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.

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.

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.

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.

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.

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.

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.

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. .

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 be suitable for WDM optical transmission systems is proposed. The simulation results show that this new concatenated code, compared with the RS(255,239)+CSOC(k0/n0=6/7, J=8) code in ITU-T G.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 more than that of RS(255,239)+CSOC(k0/n0 =6/7, J=8) code and BCH(3 860,3 824)+BCH(2 040,1 930) code in ITU-T G.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.

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.

A Novel Concatenated Chaotic Communication System

A strategy for a novel concatenated chaotic communication system is presented. The transmitter system comprises chaotic turbo encoder and logistic CSK block in a serially concatenated form. Chaotic turbo code is capable of reducing bit error rate (BER) of the chaotic system in the AWGN channel. Through the chaotic turbo encoder, the coded sequence, which has quasi-chaotic properties, will be transmitted into the logistic CSK block. Having a very sensitive dependence on initial conditions of the map, the logistic CSK block can also be taken as the chaotic authentication method. The receiver, which has logistic demodulation block and chaotic decoder, is a linear asymptotic approximation to the inverse of the transmitter system. A chaotic iterative soft-decision decoding algorithm is also developed based on conventional maximum A posteriori decoding algorithm. At last, a two-step authentication method of this chaotic system is also presented.

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。

RS-Turbo级联码的性能仿真及其在图像传输中的应用

RS码是一种纠突发错误能力很强的信道编码方式,T urbo码是一种巧妙的将卷积码和随机交织器结合在一起,同时采用软输出并通过不断迭代的方法译码来逼近最大似然编码的一种新的纠错能力很强的信道编码方式;本文分析了两种编码方式并研究了将二者级联后RS T urbo的性能,给出了将其级联码在图像传输中的应用。

RS-CR与RS-Turbo两类级联码的结构与性能分析

如果采用随机交织器和迭代的最大后验概率译码算法,Turbo码的译码性能接近Shannon限。但是当误比特率(BER)≤10-5时,性能曲线下降缓慢,趋近于水平线,影响了Turbo码的推广与应用。级联RS码能够有效地改善这一现象,但是RS Turbo级联码结构复杂,译码时延大。因此,本文基于交错与级联的思想,提出了一种新型的前向纠错码,即RS CR码(RS 复转码),设计构造了该码的编译码算法。RS码和复数旋转码同时对信息元进行编码,级联后新产生的二维前向纠错码,编码时间短,译码速度快,纠错能力可调,尤其适用于自适应的差错控制系统。

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。

RS-Turbo码在室内OFDM可见光通信系统中的仿真

针对室内OFDM可见光通信系统受多径效应干扰易出现误码的问题,文中提出一种在系统中加入级联码以纠正误码的方法。该方法依据RS码的强纠错能力和Turbo码的近香农限特性,将RS码和Turbo码串联组成RS-Turbo级联码。RS-Turbo码用在OFDM调制之前,作为系统的信道编码方式以纠正误码。文中通过MATLAB搭建室内OFDM可见光通信系统模型,仿真比较RS码、Turbo码和RS-Turbo码对系统抗误码性能的影响。仿真结果表明,在多径效应干扰下,使用RS-Turbo码的系统抗误码性能最佳,能有效降低误码率。

A Theoretical Method for Estimating Performance of Reed-Solomon Codes Concatenated with Orthogonal Space-Time Block Codes

Based on the studies of Reed-Solomon codes and orthogonalspace-time block codes over Rayleigh fading channel, a theoreticalmethod for estimating performance of Reed-Solomon codes concatenatedwith orthogonal space- time block codes is presented in this paper.And an upper bound of the bit error rate is also obtained. It isshown through computer simulations that the signal-to-noise ratioreduces about 15 dB or more after orthogonal space-time block codesare concatenate with Reed-Solomon(15,6)codes over Rayleigh fadingchannel, when the bit error rate is 10^-4.

非二进制RS-Turbo级联码性能研究

介绍了非二进制Turbo码的编码器结构,详细分析了逐符号对数MAP译码算法。在此基础上,设计了一种RS-Turbo级联码方案,该方案包括一个RS(255,239,8)外码和一个非二进制Turbo内码。仿真结果表明,与单纯使用非二进制Turbo码相比,本文提出的级联方案可明显改善高信噪比情况下的BER性能,同时可降低迭代次数。另外,级联RS码可为Turbo迭代译码提供简单可行的停止准则。