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The design of structured LDPC codes with algorithmic graph construction

Sułek Wojciech

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2022

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Vol. 70, nr 4

art. no. e141592

EN

Low-Density Parity-Check (LDPC) codes are among the most effective modern error-correcting codes due to their excellent correction performance and highly parallel decoding scheme. Moreover, the nonbinary extension of such codes further increases performance in the short-block regime. In this paper, we review the key elements for the construction of implementation-oriented binary and nonbinary codes. These Quasi-Cyclic LDPC (QC-LDPC) codes additionally feature efficient encoder and decoder implementation frameworks. We then present a versatile algorithm for the construction of both binary and nonbinary QC-LDPC codes that have low encoding complexity and an optimized corresponding graph structure. Our algorithm uses a progressive edge growth algorithm, modified for QC-LDPC graph construction, and then performs an iterative global search for optimized cyclic shift values within the QC-LDPC circulants. Strong error correction performance is achieved by minimizing the number of short cycles, and cycles with low external connectivity, within the code graph. We validate this approach via error rate simulations of a transmission system model featuring an LDPC coder-decoder, digital modulation, and additive white Gaussian noise channels. The obtained numerical results validate the effectiveness of the proposed construction algorithm, with a number of constructed codes exhibiting either similar or superior performance to industry standard binary codes and selected nonbinary codes from the literature.

2

Low Density Parity Check Codes Constructed from Hankel Matrices

Tehami M. A., Djebbari A.

Journal of Telecommunications and Information Technology

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2018

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nr 3

37--41

EN

In this paper, a new technique for constructing low density parity check codes based on the Hankel matrix and circulant permutation matrices is proposed. The new codes are exempt of any cycle of length 4. To ensure that parity check bits can be recursively calculated with linear computational complexity, a dual-diagonal structure is applied to the parity check matrices of those codes. The proposed codes provide a very low encoding complexity and reduce the stored memory of the matrix H in which this matrix can be easily implemented comparing to others codes used in channel coding. The new LDPC codes are compared, by simulation, with uncoded bi-phase shift keying (BPSK). The result shows that the proposed codes perform very well over additive white Gaussian noise (AWGN) channels.

3

A method of data encoding/decoding using variable low density parity check codes

Patsei N.V.

Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska

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2012

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nr 4b

25-27

EN

This paper presents a coding method that dynamically changes the low density parity check (LDPC) code parameters in accordance with communication channel quality. The apparatus for parity check matrices generation, storage, and dynamic change are proposed. Some simulation results for different code characteristics and performance are provided that prove the effectiveness of proposed method.

PL

Artykuł przedstawia metodę kodowania, która w dynamiczny sposób zmienia parametry kodów LDPC zgodnie z założoną jakością kanału transmisyjnego. Zaprezentowano metodę zmiennego generowania macierzy parzystości , przechowywania. Przedstawione rezultaty badań symulacyjnych przeprowadzonych dla kodów o różnych parametrach, które potwierdzają efektywność proponowanej metody.