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首页> 外文期刊>Information Theory, IEEE Transactions on >New Characterization and Efficient Exhaustive Search Algorithm for Leafless Elementary Trapping Sets of Variable-Regular LDPC Codes
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New Characterization and Efficient Exhaustive Search Algorithm for Leafless Elementary Trapping Sets of Variable-Regular LDPC Codes

机译：可变规则LDPC码的无叶基本陷印集的新特征和高效穷举搜索算法

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摘要

In this paper, we propose a new characterization for leafless elementary trapping sets (LETSs) of variable-regular low-density parity-check codes. Recently, Karimi and Banihashemi proposed a characterization of LETSs, which was based on viewing an LETS as a layered superset (LSS) of a short cycle in the code’s Tanner graph. A notable advantage of LSS characterization is that it corresponds to a simple LSS-based search algorithm (expansion technique) that starts from short cycles of the graph and finds the LETSs with LSS structure efficiently. Compared with the LSS-based characterization of Karimi and Banihashemi, which is based on a single LSS expansion technique, the new characterization involves two additional expansion techniques. The introduction of the new techniques mitigates two problems that LSS-based characterization/search suffers from: 1) exhaustiveness: not every LETS structure is an LSS of a cycle and 2) search efficiency: LSS-based search algorithm often requires the enumeration of cycles with length much larger than the girth of the graph, where the multiplicity of such cycles increases rapidly with their length. We prove that using the three expansion techniques, any LETS structure can be obtained starting from a simple cycle, no matter how large the size of the structure a or the number of its unsatisfied check nodes b are, i.e., the characterization is exhaustive. We also demonstrate that for the proposed characterization/search to exhaustively cover all the LETS structures within the (a,b) classes with a≤amax and b≤bmax , for any value of amax and bmax , the length of the short cycles required to be enumerated is less than that of the LSS-based characterization/search. We, in fact, show that such a length for the proposed search algorithm is minimal. We also prove that the three expansion techniques, proposed here, are the only expansions needed for characterization of LETS structures starting from simple cycles in the graph, if one requires each and every intermediate sub-structure to be a LETS as well. Extensive simulation results are provided to show that, compared with LSS-based search, significant improvement in search speed and memory requirements can be achieved.
机译：在本文中，我们为可变规则低密度奇偶校验码的无叶基本陷波集（LETSs）提出了一种新的特征。最近，Karimi和Banihashemi提出了LETS的特征，该特征是基于在代码的Tanner图中将LETS看作是短周期的分层超集（LSS）。 LSS表征的显着优势是，它对应于一种简单的基于LSS的搜索算法（扩展技术），该算法从图的短周期开始，并有效地找到具有LSS结构的LETS。与基于单一LSS扩展技术的Karimi和Banihashemi的基于LSS的表征相比，新的表征涉及另外两种扩展技术。新技术的引入缓解了基于LSS的特征/搜索遭受的两个问题：1）穷举性：并非每个LETS结构都是一个周期的LSS； 2）搜索效率：基于LSS的搜索算法通常需要对周期进行枚举长度远大于图表的周长，其中此类循环的多样性随其长度迅速增加。我们证明了使用这三种扩展技术，无论结构a的大小或其不满足的校验节点b的数量有多大，即表征是详尽无遗的，都可以从一个简单的周期开始获得任何LETS结构。我们还证明，对于拟议的表征/搜索，若要完全覆盖（a，b）类中所有a≤amax和b≤bmax的LETS结构，则对于amax和bmax的任何值，短周期的长度需要枚举小于基于LSS的特征/搜索。实际上，我们证明了所提出的搜索算法的这种长度是最小的。我们还证明，这里提出的三种扩展技术是从图中的简单循环开始表征LETS结构所需的唯一扩展，如果每个人都要求每个中间子结构也都必须是LETS。大量的仿真结果表明，与基于LSS的搜索相比，可以显着提高搜索速度和内存需求。

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