# Coding Gain Definition

Started by February 25, 2007
```I have a doubt. Gain code is defined as the reduction, usually expresed in
decibels, in the required Eb/No to achieve a especified error probability
of the coded system over an uncoded system with the same modulation and
channel characteristics.

But, what about Bit rate? The definition considers the same Bit Rate in
both cases?????.

For example: I have implemented a Viterbi Receptor(r=1/2 k=7. Soft
Decision and df=10) for a BFSK modulation.

Without coding, I need 5 dBs more than coding, but Bit Rate without coding
is the double that coding Bit Rate with. Then, i could transmit without
coding slower, at the same Bit Rate (the half) than coding. So i could win
3dBs and the different would not be 5 dBs, would be only 2 dBs.

Then, if I read in a Book that Gain Coded for a code is X, i want to know
if that parameter is for the same Bit Rate in both cases.

Do you understand my question?

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```
JAlbertoDJ wrote:

> I have a doubt. Gain code is defined as the reduction, usually expresed in
> decibels, in the required Eb/No to achieve a especified error probability
> of the coded system over an uncoded system with the same modulation and
> channel characteristics.
> But, what about Bit rate? The definition considers the same Bit Rate in
> both cases?????.
>
> For example: I have implemented a Viterbi Receptor(r=1/2 k=7. Soft
> Decision and df=10) for a BFSK modulation.
>
> Without coding, I need 5 dBs more than coding, but Bit Rate without coding
> is the double that coding Bit Rate with. Then, i could transmit without
> coding slower, at the same Bit Rate (the half) than coding. So i could win
> 3dBs and the different would not be 5 dBs, would be only 2 dBs.

Your reasoning is correct. When evaluating the performance of the coded
system, one has to compare the coding gain against the energy per bit
reduction. What makes it even worse are the implementation losses of the
modem. The losses are increasing when the SNR is dropping, so for the
peer-to-peer comparison the modem for the coded modulation performs
worse then for that for the the uncoded.

Thus, the coding does make sense only if the output BER has to be low.
The simple codes like the one you are using will not provide for any
gain at all if the BER is about ~1e-2.

DSP and Mixed Signal Design Consultant

http://www.abvolt.com
```
```On Sun, 25 Feb 2007 17:15:01 -0600, "JAlbertoDJ" <nietorosdj@yahoo.es>
wrote:

>
>I have a doubt. Gain code is defined as the reduction, usually expresed in
>decibels, in the required Eb/No to achieve a especified error probability
>of the coded system over an uncoded system with the same modulation and
>channel characteristics.
>
>But, what about Bit rate? The definition considers the same Bit Rate in
>both cases?????.
>
>For example: I have implemented a Viterbi Receptor(r=1/2 k=7. Soft
>Decision and df=10) for a BFSK modulation.
>
>Without coding, I need 5 dBs more than coding, but Bit Rate without coding
>is the double that coding Bit Rate with. Then, i could transmit without
>coding slower, at the same Bit Rate (the half) than coding. So i could win
>3dBs and the different would not be 5 dBs, would be only 2 dBs.
>
>Then, if I read in a Book that Gain Coded for a code is X, i want to know
>if that parameter is for the same Bit Rate in both cases.
>
>Do you understand my question?

I think I understand your question.

One of the conveniences of using Eb/No as a metric is that it is
independent of data rate or even modulation type for comparing power
efficiency.  It is an indicator only of the power efficiency of the
transmission of a bit of information in Gaussian noise.   Since power
efficiency is a very important metric in wireless systems it is a very
useful calculation.

If, however, you are interested in spectral efficiency rather than
power efficiency, i.e., how much data can you get through a given
bandwidth, then Eb/No is NOT a relevant metric for that question.

Coding gain is, generally, independent of bit rate.   A given code
will provide the same gain at 1Mbps as it does at 2Mbps.

Eric Jacobsen
Minister of Algorithms
Abineau Communications
http://www.ericjacobsen.org
```