基于差集的高效LDPC码设计与光通信应用

需积分: 9 142 浏览量更新于2024-09-20 收藏 251KB PDF 举报

本文是一篇关于"基于差集的低密度奇偶校验码(LDPC)构造"的专业研究论文，发表在2004年的IEEE Journal of Selected Topics in Quantum Electronics。文章主要关注于光通信系统中的高效纠错编码技术，特别是提出了一个新颖的结构化LDPC码家族，其特点是使用了块循环矩阵，并依赖于称为循环不变差集的新组合结构。该文介绍的LDPC码构造方法不同于传统设计，通过循环不变差集来构建码字，这种结构具有以下优势：首先，它们拥有较低的存储需求，使得编码过程更为高效；其次，编码算法快速，适合于实时数据传输；最重要的是，这些代码在与同类可比率和长度的已知结构化LDPC码相比时，通常展现出更好的性能，这意味着它们能提供更高的纠错能力和更少的错误传播，这对于保证光通信系统的高可靠性和容量扩展至关重要。文章的创新之处在于将差集理论与LDPC码设计相结合，这不仅提升了编码效率，还可能改善系统的误码率（BER）和帧错误率（FER），对于现代密集波分复用（DWDM）长途传输网络而言，这是提升信号质量和传输距离的关键因素。此外，文中还讨论了在实际应用中，如何通过优化这种新型LDPC码的循环不变差集来进一步优化编码性能，以及如何评估其在光通信系统中的实际表现。总结来说，这篇论文是关于一种利用循环不变差集原理构造的高性能LDPC码的设计和分析，对于光通信领域的纠错编码技术发展具有重要意义，为未来的通信系统提供了新的设计思路和优化方向。通过深入理解这种基于差集的LDPC码构造，工程师们可以更好地应对日益增长的数据传输需求，确保在高速、高容量的光通信系统中实现可靠的信息传输。

294 IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 10, NO. 2, MARCH/APRIL 2004

Block-Circulant Low-Density Parity-Check Codes

for Optical Communication Systems

Olgica Milenkovic, Member, IEEE, Ivan B. Djordjevic, and Bane Vasic, Senior Member, IEEE

Abstract—A novel family of structured low-density parity-check

(LDPC) codes with block-circulant parity-check matrices that con-

sist of permutation blocks is proposed. The codes from this family

are based on new combinatorial objects termed cycle-invariant dif-

ference sets, and they have low storage requirements, fast encoding

algorithms, and girth of at least six. Most importantly, they tend to

outperform many other known structured LDPCs of comparable

rate and length.

Index Terms—Cycle-invariant difference sets, forward error

correction, low-density parity-check codes, optical communica-

tions.

I. INTRODUCTION

HE role of forward error correction (FEC) in maintaining

acceptable transmission quality is becoming increasingly

important as the capacity of dense wavelength-division multi-

plexing (DWDM) long-haul transmission systems grows. FEC

can improve the performance of optical communications sys-

tems without introducing major changes to optical materials and

devices and without major paradigm shifts in hardware such as

converting to all-optical networks. This characteristic is espe-

cially important as the physical properties of optical networks

are being pushed to their limits. The FEC proposed in this paper

can readily be adapted to follow any shift in system implemen-

tation.

In state-of-the-art optical communication systems, two FEC

standards are currently in use, both based on Bose–Chaud-

huri–Hocquenghen (BCH) codes [1]. For example, “in-band”

FEC used in SONET/SDH framing is a 3-[4359, 4320] short-

ened BCH code (ITU-T G.707 standard). “Outband” FEC

coding is accomplished by using interleaved Reed–Solomon

(RS) [255, 238] codes, as specified in the digital wrapper of

the ITU G.709 standard. The FEC used in submarine systems

is based on a Reed–Solomon code with parameters [255, 239],

as specified by the ITU-T G.975 standard [2]. For optical

communication systems with bit rates exceeding 10 Gb/s, more

powerful FEC codes with large coding gains and high code

rates are desirable. Two such schemes have been proposed

Manuscript received September 2, 2003; revised January 18, 2004. This work

was supported by the National Science Foundation under Grant ITR 0325979.

O. Milenkovic is with the Department of Electrical and Computer

Engineering, University of Colorado, Boulder, CO 80303 USA (e-mail:

milenkov@colorado.edu).

I. B. Djordjevic is with the Department of Electrical and Computer Engi-

neering, University of Arizona, Tucson, AZ 85719 USA and the Faculty of

Computing, Engineering and Mathematical Sciences, University of the West of

England, Bristol, U.K. (e-mail: ivan@ece.arizona.edu; icadj@yahoo.com).

B. Vasic is with the Department of Electrical and Computer Engineering, Uni-

versity of Arizona, Tucson, AZ 85719 USA (e-mail: vasic@ece.arizona.edu).

Digital Object Identifier 10.1109/JSTQE.2004.827832

recently: Ait Sab et al. [3] proposed a concatenated scheme

with two RS codes, and Pyndiah [4] and Ait Sab et al. [5]

proposed block turbo codes.

Recently, the authors showed in [6]–[8] that the error-cor-

recting capability of turbo codes can be surpassed by low-den-

sity parity-check (LDPC) codes; at the same time, the hardware

complexity of LDPC codes tends to be significantly smaller than

that corresponding to turbo codes [9]. LDPC codes are usually

designed in a pseudorandom fashion [10], but this leads to en-

coders/decoders with complexity exceeding practical limits im-

posed on high-speed optical communication systems. A more

attractive approach that we propose in this paper is to design

block-circulant LDPC codes with permutation blocks based on

a new class of combinatorial objects; these structures allow for

small storage requirements, as well as for performing encoding

and decoding via fast and simple circuits. Such high-speed FEC

architectures are of crucial importance in optical communica-

tions, and there has been a great deal of activity in this area. For

example, Agere Systems (see Azadet et al. [11]) reported an op-

tical networking interface device with four parallel RS codecs,

each operating at 2.5 Gb/s. Additionally, Agere Systems [12],

[13] and Flarion [14] researchers developed codecs employing

LDPC designs that seem to be a combination of structured and

random-like components.

The main result of this paper is a novel class of LDPC

codes based on a combinatorial structure referred to as an

-fold cycle-invariant difference set (CIDS). The parity-check

matrices of the proposed codes are block-circulants with

permutation blocks. Both the minimum distance and the girth

of the corresponding bipartite graph [8] are at least six. By

carefully designing the cycle-invariant difference set, and by

appropriately permuting the elements in some block-rows,

code graphs with

( an odd prime) variable

nodes can be made to have girth at least 2

2. As the authors

demonstrated by extensive computer simulations in [8], codes

with high girth tend to perform very well, since a larger number

of message-passing iterations can be performed before extrinsic

information of nodes in the graph becomes correlated. Due

to the block-circulant structure of the parity-check matrix,

encoding can be performed very efficiently. Additionally,

the min-sum decoding algorithm employed for soft-decision

decoding of these codes requires a number of binary logic

operations at least one order of magnitude smaller than that

corresponding to hard-decision decoding of RS or turbo codes

[4], [5] with comparable performance. For more details on

min-sum algorithm complexity, the reader is referred to [17,

Appendix B] and [20]–[22].

Fec在光纤通信系统中的应用

ldpc码在光纤通信系统中的应用

本篇文章中的ldpc码的设计特色

下载后可阅读完整内容，剩余5页未读，立即下载

cc_cylina

粉丝: 0
资源: 2

基于差集的高效LDPC码设计与光通信应用

基于循环差集的（3，L）规则QC-LDPC码构造

基于完备循环差集的QC-LDPC码的确定性构造

基于差集的qc-ldpc

基于差集的高效能分布式请求集生成算法

基于差集的高效能分布式请求集生成算法.pdf

由平方剩余差集与差集偶构造二元 ZCZ序列偶集 (2009年)

基于分圆类方法的差集偶构造 (2009年)

基于分圆类方法的差集偶构造的进一步研究 (2010年)

利用环分解和分圆类的差集偶构造 (2012年)

不规则QC-LDPC码的构建：克隆陪集法

最新资源