f

#### Coding Gain: Huffman Code

```Hey All,

Could someone tell me how to find out the coding gain if Huffman coding i
used. The BER without coding is 0.1. I found the Huffman code of th
alphabet and got an efficiency of 98 %. How do I calculate the coding gai
or the BER when the coding is used for a specific SNR value?

Thanks,
Nisha

```
 0
12/9/2007 2:03:22 PM
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```On Sun, 09 Dec 2007 08:03:22 -0600, "Nisha_Malh"
<farah727rash@gmail.com> wrote:

>Hey All,
>
>Could someone tell me how to find out the coding gain if Huffman coding is
>used. The BER without coding is 0.1. I found the Huffman code of the
>alphabet and got an efficiency of 98 %. How do I calculate the coding gain
>or the BER when the coding is used for a specific SNR value?
>
>Thanks,
>Nisha
>

Usually 'coding gain' is expressed in dB at a particular BER.   For
example if a particular coded system achieves Pe = 10e-3 at 6dB SNR,
and the same BER at 10dB SNR when the same system is uncoded, then the
'coding gain' under those conditions is 4dB.

So typically one picks a performance metric, whether it's a particular
BER or PER or something similar, and then finds the difference in SNR
or Eb/No (or similar metric) for the coded and uncoded cases at the
same performance level in the same channel conditions.

Eric Jacobsen
Minister of Algorithms
Abineau Communications
http://www.ericjacobsen.org
```
 0
eric.jacobsen (2636)
12/9/2007 5:36:20 PM
```>Usually 'coding gain' is expressed in dB at a particular BER.   For
>example if a particular coded system achieves Pe = 10e-3 at 6dB SNR,
>and the same BER at 10dB SNR when the same system is uncoded, then the
>'coding gain' under those conditions is 4dB.
>
>So typically one picks a performance metric, whether it's a particular
>BER or PER or something similar, and then finds the difference in SNR
>or Eb/No (or similar metric) for the coded and uncoded cases at the
>same performance level in the same channel conditions.
>
>Eric Jacobsen
>Minister of Algorithms
>Abineau Communications
>http://www.ericjacobsen.org
>

So, can I design for a code to give me the coding gain I want?

And, how do I know the code rate of a Huffman code? For example, the cod
rate of a convolutional code is n/k (n bit input, k bit output).
Since Huffman code has variable output bit length, how can I know what th
code rate is? Is it the average output bit length I need to take?
```
 0
12/9/2007 8:15:46 PM
```"Nisha_Malh" <farah727rash@gmail.com> writes:

>>Usually 'coding gain' is expressed in dB at a particular BER.   For
>>example if a particular coded system achieves Pe = 10e-3 at 6dB SNR,
>>and the same BER at 10dB SNR when the same system is uncoded, then the
>>'coding gain' under those conditions is 4dB.
>>
>>So typically one picks a performance metric, whether it's a particular
>>BER or PER or something similar, and then finds the difference in SNR
>>or Eb/No (or similar metric) for the coded and uncoded cases at the
>>same performance level in the same channel conditions.
>>
>>Eric Jacobsen
>>Minister of Algorithms
>>Abineau Communications
>>http://www.ericjacobsen.org
>>
>
> So, can I design for a code to give me the coding gain I want?
>
> And, how do I know the code rate of a Huffman code? For example, the code
> rate of a convolutional code is n/k (n bit input, k bit output).
> Since Huffman code has variable output bit length, how can I know what the
> code rate is? Is it the average output bit length I need to take?

There seems to be a big disconnect. "Coding gain" is usually a term
applied to channel coding. Huffman codes are *source* codes!
--
%  Randy Yates                  % "Ticket to the moon, flight leaves here today
%% Fuquay-Varina, NC            %  from Satellite 2"
%%% 919-577-9882                % 'Ticket To The Moon'
%%%% <yates@ieee.org>           % *Time*, Electric Light Orchestra
http://www.digitalsignallabs.com
```
 0
yates (3949)
12/9/2007 8:32:33 PM
```On Sun, 09 Dec 2007 15:32:33 -0500, Randy Yates <yates@ieee.org>
wrote:

>"Nisha_Malh" <farah727rash@gmail.com> writes:
>
>>>Usually 'coding gain' is expressed in dB at a particular BER.   For
>>>example if a particular coded system achieves Pe = 10e-3 at 6dB SNR,
>>>and the same BER at 10dB SNR when the same system is uncoded, then the
>>>'coding gain' under those conditions is 4dB.
>>>
>>>So typically one picks a performance metric, whether it's a particular
>>>BER or PER or something similar, and then finds the difference in SNR
>>>or Eb/No (or similar metric) for the coded and uncoded cases at the
>>>same performance level in the same channel conditions.
>>>
>>>Eric Jacobsen
>>>Minister of Algorithms
>>>Abineau Communications
>>>http://www.ericjacobsen.org
>>>
>>
>> So, can I design for a code to give me the coding gain I want?
>>
>> And, how do I know the code rate of a Huffman code? For example, the code
>> rate of a convolutional code is n/k (n bit input, k bit output).
>> Since Huffman code has variable output bit length, how can I know what the
>> code rate is? Is it the average output bit length I need to take?
>
>There seems to be a big disconnect. "Coding gain" is usually a term
>applied to channel coding. Huffman codes are *source* codes!

Duh.  That only occurred to me when I read the response.

Ah, well...

Eric Jacobsen
Minister of Algorithms
Abineau Communications
http://www.ericjacobsen.org
```
 0
eric.jacobsen (2636)
12/9/2007 9:09:16 PM
```On Sun, 09 Dec 2007 08:03:22 -0600, Nisha_Malh wrote:

> Hey All,
>
> Could someone tell me how to find out the coding gain if Huffman coding
> is used. The BER without coding is 0.1. I found the Huffman code of the
> alphabet and got an efficiency of 98 %. How do I calculate the coding
> gain or the BER when the coding is used for a specific SNR value?
>
> Thanks,
> Nisha

The Huffman code is used to compress data, so it takes your original
stream and removes redundant bits in a way that is (hopefully) easy to
expand back to the original at the receiving end.

The codes to which the term "coding gain" is usually applied are error
correcting codes, where redundant bits are _added in_, such that below
some threshold number of bit errors in a block (or length for
convolutional codes -- I'm a bit weak on that tidbit) errors can be
completely corrected.

A Huffman code would have the characteristic of increasing the output bit
rate for a certain input bit rate, and would, furthermore, take
completely random bit errors in and return you burst errors.  Used in a
channel with no other coding, a Huffman code would have coding _loss_,
but you'd calculate it the same way that Eric outlined for an error
correcting code.

--
Tim Wescott
Control systems and communications consulting
http://www.wescottdesign.com

Need to learn how to apply control theory in your embedded system?
"Applied Control Theory for Embedded Systems" by Tim Wescott
Elsevier/Newnes, http://www.wescottdesign.com/actfes/actfes.html
```
 0
tim177 (4433)
12/9/2007 10:25:34 PM
```
Nisha_Malh wrote:

> Hey All,
>
> Could someone tell me how to find out the coding gain if Huffman coding is
> used. The BER without coding is 0.1. I found the Huffman code of the
> alphabet and got an efficiency of 98 %. How do I calculate the coding gain
> or the BER when the coding is used for a specific SNR value?

The question is incorrect. You've got to know the structure of the
original data. If it is 98% redundant, then some of this redundancy can
benefit to the error correction.

However here is the worst case estimate, if this redundancy can't be
used. You got to know the size of the message. Let the size of original
message = N bits. Huffman compression of 98% = energy boost by 50 times.
Thus you are likely to deal with the single bit errors. But one error in
the compresed block is likely to result in ~N/4 errors at the output.
In the uncompressed case, the number of errors is likely to be N/10.
Now look at the erf() function and normalize the compressed and
uncompressed cases to the same error rate. Observe the difference in the
required power to transmit the message. This is your gain.

DSP and Mixed Signal Design Consultant
http://www.abvolt.com
```
 0
12/9/2007 10:50:33 PM

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