# Constellation symbol to bit's soft-probability?

Started by January 19, 2006
```Hi all,

I am new to demodulation and FEC.

How can I get each bit's soft-probability from the constellation?
For example, the modulation method is 16QAM, How can I get
P(bit1=0),P(bit2=0),P(bit3=0),P(bit4=0)  from a symbol?

Is it belong to the subject of detection and need viterbi algorithm?

Or can you recommend some key words of this subject?

Best regards,
Davy

```
```"Davy" <zhushenli@gmail.com> wrote in message
> Hi all,
>
> I am new to demodulation and FEC.
>
> How can I get each bit's soft-probability from the constellation?
> For example, the modulation method is 16QAM, How can I get
> P(bit1=0),P(bit2=0),P(bit3=0),P(bit4=0)  from a symbol?
>
> Is it belong to the subject of detection and need viterbi algorithm?
>
> Or can you recommend some key words of this subject?
>
"bayes theorem"+"soft input"  should work.

You could also look at page 72 to 74 of this for a very direct method;
http://4more.av.it.pt/docs/D4.4.pdf

Best of luck - Mike

```
```Davy wrote:

> Hi all,
>
> I am new to demodulation and FEC.
>
> How can I get each bit's soft-probability from the constellation?
> For example, the modulation method is 16QAM, How can I get
> P(bit1=0),P(bit2=0),P(bit3=0),P(bit4=0)  from a symbol?
>
> Is it belong to the subject of detection and need viterbi algorithm?
>
> Or can you recommend some key words of this subject?
>
> Best regards,
> Davy
>
Viterbi decoding comes after soft decision making; the only real
connection is that Viterbi decoding is enhanced by soft decisions.

Mike's response is the correct one: you use Baysian estimation to figure
out what the probability that a certain bit was transmitted.  You need
to know the probability density function of your noise and have a pretty
good grasp of the signal characteristics for it to work right.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com
```
```In sci.electronics.design Mike Yarwood <mpyarwood@btopenworld.com> wrote:
>
> "Davy" <zhushenli@gmail.com> wrote in message
>> Hi all,
>>
>> I am new to demodulation and FEC.
>>
>> How can I get each bit's soft-probability from the constellation?
>> For example, the modulation method is 16QAM, How can I get
>> P(bit1=0),P(bit2=0),P(bit3=0),P(bit4=0)  from a symbol?
<snip>
"bayes theorem"+"soft input"  should work.
>
> You could also look at page 72 to 74 of this for a very direct method;
> http://4more.av.it.pt/docs/D4.4.pdf

If you get any signal, is there a nice way of back propagating to get
optimum probabilities?
```
```I don't completely comprehend what you mean by back propogation. But
yes, it is possible to get optimum probabilities for bits mapped to a
constellation symbol. You would find results on that if you search for
Bit Interleaved Coded Modulation, or BICM in short.

```
```In sci.electronics.design PraZ <prasanna.sethuraman@patni.com> wrote:
> I don't completely comprehend what you mean by back propogation. But
> yes, it is possible to get optimum probabilities for bits mapped to a
> constellation symbol. You would find results on that if you search for
> Bit Interleaved Coded Modulation, or BICM in short.

If you get a decoded signal of any form coming through the viterbi
decoder, a nice way of propagating back the actual symbol properties
into the decisions.
```