低复杂度IS-LDPC码：OFDM系统中有效减小PAPR的新方案

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本文主要探讨了"2014年IEEE Transactions on Wireless Communications第13卷第4期"的一篇研究论文，标题为"Invertible Subset LDPC Code for PAPR Reduction in OFDM Systems with Low Complexity"。作者是Daiming Qu、Li Li和Tao Jiang。该研究聚焦于在低复杂度条件下降低正交频分复用(OFDM)系统中峰值信噪比(Peak-to-Average Power Ratio, PAPR)的技术。文章的核心贡献在于提出了一种新型的低密度奇偶校验码（Low-Density Parity-Check, LDPC）编码方案，称为可逆子集LDPC (IS-LDPC) 码。IS-LDPC码的特点在于它包含多个互不重叠的可逆子集，每个子集都可以独立地进行操作，生成其他有效的LDPC码字。这种特性使得在OFDM系统中实现PAPR减小变得更为高效，因为不同的子集操作可以并行执行，从而降低了整体的计算复杂度。为了构建具有良好纠错性能的IS-LDPC码，作者提出了一个改进的逐步边增长构造算法。这个算法通过分析生成的Tanner图来验证其有效性。理论分析和数值结果表明，IS-LDPC码显示出优良的纠错能力，并且基于IS-LDPC码的PAPR降低方案显著减少了系统的峰均功率比，这对于提高无线通信系统的信号稳定性至关重要。与现有的基于编码的候选生成方案相比，所提出的IS-LDPC编码方法在搜索复杂性方面具有显著的优势，这意味着在保持高效性能的同时，能够降低对硬件资源的需求，从而降低整个系统的能耗和成本。这对于现代无线通信系统的设计者来说，是一个重要的技术突破，有助于提升系统的效率和可靠性。这篇论文不仅提供了新的编码理论，还为实际应用中的OFDM系统提供了一种有效且低复杂度的PAPR降低策略，对于优化无线通信系统的性能和减少系统开销具有重要意义。

2204 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 13, NO. 4, APRIL 2014

Invertible Subset LDPC Code for PAPR Reduction

in OFDM Systems with Low Complexity

Daiming Qu, Li Li, and Tao Jiang

Abstract—In this paper, we introduce a new family of low-

density parity-check (LDPC) codes, called as invertible subset

LDPC (IS-LDPC) code, for peak-to-average power ratio (PAPR)

reduction in OFDM systems with low complexity. An IS-LDPC

code has a number of disjoint invertible subsets, and each

invertible subset can be independently inverted to generate other

valid codewords of the LDPC code. To construct IS-LDPC codes

with good error-correcting performance, we propose a modiﬁed

progressive edge-growth construction algorithm and verify its

effectiveness by analyzing the constructed Tanner graphs. Both

theoretical analysis and numerical results show that the IS-

LDPC codes exhibit good error-correcting performance and the

proposed PAPR reduction scheme based on IS-LDPC codes

signiﬁcantly reduces the PAPR. Compared with the existing

coding-based candidate generation schemes, the proposed scheme

has a much lower searching complexity when the codeword is

transmitted by multiple OFDM symbols. With all mentioned

advantages, the proposed PAPR reduction scheme based on IS-

LDPC codes could serve as an attractive PAPR reduction solution

for future multicarrier communication systems.

Index Terms—Orthogonal frequency-division multiplexing

(OFDM), peak-to-average power ratio (PAPR), low density

parity-check codes (LDPC), progressive edge-growth (PEG).

I. INTRODUCTION

RTHOGONAL frequency-division multiplexing

(OFDM) has been widely adopted in various wireless

communication standards, due to its capability to efﬁciently

cope with frequency selective channels. However, one

major drawback of OFDM systems is high p eak-to-average

power ratio (PAPR). High PAPR signiﬁcantly complicates

implementation of the radio frequency front-end, since power

ampliﬁers with a wide linear range are required. Otherwise,

the nonlinear characteristics o f power ampliﬁers would distort

the in-band signal and raise the out-of-band radiation. To

reduce PAPR, many schemes have been proposed in the

literature [1], [2], among which coding-based approaches

have attracted considerable attentions due to their inherent

error contro l capability and the simplicity of implementation .

Particularly, coding-based approaches are classiﬁed into two

categories in this paper: low PAPR coding and coding-based

candidate generation schemes.

Manuscript received July 17, 2013; revised November 29, 2013; accepted

January 17, 2014. The associate editor coordinating the review of this paper

and approving it for publication was A. Vosoughi.

The authors are with the Department of Electronics and Information En-

gineering, Huazhong University of Science and Technology, Wuhan, 430074,

China (e-mail: Tao.Jiang@ieee.org). T. Jiang is the corresponding author.

This work was supported in part by the National Science Foundation of

China with Grants 61271228, 61172052 and 60872008, and the National and

Major Project under Grant 2013ZX03003016.

Digital Object Identiﬁer 10.1109/TWC.2014.031314.131289

The low PAPR coding: It generates low PAPR codewords

through coding. The low PAPR code was ﬁrstly proposed

in [3]. In [4], the existence of asymptotically good codes

with low PAPR was proven. In [5], efﬁcient computation of

the PAPR for any practical code was discussed. The Golay

complementary sequences and Reed-Muller (RM) codes to

achieve excellent PAPR performance were proposed in [6]

and [7]. Later, a complement block-coding (CBC) scheme

was proposed to reduce the PAPR in [8]. However, the error-

correcting performance of these codes are quite far from

the Shannon limit. In [9] and [10], time-frequency turbo

block codes (TBC) were proposed to achieve good error-

correcting performance as well as low PAPR, in which the

frequency domain component code employs codes with low

PAPR, like RM code or dual Bose-Ray-Chaudhuri code, and

the time domain component code uses low density parity-

check (LDPC) code. However, there are still appa rent error-

correcting performance gaps between the TBC codes and the

capacity achieving codes.

The coding-based candidate generation schemes: It g en-

erates candidate codewords for any given codeword and a

candidate with low PAPR is selected for transmission. In

[11], candidates are generated by employing a scrambler

before channel coding, therefore all candidates are also valid

codewords. In [12], candidate codewords are generated with

a number of interleavers before channel coding. Employment

of random-like codes, such as turbo and LDPC code, were

proposed in [13] and [14] to generate candidate codewords,

which d o not require an explicit scrambler/interleaver. More-

over, binary cyclic codes, Reed-Muller codes, Reed Solomon

and simplex codes are considered in [15]–[17]. At ﬁrst sight,

the coding-based candidate generation schemes share the same

principle of PAPR reduction with the selective mapping (SLM)

[18] or partial transmit sequence (PTS) [19] schemes, which

generate candidate signals and select a candidate of low PAPR

for transmission. However, the m ajor difference is that the

candidates of the coding-based candidate generation schemes

are valid codewords, while those of the SLM and PTS schemes

are not necessarily valid codewords. Unlike the SLM and

PTS schemes, the coding-based candidate generation schemes

refrains from the use of explicit side information in the

receiver, with the help of coding [11].

Compared with low PAPR coding schemes, the coding-

based candidate generation schemes do not suffer signiﬁcant

degradation of error-correcting performance, by employing

error-correcting codes of proven p erformance [11]. Therefore,

we focus on the coding-based candidate generation schemes

in this paper. However, the existing coding-based candidate

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