Re: [10GBT] More on Fixed Point Decoder of the (1024, 833) Code
Dariush,
The word "approximation" implies that the calculated value is close to the
actual value for all inputs.
When we omit the a-priori probablity term in the Bayesian formula for the
LLR of the 12-Dimensional PAM12 system, then we should call this a mistake
and not an approximation.
Regards,
Sailesh.
srao@phyten.com
>From: Dariush Dabiri <DDabiri@TERANETICS.COM>
>Reply-To: Dariush Dabiri <DDabiri@TERANETICS.COM>
>To: STDS-802-3-10GBT@listserv.ieee.org
>Subject: Re: [10GBT] More on Fixed Point Decoder of the (1024, 833) Code
>Date: Thu, 7 Oct 2004 15:52:32 -0700
>
>Sailesh,
>
>It seems that we both agree that a decoder that ignores the so-called
>'holes' in the constellation is very close to the optimal. On the other
>hand, the very fact that the (1024, 833) code does not show any error
>floor (down to 1e-13) with the 'approximation', makes this discussion
>rather redundant. If it works fine with the 'approximation', then it can
>only get better by the 'optimization'.
>However, I have very serious doubts about this theory that the so-called
>'holes' in the constellation could help eliminate trapping sets and
>therefore improve on the error floor for any practically interesting
>code.
>
>Regards,
>
>Dariush
>
>-----Original Message-----
>From: stds-802-3-10gbt@IEEE.ORG [mailto:stds-802-3-10gbt@IEEE.ORG] On
>Behalf Of sailesh rao
>Sent: Thursday, October 07, 2004 4:17 AM
>To: STDS-802-3-10GBT@listserv.ieee.org
>Subject: Re: [10GBT] More on Fixed Point Decoder of the (1024, 833) Code
>
>Dariush,
>
>The a-priori probability of the received points is a 12D function in the
>case of the PAM12T constellation. It is a 2D function in the case of the
>donut constellation.
>
>It may be that the BER loss due to the uniform a-priori probability
>approximation is very small at higher BERs. However, if this additional
>BER loss is caused by an induced error floor due to the approximation,
>then this is a very serious issue.
>
>Regards,
>Sailesh.
>srao@phyten.com
>
> >From: Dariush Dabiri <DDabiri@TERANETICS.COM>
> >Reply-To: Dariush Dabiri <DDabiri@TERANETICS.COM>
> >To: STDS-802-3-10GBT@LISTSERV.IEEE.ORG
> >Subject: Re: [10GBT] More on Fixed Point Decoder of the (1024, 833)
> >Code
> >Date: Wed, 6 Oct 2004 18:19:29 -0700
> >
> >Sailesh,
> >
> >I do not know what you mean by '1D LLR estimator'. If you mean the a
> >posteriori LLR's of the coded bits coming from the channel, we just
> >follow the basics:
> >
> >We assume that all points of the 12 PAM constellation are equi-probable
>
> >and their probabilities are independent across dimensions. It follows
> >immediately that the channel LLR's are separable across dimensions,
>i.e.
> >for each bit, one only need to consider the received signal on the wire
>
> >that carried the bit.
> >(One may argue that this method is 'suboptimal', however it is
> >well-known that the loss due to this approximation is very very small.)
> >
> >The derivation of bit LLR's from the received 1D symbols is also
> >straightforward.
> >One good example can be found in ungerboeck_2_0904.pdf.
> >
> >Regards,
> >
> >Dariush
> >
> >-----Original Message-----
> >From: stds-802-3-10gbt@IEEE.ORG [mailto:stds-802-3-10gbt@IEEE.ORG] On
> >Behalf Of sailesh rao
> >Sent: Tuesday, October 05, 2004 5:36 AM
> >To: STDS-802-3-10GBT@listserv.ieee.org
> >Subject: Re: [10GBT] More on Fixed Point Decoder of the (1024, 833)
> >Code
> >
> >Dariush,
> >
> >Please specify the 1D LLR estimator used in these simulations.
> >
> >Thanks,
> >Sailesh.
> >srao@phyten.com
> >
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