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Journal of Optical Communications

Affine Geometry Low-density Parity Check Codes in Long-haul Optical Communications

Bane V. Vasic, Ivan B. Djordjević

Published Jun 1, 2002• 1 citation
Publisher

Abstract

In this paper we investigate the performance of low-density parity-check (LDPC) codes in long haul optical communication systems. We are particularly concerned with high-rate codes on affine geometries. These codes have large minimum distance and simple iterative decoding algorithm, which makes them good candidates for high-speed applications such as optical communications. We consider both the bit-flipping iterative decoding and iterative decoding based on min-sum algorithm. We demonstrate a significant performance improvement with respect to the state-of-the-art error control schemes employed in long-haul systems for different signal formats (NRZ, RZ, CRZ). Contrary to the common practice of considering the error controlling schemes using the AWGN channel assumption, we consider the performance of the proposed LDPC schemes taking into account in a natural way all major impairments in a long-haul optical transmission such as ASE noise, pulse distortion due to fiber nonlinearities, chromatic dispersion or polarization dispersion, crosstalk effects, intersymbol-interference, etc.

DOI
10.1515/joc.2002.23.3.50

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In this paper we investigate the performance of low-density parity-check (LDPC) codes in long haul optical communication systems. We are particularly concerned with high-rate codes on affine geometries. These codes have large minimum distance and simple iterative decoding algorithm, which makes them good candidates for high-speed applications such as optical communications. We consider both the bit-flipping iterative decoding and iterative decoding based on min-sum algorithm. We demonstrate a significant performance improvement with respect to the state-of-the-art error control schemes employed in long-haul systems for different signal formats (NRZ, RZ, CRZ). Contrary to the common practice of considering the error controlling schemes using the AWGN channel assumption, we consider the performance of the proposed LDPC schemes taking into account in a natural way all major impairments in a long-haul optical transmission such as ASE noise, pulse distortion due to fiber nonlinearities, chromatic dispersion or polarization dispersion, crosstalk effects, intersymbol-interference, etc.
Abstract In this paper, we investigate the performance of low‐density parity‐check (LDPC) codes in long‐haul optical communication systems for different modulation formats (nonreturn to zero (NRZ), return to zero (RZ), chirped return to zero (CRZ)). We are particularly concerned with high‐rate codes based on affine geometries. These codes have large minimum distance and simple iterative decoding algorithms, which make them good candidates for high‐speed applications such as optical communications. We consider both bit‐flipping iterative decoding and iterative decoding based on min‐sum algorithms. We demonstrate a significant performance improvement with respect to the state‐of‐the‐art error control schemes employed in long‐haul systems. Contrary to the common practice of considering the performance of error controlling schemes using the AWGN channel assumption, we consider the performance of the proposed LDPC schemes taking into account, in a natural way, all major impairments in long‐haul optical transmission such as ASE noise, pulse distortion due to fiber nonlinearities, chromatic dispersion or polarization dispersion, crosstalk effects, intersymbol‐interference (ISI), etc. Copyright © 2004 AEI.
In this letter, we investigate the performance of low-density parity-check (LDPC) codes in long-haul optical communication systems for carrier-suppressed return-to-zero signal format at 40 Gb/s per channel in a wavelength-division-multiplexing environment. We are particularly concerned with high-rate codes based on projective geometries. These codes have large minimum distance and simple iterative decoding algorithms, which makes them good candidates for such high-speed application. We consider iterative decoding based on min-sum algorithm since it requires only simple addition and minimum operations and, as such, is suitable for high-speed optical transmission. Contrary to the common practice of considering the performance of error controlling schemes using the additive white Gaussian noise channel assumption, we consider the performance of the proposed LDPC schemes, taking into account in a natural way all major impairments in long-haul optical transmission such as amplifier spontaneous emission noise, pulse distortion due to fiber nonlinearities, chromatic dispersion or polarization dispersion, crosstalk effects, intersymbol interference, etc.
The increasing popularity of optical communication systems emphasizes the need for effective errorcorrection solutions, including high-efficiency hardware decoder designs and codes with strong performance. Within optical communication networks, Low-Density Parity-Check (LDPC) codes utilizing sparse matrices and decoded through the Bit-Flipping (BF) algorithm, known for its hard iterative decoding approach are extensively utilized. These codes effectively balance decoding complexity with error-correction performance.This paper focuses on comparing the optical performance of LDPC codes with and without the BF decoding algorithm using two simulation software packages: MATLAB and OptiSystem 7.0. The comparison is conducted across different wavelengths and quality factors. Through this study, we evaluate the advantages of LDPC codes in terms of error-rate reduction and enhancing the reliability of optical transmission.
Low density parity check (LDPC) codes with iterative decoding based on belief propagation achieve astonishing error performance close to Shannon limit. No algebraic or geometric method for constructing these codes has been reported and they are largely generated by computer search. As a result, encoding of long LDPC codes is in general very complex. This paper presents two classes of high rate LDPC codes whose constructions are based on finite Euclidean and projective geometries, respectively. These classes of codes a.re cyclic and have good constraint parameters and minimum distances. Cyclic structure adows the use of linear feedback shift registers for encoding. These finite geometry LDPC codes achieve very good error performance with either soft-decision iterative decoding based on belief propagation or Gallager's hard-decision bit flipping algorithm. These codes can be punctured or extended to obtain other good LDPC codes. A generalization of these codes is also presented.
Although low-density parity-check (LDPC) code has been proved as a powerful forward error correction code for fibre optic communication, its soft-decoding requires high quantisation resolution which is difficult to achieve for high-speed fibre-optic communication systems. A modification to LDPC decoding algorithms is proposed to effectively improve the performance at quantisation resolution as low as two-bit or one-bit. The good decoding performance of LDPC code for error correction is confirmed by experiment. Compared with the RS(255, 239) code commonly used in optical fibre communication, a Q-factor improvement of 2-dB is obtained in the experiment for an LDPC code with quasi-cyclic structure at the same redundancy as the RS code. Furthermore, the impacts of sampling phase and channel estimation using real data over the decoding performance are analysed.
The performance of a high-throughput long-distance communication system such as an optical transmission system is limited by the Net Coding Gain (NCG) of the Forward Error Correction (FEC) system. Summarizing the previous research works, Low-Density Parity-Check (LDPC) codes form one of the most promising FEC schemes to be applied in high-throughput communication systems. Designing a practical channel coding scheme with high code rate, low complexity, high throughput and extremely low error floor has always been a very challenging problem. Quasi-cyclic low-density parity-check (QC-LDPC) codes have been promising candidates to fulfill the above requirements but the implementation issues remain. In this paper, we propose a layered QC-LDPC decoder architecture with high code rate, low complexity, high throughput and excellent error performance. The architecture has been implemented using FPGA and the error performance has been shown to be good.