We propose a technique to design finite-length irregular low-density parity-check (LDPC) codes over the binary-input additive white Gaussian noise (AWGN) channel with good performance in both the waterfall and the error floor region. The design process starts from a protograph which embodies a desirable degree distribution. This protograph is then lifted cyclically to a certain block length of interest. The lift is designed carefully to satisfy a certain approximate cycle extrinsic message degree (ACE) spectrum. The target ACE spectrum is one with extremal properties, implying a good error floor performance for the designed code. The proposed construction results in quasi-cyclic codes which are attractive in practice due to simple encoder and decoder implementation. Simulation results are provided to demonstrate the effectiveness of the proposed construction in comparison with similar existing constructions.We propose a technique to design finite-length irregular low-density parity-check (LDPC) codes over the binary-input additive white Gaussian noise (AWGN) channel with good performance in both the waterfall and the error floor region. The design process starts from a protograph which embodies a desirable degree distribution. This protograph is then lifted cyclically to a certain block length of interest. The lift is designed carefully to satisfy a certain approximate cycle extrinsic message degree (ACE) spectrum. The target ACE spectrum is one with extremal properties, implying a good error floor performance for the designed code. The proposed construction results in quasi-cyclic codes which are attractive in practice due to simple encoder and decoder implementation. Simulation results are provided to demonstrate the effectiveness of the proposed construction in comparison with similar existing constructions.

IEEE International Symposium on Information Theory (ISIT)Jul 1, 20117 citations

Construction of Irregular Protograph-Based QC-LDPC Codes With Low Error Floor

Bashirreza Karimi, Amir H. Banihashemi

In this article, we design finite-length irregular protograph-based quasi-cyclic (QC) low-density parity-check (LDPC) codes with good waterfall performance and low error floor. To achieve a low error floor, we eliminate a targeted set of dominant elementary trapping sets (ETS) £ in the Tanner graph of the code. For a given rate and girth, the codes are designed to be free of the largest set of problematic ETSs for a given block length, or to have the shortest block length while a given set of ETSs is avoided. The design is based on a search algorithm that identifies whether any instance of any structure within £ exists in the Tanner graph of the constructed code or not. The search algorithm performs this task with minimal complexity, making it feasible to construct practical codes by running the search algorithm a large number of times. Simulation results are provided to demonstrate the superior performance of designed codes compared to similar state-of-the-art irregular QC-LDPC codes.In this article, we design finite-length irregular protograph-based quasi-cyclic (QC) low-density parity-check (LDPC) codes with good waterfall performance and low error floor. To achieve a low error floor, we eliminate a targeted set of dominant elementary trapping sets (ETS) £ in the Tanner graph of the code. For a given rate and girth, the codes are designed to be free of the largest set of problematic ETSs for a given block length, or to have the shortest block length while a given set of ETSs is avoided. The design is based on a search algorithm that identifies whether any instance of any structure within £ exists in the Tanner graph of the constructed code or not. The search algorithm performs this task with minimal complexity, making it feasible to construct practical codes by running the search algorithm a large number of times. Simulation results are provided to demonstrate the superior performance of designed codes compared to similar state-of-the-art irregular QC-LDPC codes.

IEEE Transactions on CommunicationsOct 2, 202018 citations

Lowering the Error Floor of LDPC Codes Using Cyclic Liftings

Reza Asvadi, Amir H. Banihashemi, Mahmoud Ahmadian‐Attari

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 are part of the trapping sets. We derive a necessary and sufficient condition for the cyclic permutations assigned to the edges of a cycle ξ of lengthl(ξ) in the base graph such that the inverse image of ξ in the lifted graph consists of only cycles of length strictly larger thanl(ξ). 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, and in some cases, the code rate. The constructed codes are quasi-cyclic and thus attractive from a practical point of view. 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.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 are part of the trapping sets. We derive a necessary and sufficient condition for the cyclic permutations assigned to the edges of a cycle ξ of lengthl(ξ) in the base graph such that the inverse image of ξ in the lifted graph consists of only cycles of length strictly larger thanl(ξ). 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, and in some cases, the code rate. The constructed codes are quasi-cyclic and thus attractive from a practical point of view. 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.

IEEE Transactions on Information TheoryMar 15, 2011101 citations

Lowering the error floor of LDPC codes using cyclic liftings

Reza Asvadi, Amir H. Banihashemi, Mahmoud Ahmadian‐Attari

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. 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.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. 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.

IEEE International Symposium on Information Theory (ISIT)Jun 1, 201013 citations

Lowering the Error Floor of LDPC Codes Using Cyclic Liftings

Reza Asvadi, Amir H. Banihashemi, Mahmoud Ahmadian‐Attari

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 $\ell(c)$ in the base graph such that the inverse image of $c$ in the lifted graph consists of only cycles of length strictly larger than $\ell(c)$ . 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.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 $\ell(c)$ in the base graph such that the inverse image of $c$ in the lifted graph consists of only cycles of length strictly larger than $\ell(c)$. 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.

arXiv:1002.4311Feb 23, 20100 citations

Modified CC-PEG Algorithm for Protograph-Based QC-LDPC Codes Over Non-Uniform Channel

H. Lee, Jae-Won Kim

In this paper, we propose the modified cycle-concentrating progressive-edge-growth (CC-PEG) algorithm for lifting protograph-based quasi-cyclic low-density parity-check (QC-LDPC) codes over the non-uniform additive white Gaussian noise (AWGN) channel. By introducing various selection criteria for shift values based on the non-uniform channel characteristics, we improve the decoding performances of lifted LDPC codes. From numerous simulation results, we demonstrate that each selection criterion is effective for the performance improvement and the modified CC-PEG algorithm outperforms the conventional lifting methods over the non-uniform AWGN channel. Furthermore, we analyze these simulation results based on some metrics such as the girth, number of cycles, and approximate cycle extrinsic message degree (ACE).In this paper, we propose the modified cycle-concentrating progressive-edge-growth (CC-PEG) algorithm for lifting protograph-based quasi-cyclic low-density parity-check (QC-LDPC) codes over the non-uniform additive white Gaussian noise (AWGN) channel. By introducing various selection criteria for shift values based on the non-uniform channel characteristics, we improve the decoding performances of lifted LDPC codes. From numerous simulation results, we demonstrate that each selection criterion is effective for the performance improvement and the modified CC-PEG algorithm outperforms the conventional lifting methods over the non-uniform AWGN channel. Furthermore, we analyze these simulation results based on some metrics such as the girth, number of cycles, and approximate cycle extrinsic message degree (ACE).

IEEE AccessJan 1, 20243 citations

c

of length

\ell(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

\ell(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.