> Am 19.11.2013 16:41, schrieb sg:
>
>> number of states coding gain (dB)
>> -------------------------------------
>> 4 3
>> 8 3.6
>> 16 4.1
>> : :
>>
>> I ask because I seem to have found an 8-state code that gives me a gain
>> of 4.1 dB. So, either someone is wrong (me or the author of the paper)
>> or I found an 8-state TCM for 8-PSK that beats publicly known codes.
>
> It looks like I screwed up the free distance computation. [...]
> number of states coding gain (dB)
> -------------------------------------
> 4 3
> 8 3.6
> 16 4.1
> : :
>
> I ask because I seem to have found an 8-state code that gives me a gain
> of 4.1 dB. So, either someone is wrong (me or the author of the paper)
> or I found an 8-state TCM for 8-PSK that beats publicly known codes.
It looks like I screwed up the free distance computation. I thought I
could just calculate the free distance between the "zero sequence" and
one of the closest other valid symbol sequence outputs. But that does
not seem to work. I guess this won't catch Voronoi regions of different
shapes and sizes over all possible sequences. For the 8-state recursive
rate-2/3 Ungerboeck code for 8-PSK my computation yields the right free
distance sqrt(4.58579). So, that's good. But the other 8-state
convolutional code I checked yields a free distance of sqrt(5.17157) but
performs worse in AWGN simulations. That makes me believe that the way I
tried to compute the free distance is wrong.
Any suggestions on how to properly compute the free distance?
> Cheers!
> SG
Reply by sg●November 19, 20132013-11-19
Am 18.11.2013 18:27, schrieb Vladimir Vassilevsky:
> On 11/18/2013 10:04 AM, sg wrote:
>
>> I want to make sure that what I've learned so far about Trellis-Coded
>> Modulation is correct which is why I'm asking for confirmation.
>>
>> d_free^2 is minimal the sum of squared Euclidean distances between two
>> symbol sequences that can be generated by the TCM, right?
>>
>> The coding gain is 10*log10(d_free^2/d_min^2) where d_min is the minimum
>> Euclidean distance for a pair of "uncoded" symbols, right?
>
> That's the limit of coding gain for ideal decoder when Eb/No goes to
> infinity.
Right. I should have said "asymptotic coding gain".
>> For example, if I come up with a TCM that maps 2 bits to an 8-PSK symbol
>> (a complex number on the unit circle) and compute d_free^2 to be 5.1716
>> and then compare it to QPSK where d_min^2 is 2 = norm(1-1i)^2 and say
>> that the coding gain is 4.13 dB would that be correct?
>
> You could say that coding gain would be no more then 4.13dB; depending
> on Eb/No and other things.
Right. For now, I'm just concerned about the asymptotic gains.
Next question. Can somebody confirm that the table in
http://complextoreal.com/wp-content/uploads/2013/01/tcm.pdf
on page 19 about possible asymptotic coding gains for 8-PSK (taking 2
bits and mapping it to an 8PSK symbol) is correct? Here it is for your
convenience:
number of states coding gain (dB)
-------------------------------------
4 3
8 3.6
16 4.1
: :
I ask because I seem to have found an 8-state code that gives me a gain
of 4.1 dB. So, either someone is wrong (me or the author of the paper)
or I found an 8-state TCM for 8-PSK that beats publicly known codes.
Cheers!
SG
Reply by Vladimir Vassilevsky●November 18, 20132013-11-18
On 11/18/2013 10:04 AM, sg wrote:
> I want to make sure that what I've learned so far about Trellis-Coded
> Modulation is correct which is why I'm asking for confirmation.
>
> d_free^2 is minimal the sum of squared Euclidean distances between two
> symbol sequences that can be generated by the TCM, right?
>
> The coding gain is 10*log10(d_free^2/d_min^2) where d_min is the minimum
> Euclidean distance for a pair of "uncoded" symbols, right?
That's the limit of coding gain for ideal decoder when Eb/No goes to
infinity.
> For example, if I come up with a TCM that maps 2 bits to an 8-PSK symbol
> (a complex number on the unit circle) and compute d_free^2 to be 5.1716
> and then compare it to QPSK where d_min^2 is 2 = norm(1-1i)^2 and say
> that the coding gain is 4.13 dB would that be correct?
You could say that coding gain would be no more then 4.13dB; depending
on Eb/No and other things.
Vladimir Vassilevsky
DSP and Mixed Signal Designs
www.abvolt.com
Reply by sg●November 18, 20132013-11-18
Hi!
I want to make sure that what I've learned so far about Trellis-Coded
Modulation is correct which is why I'm asking for confirmation.
d_free^2 is minimal the sum of squared Euclidean distances between two
symbol sequences that can be generated by the TCM, right?
The coding gain is 10*log10(d_free^2/d_min^2) where d_min is the minimum
Euclidean distance for a pair of "uncoded" symbols, right?
For example, if I come up with a TCM that maps 2 bits to an 8-PSK symbol
(a complex number on the unit circle) and compute d_free^2 to be 5.1716
and then compare it to QPSK where d_min^2 is 2 = norm(1-1i)^2 and say
that the coding gain is 4.13 dB would that be correct?
Cheers!
sg
[1] http://complextoreal.com/wp-content/uploads/2013/01/tcm.pdf