FPGA Central

cpshah99 <[email protected]> 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

>cpshah99 <[email protected]> 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 fo
channel decoding for higher modulation as the channel memory increases. I
I am right the complexity will grow as M^L, where M is modulation level an
L is channel memory.

>>cpshah99 <[email protected]> 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 leve
and
>L is channel memory.
>
>
>


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

I mean, it is evident how gaussian noise affects the received comple
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
will keep on reading to find an answer.

Crisanquito <[email protected]> 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