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.

Degenerate asymmetric quantum concatenated codes for correcting biased quantum errors

In most practical quantum mechanical systems,quantum noise due to decoherence is highly biased towards dephasing.The quantum state suffers from phase flip noise much more seriously than from the bit flip noise.In this work,we construct new families of asymmetric quantum concatenated codes(AQCCs)to deal with such biased quantum noise.Our construction is based on a novel concatenation scheme for constructing AQCCs with large asymmetries,in which classical tensor product codes and concatenated codes are utilized to correct phase flip noise and bit flip noise,respectively.We generalize the original concatenation scheme to a more general case for better correcting degenerate errors.Moreover,we focus on constructing nonbinary AQCCs that are highly degenerate.Compared to previous literatures,AQCCs constructed in this paper show much better parameter performance than existed ones.Furthermore,we design the specific encoding circuit of the AQCCs.It is shown that our codes can be encoded more efficiently than standard quantum codes.

Study on New Concatenated Code in WDM Optical Transmission Systems

A new concatenated code of RS（255,239）＋BCH（2 040,1 930） code to he suitable for WDM optical transmission systems is proposed. The simulation resuhs show that this new concatenated code. compared with the RS（255,239）4-CSOC（k0/n0=6/7, J= 8） code in ITU-TG. 75.1, has a lower redundancy and better error-correction performance, furthermore, its net coding gain（NCG） is respectively 0. 46 dB, 0.43 dB morethanthatofRS（255,239）＋CSOC（k0/n0= 6/7, J= 8） code and BCH（3860,3824）＋BCH （2 040,1 930） code in ITU TG. 75. 1 at the third iteration for the bit error rate（BER） of 10^-12. Therefore, the new super forward error correction（Super-FEC） concatenated code can be better used in ultra long-haul, ultra large-capacity and ultra high-speed WDM optical communication systems.

基于BCM降低OFDM系统PAPR的方法

简述了降低正交频分复用系统峰均功率比的研究进展 ,给出了基于分组编码调制降低峰均功率比的方法 ,提出了子载波数较大系统的搭建方法 ,分析了实现原理并进行了仿真研究 ,结果表明该方法不仅能有效降低正交频分复用系统的峰均功率比 。

一种接近于Shannon限的级联BCM码

给出一种新的级联分组调制 (BCM)码 ,其中内码选用带宽有效的 BCM码 ,外码采用 RS码 ,在高斯信道中的仿真结果表明 ,这种码字在误码率为 10 - 6 时较近乎相同带宽利用率下的未编码 QPSK系统有 5 .3d B的编码增益 ,距离 Shannon限只有 0 .5 d B;在 Rayleigh衰落信道中 ,误码率为 10 - 5 时较未编码 QPSK系统的编码增益可达到2 0 d B,距离无信道状态信息时的信道截止速率 R0 限为 4.2 d B,且译码复杂度适中 ,这种级联方案实现了可靠性、带宽利用率以及复杂度的最佳折衷 。

BCM码在AWGN信道与Rayleigh衰落信道中的性能仿真

采用Imai与Hirakawa提出的多层编码方法可构造出在AWGN信道与Rayleigh衰落信道中好的分组调制 (BCM)码 ,恰当选择成分码可使BCM码有较大的编码增益 .文章对几种BCM码在AWGN及Rayleigh衰落信道中的性能进行了仿真 ,并在这些BCM码之间以及它们与相同频带利用率的未编码系统之间进行了比较 ,结果表明 :在AWGN信道中 ,BCM码较相同频带利用率下的未编码系统有 1～ 3dB的编码增益 ,并且这些编码增益值主要取决于BCM码的最小平方欧氏距离 ;而在Rayleigh衰落信道中 ,编码增益值可达到 6～ 17dB ,决定此值的主要因素为BCM码的汉明距 。

BCM的多阶段译码算法

针对在某些通信系统中对译码速度较高的需求,基于分组编码调制(BCM,Block Coding Modulation)的多级结构,给出了一种多级BCM的多阶段译码算法:从BCM中第一级分量码开始,根据BCM的级数逐阶段进行译码,针对每级分量码,采用软判决最大似然译码,直到最后一级分量码,从而降低了译码复杂度.仿真结果表明,与传统Viterbi译码算法相比,提出的多阶段译码算法的误码性能与其相当,信噪比较小时甚至更好,但译码复杂度远低于传统Viterbi译码方法.

Improved Belief Propagation Decoder for LDPC-CRC-Polar Codes with Bit-Freezing

Though belief propagation bit-flip(BPBF)decoding improves the error correction performance of polar codes,it uses the exhaustive flips method to achieve the error correction performance of CA-SCL decoding,thus resulting in high decoding complexity and latency.To alleviate this issue,we incorporate the LDPC-CRC-Polar coding scheme with BPBF and propose an improved belief propagation decoder for LDPC-CRC-Polar codes with bit-freezing(LDPCCRC-Polar codes BPBFz).The proposed LDPCCRC-Polar codes BPBFz employs the LDPC code to ensure the reliability of the flipping set,i.e.,critical set(CS),and dynamically update it.The modified CS is further utilized for the identification of error-prone bits.The proposed LDPC-CRC-Polar codes BPBFz obtains remarkable error correction performance and is comparable to that of the CA-SCL(L=16)decoder under medium-to-high signal-to-noise ratio(SNR)regions.It gains up to 1.2dB and 0.9dB at a fixed BLER=10-4compared with BP and BPBF(CS-1),respectively.In addition,the proposed LDPC-CRC-Polar codes BPBFz has lower decoding latency compared with CA-SCL and BPBF,i.e.,it is 15 times faster than CA-SCL(L=16)at high SNR regions.

On Some Properties of Graph of Prefix Code

We investigate decomposition of codes and finite languages. A prime decomposition is a decomposition of a code or languages into a concatenation of nontrivial prime codes or languages. A code is prime if it cannot be decomposed into at least two nontrivial codes as the same for the languages. In the paper, a linear time algorithm is designed, which finds the prime decomposition. If codes or finite languages are presented as given by its minimal deterministic automaton, then from the point of view of abstract algebra and graph theory, this automaton has special properties. The study was conducted using system for computational Discrete Algebra GAP. .

Improved Design and SOVA Algorithm for Serial Concatenated Convolutional Code

To improve the performance of the short interleaved serial concatenated convolutional code(SCCC) with low decoding iterative times, the structure of Log MAP algorithm is introduced into the conventional SOVA decoder to improve its performance at short interleaving delay. The combination of Log MAP and SOVA avoids updating the matrices of the maximum path, and also makes a contribution to the requirement of short delay. The simulation results of several SCCCs show that the improved decoder can obtain satisfied performance with short frame interleaver and it is suitable to the high bit rate low delay communication systems.

Iterative Decoding of Parallel Concatenated Block Codes and Coset Based MAP Decoding Algorithm for F24 Code

A multi dimensional concatenation scheme for block codes is introduced, in which information symbols are interleaved and re encoded for more than once. It provides a convenient platform to design high performance codes with flexible interleaver size. Coset based MAP soft in/soft out decoding algorithms are presented for the F24 code. Simulation results show that the proposed coding scheme can achieve high coding gain with flexible interleaver length and very low decoding complexity.

Low complexity Chase-2 decoding of concatenated codes

The concatenated codes are widely used in current communication systems, such as satellite communication systems and WiMAX system. The objective of this study was to present a low complexity iterative soft decoding algorithm for concatenated codes. The concatenation was between a Reed-Solomon (RS) code and recursive systematic convolutional (RSC) code. The reduction in computational complexity was achieved by simplifying the Chase-2 decoder for RS codes with limited usage of test patterns. The processing of soft information between inner and outer decoders was also discussed. Simulation results showed that the proposed algorithm could achieve a good trade-off between complexity and performance.

Design of concatenated turbo-SPC coded space-time systems

Multiple antenna wireless systems can provide larger channel capacity and enable spatial diversity to combat fading. In this paper we conduct an investigation into the design of coded space-time system obtained by serially concatenating channel code module and space-time code module with an interleaver in between. As an example, the system is constructed by employing low decoding complexity turbo-SPC （single parity check） code as outer module and linear complex field space-time code as inner module, which achieves full diversity and lossless equivalent channel capacity. Simulation results prove that our designed system performs well and it only loses 0.8 dB from multiple-input multiple-output （MIMO） capacity at BER = 10^-5 in the case of information bit length 6048. Compared with turbo code-based systems, it also has lower error floor.

Decoding Technique of Concatenated HadamardCodes and Its Performance

The decoding technique of concatenated Hadamard codes and its performance are studied. Efficient soft in soft out decoding algorithms based on the fast Hadamard transform are developed. Performance required by CDMA mobile or PCS speech services, e.g. , BER=10 -3 , can be achieved at Eb/No =0.9 dB using short interleaving length of 192 bits.

Performance Evaluation of OFDM Coding System Using Concatenated BCH and LDPC Codes

This paper establishes a resilient concatenated coding platform for Orthogonal Frequency Division Multiplexing (OFDM) with Quadrature Amplitude Modulation (QAM) over Additive White Gaussian Noise (AWGN) channel. At the Forward Error Correction (FEC) coding unit, our proposed concatenated coding scheme utilizes standard type of BCH as external coding and LDPC as inner coding. In this scheme, Interleaver inclusion is seen as a catalyst to enhance the systems performance.

基于分层最小和译码的RS-LDPC级联码改进算法

RS-LDPC级联码能够有效提高数据传输的可靠性和系统的容错能力,在5G通信等领域中得到了广泛的应用,且在6G中具有很好的应用前景。但是RS-LDPC级联码与单码相比具有计算复杂度高、不易于在硬件上实现的不足,因此提出一种基于分层最小和的RS-LDPC级联码改进译码算法,将LDPC码的校验矩阵分解成多个子矩阵,在不同子矩阵层次上并行计算。此外,还引入了新的关于校验节点信息更新的简化函数,旨在保证译码性能的同时降低计算复杂度,达到易于硬件实现的目的。结果表明改进型分层最小和算法复杂度大大降低,且在性能上优于传统BP译码0.25 dB左右。

基于部分信息的SLT-LT联合码防窃听方案设计

近年来,信息的安全传输备受人们关注,现有的物理层安全技术从信息论的角度出发,将物理层安全编码与传输信道的动态物理特性进行结合,实现信息的保密传输。作为一种纠删码,LT(Luby transform)码由于其编码随机性、码率不固定等特性,使得窃听者不能直接从泄露的编码符号中得到有用信息,只要合法用户在窃听者之前接收到足够数量的编码符号,便可实现信息的安全传输。而作为一种转移LT(Shifted LT,SLT)码,SLT码能高效恢复信息的同时具有更小的译码开销。因此,我们将SLT码应用于Wyner降阶窃听信道模型进行研究,提出一种基于部分信息转移的SLT-LT联合码防窃听方案,信源利用接收者已知的部分信息对度分布进行调整,并对信源符号进行SLT-LT码级联编码。由于窃听信道是合法信道的降阶信道,因此外在的窃听者截获到的消息符号是合法接收者的降阶版本,在相同时间内,合法接收者能够收到更多消息符号,随着编解码过程的不断进行,合法接收者的优势不断累积,能够优先完成解码,而度分布的调整以及级联编码方案使得编码符号的平均度进一步增大,窃听者难以完成解码,进一步降低了窃听者译出率;之后,对所提方案的编解码性能以及安全性进行理论分析,并通过实验仿真进行验证,仿真结果表明,与其他防窃听LT方案相比,本文所提方案仅增加少量的译码开销但具有更好的安全性能。

面向6G空天通信的极化编码技术:需求、现状与展望

6G空天通信复杂多样的业务、场景对信息的可靠传输及系统适应能力提出了新的挑战。作为第一种理论可达信道容量的高性能编码,极化码是未来6G数据传输的重要候选方案。简要介绍了6G空天通信系统信息传输的难点及对信道编码技术的需求。对包括极化码编码构造、级联极化码、高性能译码算法在内的高可靠极化码增强技术,以及以速率适配、极化编码调制、极化编码混合重传为代表的高韧性极化码自适应传输技术等现状进行了综述。最后结合6G关键技术,展望未来极化码可能的发展方向。

LLR Processing of Polar Codes in Concatenation Systems

This paper studies the decoding performance of low-density parity-check(LDPC)codes in a serial concatenation system with polar codes employing the successive cancellation(SC)decoding.It is known that the absolute incorrect log-likelihood ratio(LLR)values from the SC decoding can be very large.This phenomenon dramatically deteriorates the error correcting performance of the outer LDPC codes.In this paper,the LLR values of polar codes are regulated by a log processing before being sent to the LDPC decoder.Simulation results show that the log processing is an efficient approach with a low optimization complexity compared with the existing procedures to improve the performance of the serial concatenation systems.

SERIALLY CONCATENATED CONTINUOUS PHASE MODULATION WITH REDUCED ITERATIVE DEMODULATION AND DETECTION

A reduced state Soft Input Soft Output (SISO) a posteriori probability algorithm for Seri-ally Concatenated Continuous Phase Modulation (SCCPM) is proposed in this paper. Based on the Reduced State Sequence Detection (RSSD),it has more general form compared with other reduced state SISO algorithms. The proposed algorithm can greatly reduce the state number,thus leads to the computation complexity reduction. It also minimizes the degradation in Euclidean distance with decision feedback in the reduced state trellis. Analysis and simulation results show that the perform-ance degradation is little with proper reduction scheme.