LDPC with Higher Order Constellations
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From: reginald on 23 Dec 2009 08:34 I have a LPDC decoder that works with soft bit estimates. This is great for the case of BPSK or QPSK, but I'd like to extend it to something like a higher order QAM constellation. Is there: (a) a straightforward way to generate soft bit estimates from higher order constellations like, say, 16QAM? (b) more specifically, an extension to an LDPC decoder that works with likelihoods of each bit? This seems complicated since in general your "check nodes" and "bit nodes" will be correlated in some way that the algorithm isn't anticipating. I would greatly appreciate any light that you may shed on my problem, and thanks in advance. Regards, Reggie
From: Vladimir Vassilevsky on 23 Dec 2009 09:38 reginald wrote: > I have a LPDC decoder that works with soft bit estimates. This is great for > the case of BPSK or QPSK, but I'd like to extend it to something like a > higher order QAM constellation. This question is been regularly asked in this NG. Steve Pope explained it no less then 10 times. Search the archives. http://www.dsprelated.com/showmessage/107583/1.php Vladimir Vassilevsky DSP and Mixed Signal Design Consultant http://www.abvolt.com
From: alos on 23 Dec 2009 14:20 >(a) a straightforward way to generate soft bit estimates from higher order >constellations like, say, 16QAM? Yes. Generally the approximation to the true likelihood of marginal probability is used: LLR(bi) = 1/(2*sigma^2) * d(S,bi=1)/d(S,bi=0) Where sigma^2 is variance of the noise (plus channel gain estimate variance) and d(S,bi=1)/d(S,bi=0) are distances along I or Q axis (depending on which axis the bi is defined) to the closest constellation point having bit 'bi' equal to 1/0 respectively. >(b) more specifically, an extension to an LDPC decoder that works with >likelihoods of each bit? This seems complicated since in general your >"check nodes" and "bit nodes" will be correlated in some way that the >algorithm isn't anticipating. I thought that standard LDPC works on bit likelihoods ?? What is being ignored in mentioned LLR calculations is in fact the joint probability of all the bits given the symbol received. Instead we calculate marginal likelihood thus pretending that each bit is independent (and they are not). BTW. I suppose that introducing the joint probabilities to the message passing algorithm would by some BER... So there are two approximations, first true probability is appoximated with independent marginal probabilities of bits, second the marginal probailities (likelihoods) are approximated with piecewise linear function LLR(bi). Regards, Alek >I would greatly appreciate any light that you may shed on my problem, and >thanks in advance. > >Regards, > Reggie > > >
From: Eric Jacobsen on 23 Dec 2009 16:40 On 12/23/2009 6:34 AM, reginald wrote: > I have a LPDC decoder that works with soft bit estimates. This is great for > the case of BPSK or QPSK, but I'd like to extend it to something like a > higher order QAM constellation. > > Is there: > > (a) a straightforward way to generate soft bit estimates from higher order > constellations like, say, 16QAM? > > (b) more specifically, an extension to an LDPC decoder that works with > likelihoods of each bit? This seems complicated since in general your > "check nodes" and "bit nodes" will be correlated in some way that the > algorithm isn't anticipating. > > I would greatly appreciate any light that you may shed on my problem, and > thanks in advance. > > Regards, > Reggie This problem has been solved for many types of soft-input decoders, for which the problem is essentially the same. You might look around for how this is done with Turbo Codes, Viterbi decoders, etc., etc., and then formulate an application for LDPCs. It's actually a little easier for most LDPCs since there is no formal trellis structure. The randomness of the code (assuming it's not a highly structured code, which most LDPCs are not for performance reasons), tends to naturally decorrelate the bits. In other words, the symbol correlation that is usually decorrelated with a channel interleaver is essentially done inside the code. -- Eric Jacobsen Minister of Algorithms Abineau Communications http://www.abineau.com
From: alos on 24 Dec 2009 04:52
>Yes. Generally the approximation to the true likelihood of >marginal probability is used: LLR(bi) = 1/(2*sigma^2) * >d(S,bi=1)/d(S,bi=0) Sorry. I meant LLR(bi) = 1/(2*sigma^2) * (d(S, bi=0) - d(S, bi=1)) |