# Repetition Coding and Soft demodulation

Started by April 13, 2006
```Dear All,

Okay, probably this sound a bit silly, but what happens when repetition
coding is used and when soft demodulation is used ? Soft QAM
demodulation produces Log Likelihood Ratio (LLR), and  should I take
average value of the repeated symbols ? Here's the simple view of the

Channel -->Soft QAM demodulator-->Repetition Decoding-->De
Interleaver--> FEC decoder

Any impact if I take the average ? Or should I take the maximum (or
minimum) value ? Thanks. Hear from you guys.

Regards,
Arthur.

```
```Dear All,

Okay, probably this sound a bit silly, but what happens when repetition
decoding is done along with soft demodulation ? Soft QAM
demodulation produces Log Likelihood Ratio (LLR) of repeated bits, and
how LLR of repeated bits decoded with a repetition decoder ? Here's the
simple view of the

Channel -->OFDM Demodulator-->Soft QAM demodulator-->Repetition
Decoding-->De
Interleaver--> FEC decoder

Usually majority logic decoding is used with hard demodulation, but if
hard demodulation is used, does it have any impact on soft decoder like
LDPC, turbo or virtebi decoder ?

Regards,
Arthur.

```
```Arthur wrote:

> Dear All,
>
> Okay, probably this sound a bit silly, but what happens when repetition
> coding is used and when soft demodulation is used ? Soft QAM
> demodulation produces Log Likelihood Ratio (LLR), and  should I take
> average value of the repeated symbols ? Here's the simple view of the
>
> Channel -->Soft QAM demodulator-->Repetition Decoding-->De
> Interleaver--> FEC decoder
>
> Any impact if I take the average ? Or should I take the maximum (or
> minimum) value ? Thanks. Hear from you guys.
>
> Regards,
> Arthur.
>
Soft demodulation + repetition coding = longer symbols.  If your soft
decisions reflect the a posteriori probability of a given bit being
correct answer is _exactly_ the same one as just using longer symbols to
start.  So if you're always sending symbols out in groups of (say)
three, you have no gain over just using symbols that are three times
longer.  I suppose that if you scattered your symbols around you'd get
some gain in a bursty noise environment, but only if your soft
demodulation is no longer linear.

You get better coding gain from real codes -- I've seen this proven it
at least one book on coding theory, and I'd be surprised if it wasn't
there in every elementary coding theory book.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

```
```But in real life scenerio where channel experience multipath fading,
doesn't repetition codes provide some kind of delay diversity gain ?

Actually what kind of decoding logic optimal for this kind of
concatenated code ? It is in fact in wimax, where repetition code is
use as inner code to outter code LDPC.

```
```Arthur wrote:

> But in real life scenerio where channel experience multipath fading,
> doesn't repetition codes provide some kind of delay diversity gain ?
>
> Actually what kind of decoding logic optimal for this kind of
> concatenated code ? It is in fact in wimax, where repetition code is
> use as inner code to outter code LDPC.
>
Are they repeating each bit several times in a row, or are they sending
sequences where the bits are separated like 1, 2, 3, 4, 3, 2, 1, 4?

In a non-Gaussian channel, particularly one with bursty noise, a
straight repetitive code may give better gain.  If it's predictably
non-Gaussian you have a better idea of which bits have been hammered,
and can therefore be neglected.  If it's bursty then something that
takes out several bits in a row may only take out a fraction of each bit
in a repetition code.  I suppose that if your bit rate is very high
compared to your multipath then the intersymbol interference may look
like bursty noise.

As for why they used it in Wi-Fi -- I dunno.  I'll put finding out on my
'to do' list.  Unfortunately it'll be toward the bottom, though.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

```
```I think they repeat it several time immediately after each bit, like,
1,1,1,2,2,2,3,3,3,4,4,4, where there repetition factor is three. WIMAX
include it to increase reliability of control signals like FCH, DL-MAP
and UL-MAP.

I am implementing it, just that I am not too sure how the decoder
should be when log likelihood ratio (LLR) is used. In hard decision, I
can easily use major logic decoding, but for soft value like LLR, not

```
```Arthur wrote:
> I think they repeat it several time immediately after each bit, like,
> 1,1,1,2,2,2,3,3,3,4,4,4, where there repetition factor is three. WIMAX
> include it to increase reliability of control signals like FCH, DL-MAP
> and UL-MAP.
>
> I am implementing it, just that I am not too sure how the decoder
> should be when log likelihood ratio (LLR) is used. In hard decision, I
> can easily use major logic decoding, but for soft value like LLR, not