2017/06/06 by Farzane Amirzade, Amirzade, Farzane, Mohammad‐Reza Sadeghi +1
Computer Science · Engineering · #Advanced Wireless Communication Techniques #Cooperative Communication and Network Coding #Error Correcting Code Techniques #FOS: Computer and information sciences #Information Theory (cs.IT)
paper · pdf · doi:10.48550/arxiv.1706.01703
openalex publication_date 2017/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we give lower bounds on the size of (a,b) elementary trapping\nsets (ETSs) belonging to variable-regular LDPC codes with any girth, g, and\nirregular ones with girth 8, where a is the size, b is the number of\ndegree-one check nodes and satisfy the inequality \(b)/(a)<1. Our proposed\nlower bounds are analytical, rather than exhaustive search-based, and based on\ngraph theories. The numerical results in the literarture for g=6,8 for\nvariable-regular LDPC codes match our results. Some of our investigations are\nindependent of the girth and rely on the variables a, b and \γ, the\ncolumn weight value, only. We prove that for an ETS belonging to a\nvariable-regular LDPC code with girth 8 we have a\≥2\γ-1 and\nb\≥\γ. We demonstrate that these lower bounds are tight, making use of\nthem we provide a method to achieve the minimum size of ETSs belonging to\nirregular LDPC codes with girth 8 specially those whose column weight values\nare a subset of 2,3,4,5,6 . Moreover, we show for variable-regular LDPC\ncodes with girth 10, a\≥(\γ-1)2+1. And for \γ=3,4 we obtain\na\≥7 and a\≥12, respectively. Finally, for variable-regular LDPC codes\nwith girths g=2(2k+1) and g=2(2k+2) we obtain a\≥(\γ-2)k+1 and\na\≥2(\γ-2)k+1, respectively.\n