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Forschungszentrum Telekommunikation Wien [Telecommunications Research Center Vienna] Göttfried Lächner, Ingmør Lønd, Jössy Säyir Optimization of LDPC codes for generalized joint detection and decoding Newcom SPW1 Meeting December 15, 2005
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-2- Outline Introduction – Turbo Demapping EXIT function of demapper LDPC code design Stability condition Code search Simulation results
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-3- Example: “Turbo-Demapping” Binary Source Channel Encoder Bit- Interl. QAM Mapper uxt Channel y Soft Demapper Bit- Deinterl. Channel Decoder Hard Decision Sink yxDxD ûxMxM Bit- Interl. For LDPC codes, bit-interleaving can be omitted.
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-4- EXIT Function of Demapper - 16 QAM signal constellation - set partitioning mapping - AWGN channel =0.53 - a-priori messages modelled according to Gaussian distribution
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-5- LDPC Code Design I * CV I * VC check nodes variable nodes
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-6- Approximations: - Gaussian densities - Duality property EXIT function of variable nodes: EXIT function of check nodes: LDPC EXIT Functions
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-7- The intersection point of the curves can be found by solving for the smallest I * CV in the intervall [0,1]. The transfer function of the code is then given by LDPC EXIT Functions i is the node perspective of the variable node distribution
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-8- Code Design LDPC code design aims to maximize the rate under the constraint that Joint optimization of and is a hard problem. For a fixed , optimization of is still hard. For a fixed, optimization of is a linear optimization problem.
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-9- Stability Condition In order to converge to zero error probability, the stability condition has to be satisfied For Gaussian message distributions, this condition can be written as constraint on 2 given constraint on given 2
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-10- Code Search – Fixed In order to get practical distributions, we limit the search space to = [0 2 3 0 0 0 0 0 0 10 ] R=0.4624
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-11- Code Search – Optimized We do the same search but now is optimized (using linear programming) for every R=0.5065
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-12- Optimized Distributions
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-13- EXIT Chart - LDPC code optimized for demapper - threshold = 2.5dB - LDPC code optimized for AWGN channel - threshold = 5.5dB
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-14- Simulation Results
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-15- Conclusion LDPC codes can be matched to the EXIT function of an inner component by jointly optimizing variable and check node distributions. Optimization of the variable node distribution is hard to perform. Optimization of the check node distribution is a linear optimization problem. The overall code search can be performed efficiently by reducing the search space for the variable node distribution.
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