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European Transactions on Telecommunications

Performance of affine geometry low‐density parity‐check codes in long‐haul optical communications

Ivan B. Djordjević, Bane V. Vasic

Published Sep 1, 2004• 5 citations
Publisher

Abstract

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.

DOI
10.1002/ett.998

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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 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.
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.
Low Density Parity Check Codes (LDPC) is a class of linear block codes best suited for forward error control in communication systems. When compared with other codes, LDPC codes have significant performance gain, which can be turned to an increase of the coverage range or a reduction of transmission power. Hence a convenient and practical receiver is obtained. The analysis done in this paper is based on the Bit Error Rate of the decoded output. The factors considered for the analysis are multiple code rate, different number of iterations and various decoding schemes. For lower code rate, soft decision decoding and increased number of iterations LDPC codes yields a better performance.
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.
Scientists have competed to find codes that can be decoded with optimal decoding algorithms. Generalized LDPC codes were found to compare well with such codes. LDPC codes are well treated with both types of decoding; HDD and SDD. On the other hand GLDPC codes iterative decoding, on both AWGN and BSC channels, was not sufficiently investigated in the literature. This chapter first describes its construction then discusses its iterative decoding algorithms on both channels so far. The SISO decoders, of GLDPC component codes, show excellent error performance with moderate and high code rate. However, the complexities of such decoding algorithms are very high. When the HDD BF algorithm presented to LDPC for its simplicity and speed, it was far from the BSC capacity. Therefore involving LDPC codes in optical systems using such algorithms is a wrong choice. GLDPC codes can be introduced as a good alternative of LDPC codes as their performance under BF algorithm can be improved and they would then be a competitive choice for optical communications. This chapter will discuss the iterative HDD algorithms that improve decoding error performance of GLDPC codes. SDD algorithms that maintain the performance but lowering decoding simplicity are also described.
Low-density parity-check (LDPC) codes have the potential for applications in future high throughput optical communications due to their significant error correction capability and the parallel decoding. However, they are not able to satisfy the very low bit error rate (BER) requirement due to the error floor phenomenon. In this paper, we propose a low-complexity iterative decoding scheme for product codes consisting of very high rate outer codes and LDPC codes. The outer codes aim at eliminating the residual error floor of LDPC codes with quite low implementation costs. Furthermore, considering the long simulation time of computer simulation for evaluating very low BER, the hardware platform is built to accelerate the evaluation of the proposed iterative decoding methods. Simultaneously, the fixed-point effects of the decoding algorithms are also be evaluated. The experimental results show that the iterative decoding of the product codes can achieve a quite low bit error rate. The evaluation using field programmable gate array (FPGA) also proves that product codes with LDPC codes and high-rate algebraic codes can achieve a good trade-off between complexity and throughput.