研究目的
To perform a finite length analysis of regular and irregular LDPC codes to derive the block and bit-error probabilities on additive impulsive noise channels with SαS pdfs.
研究成果
The paper shows that for a given degree distribution pair, the method can be used to obtain accurate estimates of the block and bit error probabilities of finite length LDPC codes on SαS additive impulsive noise channels. The analysis implies that for a given uncoded BEP and threshold, the prediction of the actual performance for short LDPC codes could be accomplished on more general memoryless channels.
研究不足
The gap between the estimated and simulated results is greater at shorter block lengths due to the effect of short cycles in the Tanner graph and the Gaussian approximation of the observed error probabilities becoming weaker as the block length is reduced.
1：Experimental Design and Method Selection:
The methodology involves deriving an exact uncoded bit error probability (BEP) of an impulsive noise channel, modeled as a symmetric α-stable (SαS) distribution, and applying density evolution to evaluate the asymptotic performance of LDPC codes on SαS channels.
2：Sample Selection and Data Sources:
The study uses LDPC codes of different block lengths (N = 1000, 4000, 20000) at different values of α (α =
3：8, 1, 5, 9). List of Experimental Equipment and Materials:
The study involves simulations of rate 1/2 regular and irregular LDPC codes using the sum-product algorithm.
4：Experimental Procedures and Operational Workflow:
The study involves deriving closed-form expressions for the BEP and block error probability of short LDPC codes on SαS channels and comparing theoretical bit-error probabilities with bit-error rates obtained by simulations.
5：Data Analysis Methods:
The study uses the Kullback-Leibler (KL) divergence to calculate the difference between the true pdf and its Gaussian approximation.
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