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In this paper, we study the graphical structure of elementary trapping sets (ETS) of variable-regular low-density parity-check (LDPC) codes. ETSs are known to be the main cause of error floor in LDPC coding schemes. For the set of LDPC…
In this paper, we propose a characterization for non-elementary trapping sets (NETSs) of low-density parity-check (LDPC) codes. The characterization is based on viewing a NETS as a hierarchy of embedded graphs starting from an ETS. The…
In this paper, we propose a characterization of elementary trapping sets (ETSs) for irregular low-density parity-check (LDPC) codes. These sets are known to be the main culprits in the error floor region of such codes. The characterization…
One of the phenomena that influences significantly the performance of low-density parity-check codes is known as trapping sets. An $(a,b)$ elementary trapping set, or simply an ETS where $a$ is the size and $b$ is the number of degree-one…
The performance of low-density parity-check (LDPC) codes in the error floor region is closely related to some combinatorial structures of the code's Tanner graph, collectively referred to as {\it trapping sets (TSs)}. In this paper, we…
We prove that approximating the size of stopping and trapping sets in Tanner graphs of linear block codes, and more restrictively, the class of low-density parity-check (LDPC) codes, is NP-hard. The ramifications of our findings are that…
Elementary trapping sets (ETSs) are the main culprits for the performance of LDPC codes in the error floor region. Due to the large quantity, complex structures, and computational difficulties of ETSs, how to eliminate dominant ETSs in…
In this paper we give lower bounds on the size of $(a,b)$ elementary trapping sets (ETSs) belonging to variable-regular LDPC codes with any girth, $g$, and irregular ones with girth 8, where $a$ is the size, $b$ is the number of degree-one…
It is proved in this work that exhaustively determining bad patterns in arbitrary, finite low-density parity-check (LDPC) codes, including stopping sets for binary erasure channels (BECs) and trapping sets (also known as near-codewords) for…
Cages, defined as regular graphs with minimum number of nodes for a given girth, are well-studied in graph theory. Trapping sets are graphical structures responsible for error floor of low-density parity-check (LDPC) codes, and are well…
In this paper, we propose a new characterization for elementary trapping sets (ETSs) of variable-regular low-density parity-check (LDPC) codes. Recently, Karimi and Banihashemi proposed a characterization of ETSs, which was based on viewing…
One of the phenomena that causes high decoding failure rates is trapping sets. Characterization of $(a,b)$ elementary trapping sets (ETSs), their graphical properties and the lower bounds on their size in variable regular LDPC codes with…
LDPC codes have attracted significant attention because of their superior performance close to the Shannon limit. Elementary trapping sets are the main cause of the error floor phenomenon in LDPC codes. We consider typical graphs related to…
This paper presents an efficient algorithm for finding the dominant trapping sets of a low-density parity-check (LDPC) code. The algorithm can be used to estimate the error floor of LDPC codes or to be part of the apparatus to design LDPC…
It is well known that, given \(b\ge 0\), finding an $(a,b)$-trapping set with the minimum \(a\) in a binary linear code is NP-hard. In this paper, we demonstrate that this problem can be solved with linear complexity with respect to the…
We propose a systematic design of protograph-based quasi-cyclic (QC) low-density parity-check (LDPC) codes with low error floor. We first characterize the trapping sets of such codes and demonstrate that the QC structure of the code…
LDPC codes are used in many applications, however, their error correcting capabilities are limited by the presence of stopping sets and trapping sets. Trapping sets and stopping sets occur when specific low-wiehgt error patterns cause a…
Elementary trapping sets (ETSs) are the main culprits of the performance of low-density parity-check (LDPC) codes in the error floor region. Due to their large quantities and complex structures, ETSs are difficult to analyze. This paper…
Iterative decoders for finite length quantum low-density parity-check (QLDPC) codes are attractive because their hardware complexity scales only linearly with the number of physical qubits. However, they are impacted by short cycles,…
In this paper we construct low-density parity-check (LDPC) codes from transversal designs with low error-floors over the additive white Gaussian noise (AWGN) channel. The constructed codes are based on transversal designs that arise from…