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IEEE Photonics Technology Letters

Projective geometry LDPC codes for ultralong-haul WDM high-speed transmission

Ivan B. Djordjević, Bane V. Vasic

Published May 1, 2003• 31 citations
Publisher

Abstract

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.

DOI
10.1109/lpt.2003.810250

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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.
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.
This paper presents a geometric approach to the construction of low-density parity-check (LDPC) codes. Four classes of LDPC codes are constructed based on the lines and points of Euclidean and projective geometries over finite fields. Codes of these four classes have good minimum distances and their Tanner (1981) graphs have girth 6. Finite-geometry LDPC codes can be decoded in various ways, ranging from low to high decoding complexity and from reasonably good to very good performance. They perform very well with iterative decoding. Furthermore, they can be put in either cyclic or quasi-cyclic form. Consequently, their encoding can be achieved in linear time and implemented with simple feedback shift registers. This advantage is not shared by other LDPC codes in general and is important in practice. Finite-geometry LDPC codes can be extended and shortened in various ways to obtain other good LDPC codes. Several techniques of extension and shortening are presented. Long extended finite-geometry LDPC codes have been constructed and they achieve a performance only a few tenths of a decibel away from the Shannon theoretical limit with iterative decoding.
Very powerful long low-density parity-check (LDPC) codes, such as the ITU G.975.1 Standard (32643, 30592) LDPC Code [1], have been considered for optical communications. Traditional implementations of such long codes result in circuits requiring millions of interconnections, which are not affordable. This thesis investigates the performance of the hard-decision differential decoding with binary message-passing (DD-BMP) algorithm [2], a low-complexity algorithm requiring a minimal number of wires due to its binary messages. Our simulation results for the ITU G.975.1 standard demonstrate that hard-decision DD-BMP algorithm outperforms the results provided in the standard, and that the gap between the decoding performance of hard-decision DD-BMP and hard-decision sum-product is small at high signal-to-noise ratios (SNR). We also present a novel design methodology for implementing a soft-decision decoder by exploiting the code's structure. An implementation-efficient architecture is presented using a partially-parallel adaptation of the min-sum algorithm known as the line-passing algorithm. The line-passing algorithm makes soft-decision decoding available while requiring a minimal number of interconnections, which is attractive for long-haul optical communication systems.
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.
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.