Re: [10GBT] More on Fixed Point Decoder of the (1024, 833) Code
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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