BCJR algorithm for M-ary modulations

>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
>

%%%

You are right. It just slipped out of mind.

Even Viterbi algorithm (or BCJR) will be difficult to implement for
channel decoding for higher modulation as the channel memory increases. If
I am right the complexity will grow as M^L, where M is modulation level and
L is channel memory.

>>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
>>
>
>%%%
>
>You are right. It just slipped out of mind.
>
>Even Viterbi algorithm (or BCJR) will be difficult to implement for
>channel decoding for higher modulation as the channel memory increases.
If
>I am right the complexity will grow as M^L, where M is modulation level
and
>L is channel memory.
>
>
>


I am trying to understand it for FEC decoding. If I am not wrong, you
Steve explained me how to compute the soft bit metrics which are the input
of the APP decoding, isnt it? Now I know how they are computed and its
meaning, but I do not see how I can related them to gamma(s',s) = function
of (P(ykl|xkl))

I mean, it is evident how gaussian noise affects the received complex
symbols and its conditional density is easily computed, but P(bit
j of the receivedcodeword|bit j of the transmittedcodeword)=
P(ykl|xkl)? I do not see it. 

Thank you again, I will appreciate a post opening my eyes, meanwhile I
will keep on reading to find an answer.

 

Crisanquito <crisancost@hotmail.com> wrote:

>I mean, it is evident how gaussian noise affects the received complex
>symbols and its conditional density is easily computed, but P(bit
>j of the receivedcodeword|bit j of the transmittedcodeword)=
>P(ykl|xkl)? I do not see it. 

This is a little difficult because you actually don't have a 
probability, you have a measure.  People sometimes say things 
like "the probability of receiving signal X given that a certain 
transmitted bit is a one" but obviously the probability of
receiving a given signal point is always zero.  So what you
need to do is construct a measure m0 for the zero-transmitted-bit
case and m1 for the one-transmitted-bit case, and state
the "probability of a one" as m1/(m0+m1).  These meausres are 
constructed by fixing one of the transmitted bits within the QAM 
symbol, letting the other bits range over their possible values
(which are equiprobable, comprising half of the total number of
constellation points), and adding up the individual densities.
This leads to equations like I stated earlier.

Is this rigorous?  Not really sure, but it gives you the right answer.
Practically speaking if your turbo or LDPC decoder is performing
close to capacity (within one dB) then you probably constructed
the measures correctly.

Steve