Jingyu Kang

Construction of non-binary quasi-cyclic LDPC codes by arrays and array dispersions - [transactions papers]

This paper presents two algebraic methods for constructing high performance and efficiently encodable nonbinary quasi-cyclic LDPC codes based on arrays of special circulant permutation matrices and multi-fold array dispersions. Codes constructed based on these methods perform well over the AWGN and other types of channels with iterative decoding based on belief-propagation. Experimental results show that over the AWGN channel, these non-binary quasi-cyclic LDPC codes significantly outperform Reed-Solomon codes of the same lengths and rates decoded with either algebraic hard-decision Berlekamp-Massey algorithm or algebraic soft-decision Kotter-Vardy algorithm. Also presented in this paper is a class of asymptotically optimal LDPC codes for correcting bursts of erasures. Codes constructed also perform well over flat fading channels. Non-binary quasi-cyclic LDPC codes have a great potential to replace Reed-Solomon codes in some applications in communication environments and storage systems for combating mixed types of noises and interferences.

Quasi-cyclic LDPC codes: an algebraic construction

This paper presents two new large classes of QC-LDPC codes, one binary and one non-binary. Codes in these two classes are constructed by array dispersions of row-distance constrained matrices formed based on additive subgroups of finite fields. Experimental results show that codes constructed perform very well over the AWGN channel with iterative decoding based on belief propagation. Codes of a subclass of the class of binary codes have large minimum distances comparable to finite geometry LDPC codes and they offer effective tradeoff between error performance and decoding complexity when decoded with low-complexity reliability-based iterative decoding algorithms such as binary message passing decoding algorithms. Non-binary codes decoded with a Fast-Fourier Transform based sum-product algorithm achieve significantly large coding gains over Reed-Solomon codes of the same lengths and rates decoded with either the hard-decision Berlekamp-Massey algorithm or the algebraic soft-decision Kotter-Vardy algorithm. They have potential to replace Reed-Solomon codes in some communication or storage systems where combinations of random and bursts of errors (or erasures) occur.

Two reliability-based iterative majority-logic decoding algorithms for LDPC codes

This paper presents two novel reliability-based iterative majority-logic decoding algorithms for LDPC codes. Both algorithms are binary message-passing algorithms and require only logical operations and integer additions. Consequently, they can be implemented with simple combinational logic circuits. They either outperform or perform just as well as the existing weighted bit-flipping or other reliability-based iterative decoding algorithms for LDPC codes in error performance with a faster rate of decoding convergence and less decoding complexity. Compared to the sum-product algorithm for LDPC codes, they offer effective trade-offs between performance and decoding complexity.

A Two-Stage Iterative Decoding of LDPC Codes for Lowering Error Floors

In iterative decoding of LDPC codes, trapping sets often lead to high error floors. In this work, we propose a two-stage iterative decoding to break trapping sets. Simulation results show that the error floor performance can be significantly improved with this decoding scheme.

High Performance Non-Binary Quasi-Cyclic LDPC Codes on Euclidean Geometries LDPC Codes on Euclidean Geometries

This paper presents algebraic methods for constructing high performance and efficiently encodable non-binary quasi-cyclic LDPC codes based on flats of finite Euclidean geometries and array masking. Codes constructed based on these methods perform very well over the AWGN channel. With iterative decoding using a fast Fourier transform based sum-product algorithm, they achieve significantly large coding gains over Reed-Solomon codes of the same lengths and rates decoded with either algebraic hard-decision Berlekamp-Massey algorithm or algebraic soft-decision Kotter-Vardy algorithm. Due to their quasi-cyclic structure, these non-binary LDPC codes on Euclidean geometries can be encoded using simple shift-registers with linear complexity. Structured non-binary LDPC codes have a great potential to replace Reed-Solomon codes for some applications in either communication or storage systems for combating mixed types of noise and interferences.

High Performance Nonbinary Quasi-Cyclic LDPC Codes on Euclidean Geometries

This paper presents algebraic methods for constructing efficiently encodable and high performance nonbinary quasi-cyclic LDPC codes based on hyperplanes of Euclidean geometries and masking. Codes constructed from these methods perform very well over the AWGN channel. With iterative decoding using a Fast Fourier Transform based sum-product algorithm, they achieve significantly large coding gains over Reed-Solomon codes of the same lengths and rates decoded with either the algebraic hard-decision Berlekamp-Massey algorithm or the algebraic soft-decision Kötter-Vardy algorithm. Due to their quasi-cyclic structure, these nonbinary LDPC codes on Euclidean geometries can be encoded with simple shift-registers with linear complexity. Structured nonbinary LDPC codes have a great potential to replace Reed-Solomon codes for some applications in either communication systems or storage systems for combating mixed types of noise and interferences.

Array dispersions of matrices and constructions of quasi-cyclic LDPC codes over non-binary fields

This paper presents two new algebraic constructions of high performance non-binary quasi-cyclic LDPC codes based on array dispersions of matrices over non-binary fields. Codes constructed perform well over the AWGN channel with iterative decoding using a Fast Fourier Transform based sum-product algorithm. They achieve significantly large coding gains over Reed-Solomon codes of the same lengths and rates decoded with either the hard-decision Berlekamp-Massey algorithm or the algebraic soft-decision Koetter-Vardy algorithm. Due to their quasi-cyclic structure, they can be efficiently encoded using simple shift-registers with linear complexity. They have a potential to replace RS codes for some applications in communication and storage systems.

Non-binary LDPC codes vs. Reed-Solomon codes

This paper investigates the potential of non-binary LDPC codes to replace widely used Reed-Solomon (RS) codes for applications in communication and storage systems for combating mixed types of noise and interferences. The investigation begins with presentation of four algebraic constructions of RS-based non-binary quasi-cyclic (QC)-LDPC codes. Then, the performances of some codes constructed based on the proposed methods with iterative decoding are compared with those of RS codes of the same lengths and rates decoded with the hard-decision Berlekamp-Massey (BM)-algorithm and the algebraic soft-decision Kotter-Vardy (KV)-algorithm over both the AWGN and a Rayleigh fading channels. Comparison shows that the constructed non-binary QC-LDPC codes significantly outperform their corresponding RS codes decoded with either the BM-algorithm or the KV-algorithm. Most impressively, the orders of decoding computational complexity of the constructed non-binary QC-LDPC codes decoded with 5 and 50 iterations of a Fast Fourier Transform based sum-product algorithm are much smaller than those of their corresponding RS codes decoded with the KV-algorithm, while achieve 1:5 to 3 dB coding gains. The comparison shows that well designed non-binary LDPC codes have a great potential to replace RS codes for some applications in communication or storage systems, at least before a very efficient algorithm for decoding RS codes is devised.

A binary message-passing decoding algorithm for LDPC codes

This paper presents a soft reliability-based binary message-passing algorithm for decoding LDPC codes. This algorithm outperforms the existing weighted bit-flipping algorithms with much less computational complexity. It is particularly effective for decoding LDPC codes constructed based on finite-geometries and finite fields. The proposed algorithm can be simplified for applications in communication or storage systems where either soft reliability information is not available to the decoder or a simple decoder is needed.

Two efficient and low-complexity iterative reliability-based majority-logic decoding algorithms for LDPC codes

This paper presents two novel iterative reliability-based majority-logic algorithms for decoding LDPC codes. Both algorithms are binary message-passing algorithms and require only logical operations and integer additions. Consequently, they can be implemented with simple combinational logic circuits. They either outperform or perform just well as the existing weighted bit-flipping or other reliability-based decoding algorithms for LDPC codes in error performance with a faster rate of decoding convergence and less decoding complexity. Compared to the sum-product algorithm for LDPC codes, they offer effective trade-offs between performance and decoding complexity.