodeword|bit j of the transmittedcodeword)
>
>Maybe it is very evident, but I do not see it. 

Go back and read my post <gl7ess$csg$3@blue.rahul.net> which was
my reply to you the first time you asked this question several days
ago.  The answer you need is in there.  Or if it is not, make sure
you understand the information in that post, then ask again.

Steve

>Yes, exactly, and I do not find any reference explaining how to compute
>gamma(s',s) when log likelihood ratios are the input to the decoder and
the
>modulation employed is M-QAM, with M>4. That makes me think it must be
very
>easy, evident, but I just do not see how to calculate the conditional
>distribution P(received codeword|transmitted codeword)
>

%%%

As far as I think (I might be wrong) but BCJR decoding does not depend on
any modulation scheme.

Lets say: if u r using rate 1/2 concolution code of polynomial (5,7) and
QPSK modulation, and ur i/p to the encoder is 100 bits long message, then u
will have 204 encoded bits as o/p of encoder. Means, u will have 102 QPSK
symbols.

Now, when u use soft demapper, instead of conventional demodulation, u
will get 204 soft LLRs (Extrinsic information) of the encoded bits.

So basically it does not matter, which modulation u use. You might find
these papers useful:

''Comparative study of turbo decoding techniques: an overview,'' by J P
Woodward and Lajos Hanzo.

http://tmo.jpl.nasa.gov/progress_report/42-127/127H.pdf


Chintan

Another chapter:

http://www.stanford.edu/class/ee379b/class_reader/chap9.pdf

>Another chapter:
>
>http://www.stanford.edu/class/ee379b/class_reader/chap9.pdf
>

I will have a look at both, thank you very much

cpshah99 <cpshah99@rediffmail.com> wrote:

> As far as I think (I might be wrong) but BCJR decoding does not 
> depend on any modulation scheme.

It depends upon what you are decoding with BCJR.

If you're using the BCJR to decode the channel (e.g., analogous
to a Forney equalizer, but with BCJR instead of Viterbi) you
most certainly need to include the modulation.

If you're only using BCJR to decode the FEC code, which is the
most common scenario, then you only need bit probabilities
at the input to the BCJR decoder.  The modulation method
is involved in producing those probabilities but is not otherwise
involved.

What you want to ask yourself is: what state is the BCJR algorithm
operating over?  Is it channel state, or just FEC encoder state,
or both?   I have encountered BCJR channel decoding in systems
such as GSM GMSK modulation, or 802.11b (BPSK) but it
is often regarded as too complex for higher-order modulation.

Steve