Low density parity-check (LDPC) codes are a class of linear block codes that are decoded by running belief propagation (BP) algorithm or log-likelihood ratio belief propagation (LLR-BP) over the factor graph of the code. One of the disadvantages of LDPC codes is the onset of an error floor at high values of signal to noise ratio caused by trapping sets. In this paper, we propose a two stage decoder to deal with different types of trapping sets. Oscillating trapping sets are taken care by the first stage of the decoder and the elementary trapping sets are handled by the second stage of the decoder. Simulation results on regular PEG (504,252,3,6) code shows that the proposed two stage decoder performs significantly better than the standard decoder.
In @cite_3 , the problems caused by the trapping sets and why the decoder fails in overcoming these problems are well studied. @cite_3 , @cite_2 propose an averaging decoder that averages the LLR value of the node over several iterations. Averaging prevents the erroneous information from being trapped in the code graph by slowing down the convergence speed of the nodes. This method though computationally less complex, it slows down the convergence of the reliable nodes. This affects the performance of the decoder in the waterfall region as oscillating trapping sets are prevalent in this region than the elementary trapping sets.
@cite_3 @cite_2
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Several combinatorial properties of low-density parity-check (LDPC) codes, such as minimum distance, diameter, stopping number, girth and cycle-length distribution of the corresponding Tanner graph, are known to influence their performance under iterative decoding. Recently, a new class of combinatorial configurations, termed trapping sets, was shown to be of significant importance in determining the properties of LDPC codes in the error-floor region. Very little is known both about the existence parameters of trapping sets in structured LDPC codes and about possible techniques for reducing their negative influence on the code's performance. In this paper, we address both these problems from an algorithmic and combinatorial perspective. We first provide a numerical study of the trapping phenomena for the Margulis code, which exhibits a fairly high error-floor. Based on this analysis, conducted for two different implementations of iterative belief propagation, we propose a novel decoding process, termed averaged decoding. Averaged decoding provides for a significant reduction in the number of incorrectly decoded frames in the error-floor region of the Margulis code. Furthermore, based on the results of the algorithmic approach, we suggest a novel combinatorial characterizations of trapping sets in the class of LDPC codes based on finite geometries. Projective geometry LDPC codes are suspected to have extremely low error-floors, which is a property that we may attribute to the non-existence of certain small trapping sets in the code graph. We generalize the notion of the stopping redundancy in order to study the smallest size of a trapping set in Tanner graphs of linear block codes. In this context, we introduce the notion of the trapping redundancy of a code, which quantifies the relationship between the number of redundant rows in any parity-check matrix of a given code and the size of its smallest trapping set. Trapping sets with certain parameter sizes are known to cause error-floors in the performance curves of iterative belief propagation (BP) decoders, and it is therefore important to identify decoding matrices that avoid such sets. Bounds on the trapping redundancy are obtained using probabilistic and constructive methods, and the analysis covers both general and elementary trapping sets. Numerical values for these bounds are computed for the [2640, 1320] Margulis code and the class of projective geometry codes, and compared with some new code-specific trapping set size estimates.