Efficient Algorithm for Finding Dominant Trapping Sets of LDPC Codes

Abstract

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 used as a tool to design LDPC codes with low error floors. For regular codes, the algorithm is initiated with a set of short cycles as the input. For irregular codes, in addition to short cycles, variable nodes with low degree and cycles with low approximate cycle extrinsic message degree (ACE) are also used as the initial inputs. The initial inputs are then expanded recursively to dominant trapping sets of increasing size. At the core of the algorithm lies the analysis of the graphical structure of dominant trapping sets and the relationship of such structures to short cycles, low-degree variable nodes and cycles with low ACE. The algorithm is universal in the sense that it can be used for an arbitrary graph and that it can be tailored to find a variety of graphical objects, such as absorbing sets and Zyablov-Pinsker (ZP) trapping sets, known to dominate the performance of LDPC codes in the error floor region over different channels and for different iterative decoding algorithms. Simulation results on several LDPC codes demonstrate the accuracy and efficiency of the proposed algorithm. In particular, the algorithm is significantly faster than the existing search algorithms for dominant trapping sets.

Error Errore Eicitur: A Stochastic Resonance Paradigm for Reliable Storage of Information on Unreliable Media

“…8(b) we present the performance of two longer codes, Margulis (2640, 1320) code and PEG (1008, 504) code, both (3, 6)-regular LDPC codes. Although the dominant trapping sets are not the same for these codes [30], for both codes the performance improvement can be observed if L ≥ 20. Allowing larger number of iterations results in additional performance improvement.…”

Construction of Structured Nonbinary Low-Density Parity-Check Codes

“…In this paper we also use a term of closed walk, which is a sequence of adjacent edges without restriction of their single appearance [16]. Cycles and closed walks are denoted as and its neighbors contains b odd-degree check nodes [11], for example see Fig. 2.…”

“…2. As was proved [10], [11], the performance of an iteratively decoded LDPC code is limited by the existence of small stopping sets and trapping sets in the graph of the code. Since there are very few check nodes capable of correcting errors within the trapping set, this incorrect information remains "trapped" until the termination of the decoding process.…”

“…In this paper we present a flexible algorithm based on computer search for "good" structured nonbinary LDPC codes. We use the known fact of the relationship between performance of the code and existence of some harmful subgraphs [10], [11] in the code graph (Tanner graph [12]). Moreover we take into account the performance dependence on the coefficients selection for the nonzero parity check matrix entries [2], [13].…”

An efficient exhaustive low-weight codeword search for structured LDPC codes

“…Previous work on exhaustive search for trapping sets ( [11], [12]) has demonstrated that search for (a, b) trapping sets is practical only when a ≤ 11 and a Tanner graph has no more than 1000 variable nodes. Efficient algorithms to find trapping sets with a dominant contribution to the error floor have been proposed by Karimi and Banihashemi [13]. Although these algorithms can handle trapping set of larger size, they may miss lowweight codewords.…”