In this paper, we devise a new alternating direction method of multipliers (ADMM) decoder for non-binary low-density parity-check (LDPC) codes in Galois fields of characteristic two $\left( {{\mathbb{F}_{{2^q}}}} \right)$ . Its main content are threefold: first, the procedure of formulating the maximum likelihood (ML) decoding problem in ${\mathbb{F}_{{2^q}}}$ to a linear integer problem in real space is presented; Second, after relaxing the integer problem to a continuous one, an efficient ADMM algorithm is customized to solve the latter, where all the entries of the variable vectors can be obtained in parallel; Third, we show that the proposed ADMM decoder satisfies the favorable codeword-independent property under some mild conditions and its computation complexity in each ADMM iteration is roughly $\mathcal{O}\left( {nq} \right)$ , where n is code length of the considered non-binary LDPC code. Simulation results demonstrate that its performance, such as error-correction and decoding efficiency, is very competitive in comparison with state-of-the-art non-binary LDPC decoders.In this paper, we devise a new alternating direction method of multipliers (ADMM) decoder for non-binary low-density parity-check (LDPC) codes in Galois fields of characteristic two $\left( {{\mathbb{F}_{{2^q}}}} \right)$. Its main content are threefold: first, the procedure of formulating the maximum likelihood (ML) decoding problem in ${\mathbb{F}_{{2^q}}}$ to a linear integer problem in real space is presented; Second, after relaxing the integer problem to a continuous one, an efficient ADMM algorithm is customized to solve the latter, where all the entries of the variable vectors can be obtained in parallel; Third, we show that the proposed ADMM decoder satisfies the favorable codeword-independent property under some mild conditions and its computation complexity in each ADMM iteration is roughly $\mathcal{O}\left( {nq} \right)$, where n is code length of the considered non-binary LDPC code. Simulation results demonstrate that its performance, such as error-correction and decoding efficiency, is very competitive in comparison with state-of-the-art non-binary LDPC decoders.

IEEE International Symposium on Information Theory (ISIT)Jun 26, 20221 citation

Adaptive Sub-Optimal Bit Flipping Decoding Algorithm for LDPC

S. Ashwin Kumar, R. Aravinthan, Ch. Sriram Reddy +2 more

Lecture notes on data engineering and communications technologiesJan 1, 20210 citations

Lowering the error floor of ADMM penalized decoder for LDPC codes

Xiaopeng Jiao, Jianjun Mu

Decoding by alternating direction method of multipliers (ADMM) is a promising linear programming decoder for low-density parity-check (LDPC) codes. In this paper, we propose a two-step scheme to lower the error floor of LDPC codes with ADMM penalized decoder. For the undetected errors that cannot be avoided at the decoder side, we modify the code structure slightly to eliminate low-weight code words. For the detected errors induced by small error-prone structures, we propose a post-processing method for the ADMM penalized decoder. Simulation results show that the error floor can be reduced significantly over three illustrated LDPC codes by the proposed two-step scheme.Decoding by alternating direction method of multipliers (ADMM) is a promising linear programming decoder for low-density parity-check (LDPC) codes. In this paper, we propose a two-step scheme to lower the error floor of LDPC codes with ADMM penalized decoder. For the undetected errors that cannot be avoided at the decoder side, we modify the code structure slightly to eliminate low-weight code words. For the detected errors induced by small error-prone structures, we propose a post-processing method for the ADMM penalized decoder. Simulation results show that the error floor can be reduced significantly over three illustrated LDPC codes by the proposed two-step scheme.

China CommunicationsAug 1, 20165 citations

Reliability-Based Single Bit-Flipping Decoding Algorithm for LDPC Codes

Soufian Addi, Mostafa Belkasmi, Ahlam Berkani +1 more

Lecture notes in electrical engineeringJan 1, 20240 citations

In this paper, we devise a new alternating direction method of multipliers (ADMM) decoder for non-binary low-density parity-check (LDPC) codes in Galois fields of characteristic two

\left( {{\mathbb{F}_{{2^q}}}} \right)

. Its main content are threefold: first, the procedure of formulating the maximum likelihood (ML) decoding problem in

{\mathbb{F}_{{2^q}}}

to a linear integer problem in real space is presented; Second, after relaxing the integer problem to a continuous one, an efficient ADMM algorithm is customized to solve the latter, where all the entries of the variable vectors can be obtained in parallel; Third, we show that the proposed ADMM decoder satisfies the favorable codeword-independent property under some mild conditions and its computation complexity in each ADMM iteration is roughly

\mathcal{O}\left( {nq} \right)

, where n is code length of the considered non-binary LDPC code. Simulation results demonstrate that its performance, such as error-correction and decoding efficiency, is very competitive in comparison with state-of-the-art non-binary LDPC decoders.