Lowering the Error Floor of LDPC Codes Using Cyclic Liftings

Abstract

Cyclic liftings are proposed to lower the error floor of low-density parity-check (LDPC) codes. The liftings are designed to eliminate dominant trapping sets of the base code by removing the short cycles which form the trapping sets. We derive a necessary and sufficient condition for the cyclic permutations assigned to the edges of a cycle c of length ℓ(c) in the base graph such that the inverse image of c in the lifted graph consists of only cycles of length strictly larger than ℓ(c). The proposed method is universal in the sense that it can be applied to any LDPC code over any channel and for any iterative decoding algorithm. It also preserves important properties of the base code such as degree distributions, encoder and decoder structure, and in some cases, the code rate. The proposed method is applied to both structured and random codes over the binary symmetric channel (BSC). The error floor improves consistently by increasing the lifting degree, and the results show significant improvements in the error floor compared to the base code, a random code of the same degree distribution and block length, and a random lifting of the same degree. Similar improvements are also observed when the codes designed for the BSC are applied to the additive white Gaussian noise (AWGN) channel.

Robustness against the effects of multipath in an ISDB-T LDM broadcast system using diversity at reception

“…However, for a good performance of the LDM technique, an efficient error correction code is required. Therefore, the concatenated BCH and LDPC codes were used in order to reduce the error floor (phenomenon encountered in modern iterated sparse graph-based error correction codes) [8], [15].…”

“…These segments create up to 3 different layers: A, B and C. Layer A is used to 1seg (mobile), layer B to Standard Definition Television (SDTV) and layer C to High Definition Television (HDTV), but most TV channel transmitters use layer A for 1seg and layer B to HDTV [15], [4]. The bandwidth required for the system can be of 6, 7 or 8 MHz.…”

Modified Algorithm for Medium Length Irregular Low Density Parity Check Code with Low Computational Complexity and Error Floor Rate

“…Xia Zheng, proposed an algorithm for short length irregular LDPC codes to avoid major error-contributing trapping sets (TSs) during the code construction process [3]. Reza Asvadi, worked with structured and random codes over binary symmetric channels (BSC) and suggested the methods to eliminate short cycles in trapping sets which ultimately contribute for low error floor [4]. Jaehong Kim, proposed a new class of irregular LDPC codes, a simple rate compatible, puncture structure for finite block length with simplified decoding.…”

Quasi-cyclic LDPC codes based on pre-lifted protographs

“…For the masked version of H in the form of (30), the number of permutation matrices that must be checked is reduced to these 13:…”

“…QC-LDPC codes based on protographs have also been designed to improve certain characteristics, such as girth [27]- [29] or lowering the "error floor" [30]. In [31], lower bounds on the size of the necessary lifting factor N of a protograph required to achieve a certain girth is investigated for QC-LDPC codes derived from several simple protograph types.…”