Reduction of PAPR in coded OFDM using fast Reed-Solomon codes over prime Galois fields

In this work, two new techniques using Reed–Solomon (RS) codes over GF(257) and GF(65,537) are proposed for peak-to-average power ratio (PAPR) reduction in coded orthogonal frequency division multiplexing (OFDM) systems. The lengths of these codes are well-matched to the length of OFDM frames. Over these fields, the block lengths of codes are powers of two and we fully exploit the radix-2 fast Fourier transform algorithms. Multiplications and additions are simple modulus operations. These codes provide desirable randomness with a small perturbation in information symbols that is essential for generation of different statistically independent candidates. Our simulations show that the PAPR reduction ability of RS codes is the same as that of conventional selected mapping (SLM), but contrary to SLM, we can get error correction capability. Also for the second proposed technique, the transmission of side information is not needed. To the best of our knowledge, this is the first work using RS codes for PAPR reduction in single-input single-output systems.     

Combined Selective Mapping and Binary Cyclic Codes for PAPR Reduction in OFDM Systems

In this paper, we consider reduction of PAPR in OFDM systems with BPSK subcarriers by combining SLM and binary cyclic codes. This combining strategy can be used for both error correction and PAPR reduction. We decompose a binary cyclic code into direct sum of two cyclic subcodes: the correction subcode used for error correction and the scrambling subcode for PAPR reduction. The transmitted OFDM signal is selected that achieves minimum PAPR, from the set of binary cyclic codewords. The received signal can be easily decoded without the need of any side information. Simulations show that the proposed scheme with simplex code as scrambling subcode achieves good PAPR reduction.     

PAPR Reduction of OFDM Signals Using Partial Transmit Sequences and Reed-Muller Codes

This letter proposes a modified PTS technique using binary Reed-Muller (RM) codes for error correction and PAPR control in BPSK OFDM systems. A RM code is divided into the direct sum of a correcting subcode for encoding information bits and a scrambling subcode for encoding PAPR bits. The transmitted signal of the resulting OFDM sequence is selected with minimum PAPR from a number of candidates which are codewords of a coset of the scrambling subcode. We consider the RM codes in natural and cyclic orderings. Numerical results show that RM codes in cyclic ordering achieve better performance in PAPR reduction than RM codes in natural ordering.     

Performance of the deliberate clipping with adaptive symbolselection for strictly band-limited OFDM systems

The performance of the strictly band-limited OFDM systems with deliberate clipping is examined in terms of the peak-to-average power ratio (PAPR) and the resultant bit error performance. The clipping is performed on the OFDM signals sampled at the Nyquist rate, followed by the ideal low-pass filter, Since the low-pass filter considerably enlarges the PAPR, there is a severe limitation in PAPR reduction capability. Thus, in order to achieve further reduction of the PAPR, the application of the adaptive symbol selection scheme is also considered. It is shown that the significant PAPR reduction with moderate complexity can be achieved by the combination of the clipping and the adaptive symbol selection. The price to be paid for PAPR reduction by this scheme is its performance degradation. The paper theoretically analyzes the bit error rate performance of the OFDM system with the Nyquist-rate clipping combined with the adaptive symbol selection, and considers the use of the forward error correction for compensation of the degradation. It is shown that even though the clipping scheme causes severe loss in required signal-to-noise ratio, the use of a powerful channel coding scheme such as turbo codes significantly alleviates the bit error rate performance degradation     

Peak power reduction scheme base on transform kernel scrambling for OFDM systems

This work presents a novel transform kernel scrambling (TKS) scheme for reducing the peak-to-average transmitter power ratio (PAPR) for Orthogonal Frequency Division Multiplexing (OFDM) symbols. This scrambling scheme suppresses the peak envelope power of OFDM signals due to de-correlation among the original QAM constellation in multiple OFDM symbols via transformation. The performance of the reduction of PAPR for OFDM signals with various unitary transform kernels is also evaluated. Since specific unitary transform kernels in TKS processing block is only used for scrambling, no side information is required. For the ease of presentation, the system performance has been demonstrated by a computer simulation. Simulation results confirm the superiority of the proposed scheme in the PAPR reduction.     

Selective Time-Domain Filtering for Reduced-Complexity PAPR Reduction in OFDM

A new selective time-domain filtering scheme for reducing the peak-to-average power ratio (PAPR) in orthogonal frequency-division multiplexing (OFDM) systems is proposed. The proposed scheme not only relies on conventional pilot symbol channel estimation and demodulation techniques to recover the data in OFDM systems but also uses additional pilot symbols. The proposed scheme has greatly reduced complexity compared with the selective mapping (SLM) scheme and only slightly poorer performance than the SLM scheme. The new scheme achieves significant PAPR reduction at a cost of typically 0.1–0.75 dB in signal-to-noise ratio (SNR) relative to pilot symbol OFDM not having PAPR reduction.      

一种降低OFDM峰均比的编码方法

讨论了一种降低正交频分复用(OFDM)系统峰均比的分组编码方法.对于4载波OFDM系统,通过对已有QPSK调制下具有最小峰均比(PAR)的码字进行分析,表明了能使峰均比降低至少3 dB的码字所满足的相位关系,并以此为基础,研究推广了这类码字在M-PSK调制下的一种一般获取过程.对于子载波个数增大的OFDM系统,讨论了以4载波编码方法为基础降低峰均比的办法,对其进行了理论分析并给出了仿真研究.仿真结果表明文中编码方法不仅能有效降低OFDM系统的PAR,而且具有一定的纠错能力.     

Reed-Solomon codes for correcting phased error bursts

A code structure is introduced that represents a Reed-Solomon (RS) code in two-dimensional format. Based on this structure, a novel approach to multiple error burst correction using RS codes is proposed. For a model of phased error bursts, where each burst can affect one of the columns in a two-dimensional transmitted word, it is shown that the bursts can be corrected using a known multisequence shift-register synthesis algorithm. It is further shown that the resulting codes posses nearly optimal burst correction capability, under certain probability of decoding failure. Finally, low-complexity systematic encoding and syndrome computation algorithms for these codes are discussed. The proposed scheme may also find use in decoding of different coding schemes based on RS codes, such as product or concatenated codes.     

Block coding scheme for reducing PAPR in OFDM systems with large number of subcarriers

The major drawback in Orthogonal Frequency Division Multiplexing (OFDM) system is due to the high Peak-to-Average Power Ratio (PAPR), so the performance of the system is significantly degraded by the nonlinearity of a High Power Amplifier (HPA) in the transmitter. In order to mitigate distortion, a block coding scheme for reducing PAPR in OFDM systems with large number of subcarriers based on complementary sequences and predistortion is proposed, which is capable of both error correction and PAPR reduction. Computer simulation results show that the proposed scheme significantly improves Bit Error Rate(BER) performance as compared to an uncoded system when an HPA is employed or a coded system without predistortion.     

An error control system with multiple-stage forward errorcorrections

A robust error control coding system is presented. This system is a cascaded FEC (forward error control) scheme supported by parity retransmissions for further error correction in the erroneous data words. The error performance and throughput efficiency of the system are analyzed. Two specific examples of the error control system are studied. The first example does not use an inner code, and the outer code, which is not interleaved, is a shortened code of the NASA standard RS code over GF(2⁸). The second example, as proposed for NASA uses the same shortened RS code as the base outer code C₂, except that it is interleaved to a depth of 2. It is shown that both examples provide high reliability and throughput efficiency even for high channel bit-error rates in the range of 10^-2     

Comments on “Weighted sum codes for error detection and theircomparison with existing codes”

A.J. McAuley (IEEE/ACM Trans. Networking, vol.2, p.16-22, 1994) proposed a new family of error detection codes called weighted sum codes. In the present paper it is noted, that these codes are equivalent to lengthened Reed Solomon codes, resp. shortened version of lengthened Reed Solomon codes over GF(2^h/2). It is also shown, that it is possible to use these codes for error correction of one error in the code word over GF(2^h/2)     

A versatile time-domain Reed-Solomon decoder

A versatile Reed-Solomon (RS) decoder structure based on the time-domain decoding algorithm (transform decoding without transforms) is developed. The algorithm is restructured, and a method is given to decode any RS code generated by any generator polynomial. The main advantage of the decoder structure is its versatility, that is, it can be programmed to decode any Reed-Solomon code defined in Galois field (GF) 2^m with a fixed symbol size m. This decoder can correct errors and erasures for any RS code, including shortened and singly extended codes. It is shown that the decoder has a very simple structure and can be used to design high-speed single-chip VLSI decoders. As an example, a gate-array-based programmable RS decoder is implemented on a single chip. This decoder chip can decode any RS code defined in GF (2⁵) with any code word length and any number of information symbols. The decoder chip is fabricated using low-power 1.5-μ, two-layer-metal, HCMOS technology     

GF(2p)LDPC编码的相位调制OFDM系统在瑞利衰落信道的性能

OFDM是一项能有效对抗高速无线通信中多径衰落的关键技术，为了进一步提高OFDM系统的误码性能，许多信道编码技术已被应用于OFDM系统中，二元域LDPC码以其近香农限的误码性能和较低的译码复杂度成为研究的热点。在AWGN信道下，多元域LDPC码比等效码长的二元域LDPC码有更好的纠错性能。本文提出了一种将多元域LDPC码经过MPSK调制后用于OFDM系统的新方法。仿真结果表明，在多径衰落信道下，通过合理选择多元LDPC码域的阶数和调制的方法，多元域LDPC编码的高阶调制OFDM系统比等效码长的二元域LDPC编码OFDM系统具有更好的性能，并且由于采用了多元域LDPC的快速BP译码，译码复杂度只是稍有增加。     

Improved FEC Code Based on Concatenated Code for Optical Transmission Systems

The improved three novel schemes of the super forward error correction(super-FEC) concatenated codes are proposed after the development trend of long-haul optical transmission systems and the defects of the existing FEC codes have been analyzed. The performance simulation of the Reed-Solomon(RS)+Bose-Chaudhuri-Hocguenghem(BCH) inner-outer serial concatenated code is implemented and the conceptions of encoding/decoding the parallel-concatenated code are presented. Furthermore, the simulation results for the RS(255,239)+RS(255,239) code and the RS(255,239)+RS(255,223) code show that the two consecutive concatenated codes are a superior coding scheme with such advantages as the better error correction, moderate redundancy and easy realization compared to the classic RS(255,239) code and other codes, and their signal to noise ratio gains are respectively 2～3dB more than that of the RS(255,239)code at the bit error rate of 1×10 -13 . Finally, the frame structure of the novel consecutive concatenated code is arranged to lay a firm foundation in designing its hardware.     

结合6-QAM和双层LDPC码的编码调制研究

针对阶数为3×2p的非标准调制与纠错编码难以匹配的问题,提出了一种面向6阶正交幅度调制（QAM）的双层编码调制传输方案。在发送端,采用有限域GF(2)低密度奇偶校验（LDPC）码与GF(3) LDPC码进行分层编码,并将两种编码码字映射为6进制码字后进行6-QAM调制;在接收端,根据GF(2) LDPC码和GF(3) LDPC码的译码顺序,设计了两种双层迭代译码方法。仿真结果表明,在加性高斯白噪声（AWGN）信道下,执行一次整体迭代译码时,先执行GF(3) LDPC码译码的6-QAM分层编码调制方案比先执行GF(2) LDPC码译码的方案获得了更优的误符号率（SER）性能;随着迭代次数增加,纠错性能可获得进一步改善。比较6-QAM与6阶相移键控（6-PSK）调制,若先执行GF(3) LDPC码译码,当SER为10-5时,6-QAM结合双层LDPC码的传输方案在AWGN信道下可获得约1.3dB的增益。      

A Low-BER Clipping Scheme for PAPR Reduction in STBC MIMO-OFDM Systems

Clipping is a simple scheme to reduce the peak-to-average power ratio (PAPR) in orthogonal frequency division multiplexing (OFDM) systems. Further, it can be extended to space-time block coding (STBC) multiple-input multiple-output (MIMO) OFDM systems for the PAPR reduction. In the conventional clipping schemes for STBC MIMO-OFDM systems, the input symbols are first encoded and then clipped. In this paper, a new scheme is proposed, where the clipping operation is performed before space-time block coding. We theoretically prove that the proposed scheme has better bit-error rate (BER) performance while maintaining the same PAPR reduction as the conventional schemes. Additionally, we derive the symbol-error rate (SER) and BER expressions for the new scheme over multipath fading channels. The simulation results show a good match with our analysis.     

A PAPR reduction scheme based on a new spreading code in optical direct detection OFDM system

In this paper, we propose and experimentally demonstrate a peak-to-average power ratio (PAPR) reduction scheme based on a new spreading code in direct detection optical orthogonal frequency division multiplexing (OFDM) system. The new spreading code with low cross correlation and high auto-correlation can support \(2N+1\) users. Thus, \(2N+1\) users or data symbols can be transmitted over only N subcarriers. The experimental results show that, after transmission over 70 km single-mode fiber, at the bit error rate of \(10^{-3}\), with fiber launch power of 2.75 dBm, the receiver sensitivity can be improved 2.1 dB by using the proposed scheme based on new spreading code. The PAPR can be reduced about 4.6 dB, compared with the original OFDM signal at a complementary cumulative distribution function of \(10^{-4}\).     

Reed-Solomon Codes Implementing a Coded Single-Carrier with Cyclic Prefix Scheme

This paper presents a novel Reed-Solomon codes based transmission scheme called RS-SC-CP. While RS-SC-CP is essentially a Reed-Solomon (RS) coded single carrier with cyclic prefix (SC-CP) system, a filter bank representation of the RS code is used. This filter bank representation unveils a DFT synthesis bank, just as in a traditional Orthogonal Frequency Division Multiplexing (OFDM) system (allbeit in a finite field). Therefore, RS-SC-CP is topologically equivalent with OFDM. As such, the RS-SC-CP system inherits the advantages of an SC-CP system over a traditional OFDM system like a low Peak to Average Power Ratio (PAPR). But, more importantly, it allows us to use a novel equalization technique that resembles a traditional OFDM equalizer. The equalizer of an RS-SC-CP receiver is split into two stages: the first stage encompasses a partial equalization in the complex field, which ensures that the residual channel response has integer coefficients. It is calculated using a Minimum Mean Square Error (MMSE) criterion. The residual ISI is removed by a Galois field equalizer in the second stage, posterior to the RS decoding removing the noise. Finally, the performance of the RS-SC-CP system is further evaluated by simulations showing the performance gain of the RS-SC-CP system compared to a traditional coded OFDM or single carrier with cyclic prefix (SC-CP) scheme.     

The New Peak-to-Average Power Reduction Algorithm in the OFDM System

In this paper, we proposed a new peak-to-average power reduction (PAPR) algorithm of orthogonal frequency division multiplexing (OFDM) system using block coding scheme and discrete cosine transform (DCT). We are using DCT to concentrate the energy of the original signal into a few coefficients. After the DCT data were fed into the IDFT, the output of signal of OFDM appeared to have uniform distribution. With the newly proposed schemes, that we founded those three important properties, the first property is the PAPR used be reduced by 9.4419 dB for BPSK mapper. The second property is the OFDM signals have capability of noise immunity and of error correction. And the third property is the effect of PAPR reduced can be implement by cascaded different method.     

Energy Savings in OFDM Systems through Cooperative Relaying

Energy savings in orthogonal frequency division multiplexing (OFDM) systems is an active research area. In order to achieve a solution, we propose a new cooperative relaying scheme operated on a per subcarrier basis. This scheme improves the bit error rate (BER) performance of the conventional signal‐to‐noise ratio (SNR)‐based selection relaying scheme by substituting SNR with symbol error probability (SEP) to evaluate the received signal quality at the relay more reliably. Since the cooperative relaying provides spatial diversity gain for each subcarrier, thus statistically enhancing the reliability of subcarriers at the destination, the total number of lost subcarriers due to deep fading is reduced. In other words, cooperative relaying can alleviate error symbols in a codeword so that the error correction capability of forward error correction codes can be fully exploited to improve the BER performance (or save transmission energy at a target BER). Monte‐Carlo simulations validate the proposed approach.