Bit Error Probability of Trellis-Coded Quadrature Amplitude Modulation Over Cross-Coupled Multidimensional Channels

Convolutionally encodedM-ary quadrature amplitude modulation (M-QAM) systems operated over multidimensional channels, for example dual-polarized radio systems, are considered in this paper. We have derived upper bounds on the average bit-error probability for 4QAM (QPSK) with conventional convolutional coding by means of a truncated union bound technique and averaging over the cross-polarization interference by means of the method of moments. By modifying this technique, we have found approximate upper bounds on the average biterror probability for bandwidth efficient trellis-coded QAM systems. This is an extension of our previous work [1] that was based on one dominating error event probability as a performance measure. Our evaluations seem to indicate that bandwidth efficient trellis-codedMQAM schemes offer much larger coding gains in an interference environment, e.g., a cross-coupled interference channel, than in a Gaussian noise channel. In general, our findings point out that optimum codes for a Gaussian channel are not optimum when applied in an interference environment. We note that a rate 1/2 convolutional code for example, with a code memory greater than two, if applied to two of the bits in each signal point representation, can be utilized with a simple decoder to greatly improve the performance of a QAM signal in interference. Also, we have introduced a new concept referred to as dualchannel polarization hopping in this paper which can improve the system performance significantly for systems with nonsymmetrical interference.     

Error Probability for Convolutional Codes with Weight Enumerating Function

The paper introduces the state reduction algorithm and accelerated state reduction algorithm are used to compute the distance weight enumerator(transfer function) T[x,y] of convolutional codes.Next use computer simulation to compare upper bound on the bit error probability on an additive white Gaussian noise (AWGN) for maximum free distance (MFD) codes of previously found and optimum distance spectrum (ODS) codes with rate 1/4,overall constraint length are 5 and 7,respectively. Finally,a method of how to search for good convolutional codes is given.     

结合Turbo码的多级编码调制研究介绍

论文作者在对已有的多级编码调制方案深入研究的基础上 ,进一步研究了Turbo码编码技术 ,并把Turbo码作为分量码结合多级编码调制方案进行了理论研究 .符合当今移动通信的大容量、高可靠性的要求 .论文的主要创新点有 ,通过理论研究 ,证明了以Turbo码为分量码的多级编码方案比以往的以分组码及卷积码为分量码的方案具有一定的优越性     

On Improving Bit Error Probability of QPSK and 4-Level Amplitude Modulation Systems by Convolutional Coding

We consider Amplitude Modulation (AM) systems, PhaseShift-Keying (PSK) and Amplitude-Phase-Keying (APK) systems in which each symbol can take 2ⁿvalues. After a systematic search of(n, n - 1)binary convolutional codes with large values of free distance and minimal number of code words at that distance, simulations have been performed with an 8-symbol modulation system (n = 3). For a bit error probability of less2 times 10^{-4}, the saving in average power signal-signal-to-noise ratio over that required for an uncoded system with the same channel symbol rate was more than 2 dB with PSK and APK, and 1.5 dB with AM.     

一种网格空时码优化的新方法

我们研究表明:在达最大分集增益前提下,网格空时码的性能不仅与差矩阵的最小行列式值有关,而且还与该最小值的出现概率有关.本文在此基础之上,提出一种基于距离谱的网格空时码优化算法,并给出了一些性能更好的网格空时码编码方案.仿真结果显示,本文给出的网格空时码比采用穷搜索算法得到的有0.3-1dB的增益.     

Error Probability and Bandwidth of Digital Modulation

The bandwidth in which 99 percent of the power is contained is presented for ASK, QASK, OQASK, PSK, FSK, and MSK. An example is given in which the bandwidth of FSK is one eighth the bandwidth of ASK and of the modulating signal. Error probability is presented for the various types of modulation with various detectors, detector filters and Butterworth receiver filters of orderN = 4orinfty. Comparisons are made between the performance and bandwidth efficiency of the various systems.     

空时格码迹准则在频选衰落信道下的证明

迹准则是当系统中发射与接收天线数之积较大时设计空时格码的准则,该准则最初是为平衰落信道而设计的。该文证明了迹准则在频选衰落信道下仍然成立,且仿真亦表明当信道为频选衰落时,迹准则意义下好码的性能优于其它码的性能。     

关于某些BCH码的不可检错误概率

本文研究了二元对称信道上，某些ＢＣＨ码的不可检错误概率。首先得到了几个重要的不等式。然后证明了纠正两个错误二进制本原ＢＣＨ码的扩展码是最佳检错码。     

关于等重码不可检错误概率的界

本文研究了二元等重码不可检错误概率(UEP)的界.首先,我们通过研究二元等重码的对偶距离分布及其性质,给出二元等重码UEP的一个新的下界,该下界改进了Fu-Kl  ve-Wei的最新结果;然后,我们指出2003年Fu-Kl  ve-Wei关于二元等重码UEP上界的某些结果有错误,我们随后给出更正后的结果,即二元等重码UEP的平均值和一个上界.     

On the Probability of Undetected Error for Linear Block Codes

The problem of computing the probability of undetected error is considered for linear block codes used for error detection. The recent literature is first reviewed and several results are extended. It is pointed out that an exact calculation can be based on either the weight distribution of a code or its dual. Using the dual code formulation, the probability of undetected error for the ensemble of all nonbinary linear block codes is derived as well as a theorem that shows why the probability of undetected error may not be a monotonic function of channel error rate for some poor codes. Several bounds on the undetected error probability are then presented. We conclude with detailed examples of binary and nonbinary codes for which exact results can be obtained. An efficient technique for measuring an unknown weight distribution is suggested and exact results are compared with experimental results.     

Effect of Intersymbol and Quadrature Channel Interference on Error Probability of 16-ary Offset Quadrature Amplitude Modulation with Sinusoidal and Rectangular Shaping

In this paper we study the effect of intersymbol and quadrature channel interference on the average error probability of 16-ary offset quadrature amplitude modulation with rectangular or sinusoidal shaping functions. We present numerical results assuming that the transmitter and receiver filters are identical Butterworth filters of orderN = 1,2,..., 6,and the decision rule is either fixed or adaptive.     

Error Analysis of Grouped Multilevel Space-Time Trellis Coding with the Combined Application of Massive MIMO and Cognitive Radio

In today’s scenario, demand for error-correcting codes with minimal error constraints for wireless communications. Multilevel coding scheme with trellis codes as component codes provides flexible data transmission rates, coding gain, diversity gain with improved spectral efficiency and low decoding complexity. This paper investigates the potential improvements by using the Multilevel coding scheme with massive Multiple-Input Multiple-Output in Cognitive Radio Networks with trellis codes as component codes. This paper discussed space-time coding with beamforming and antenna grouping according to the channel state information. Multilevel Space-time coding is based on multi-level Quadrature Amplitude Modulation signaling and beamforming to mitigate the effect of primary users for the enactment of secondary users in Cognitive Radio. The primary users provide channels dynamically to the secondary user for an unknown duration. Our transmission use Quadrature Amplitude Modulation based signals, with an adaptive grouping of antenna which weight according to the optimization, which inherently depends upon the resource allocation of the secondary user. The results show that the proposed coded system achieves Bit error rate/Symbol error rate/Frame error rate and Signal to noise ratio varies according to sources sensing time.

     

Evaluation of the Undetected Error Probability of Single Parity-Check Product Codes

In this paper, an expression for the undetected error probability(Pepsilon)of single parity-check product (SPCP) codes used for error detection over a binary symmetric channel is derived. It is shown that square SPCP codes need not obey a certain commonly used bound. Approximate expressions for the maximum(Pepsilon)and the corresponding maximizing ε are given.     

高误码率下归零Turbo码帧结构识别

现有的高斯消元法在Turbo码帧结构识别中,存在着容错性差且计算量大的缺点,直接导致后续分量编码器以及交织器识别算法无法应用.为此,提出了一种基于矩阵模型列相关性的识别方法.首先在待定帧长下构建分析矩阵,并对其前后相邻两列进行差分处理,然后建立关于差分后矩阵列重的统计量,根据码长及其整数倍处必有统计值能通过判决这一特点确定帧长.最后,通过分析正确码长下通过判决的统计值对应的相对位置关系,归纳帧起点的同步方法.仿真结果表明,本文算法在误码率高达0.1条件下,Turbo帧结构参数识别能够达到100%的识别率,与现有方法相比,本文算法计算复杂度更低且识别性能更好,可应用于认知无线电等非协作通信领域.     

极低误码率下Turbo码的性能估计

Turbo码在中低信噪比下具有接近信道容量极限的优异性能,但在误码率极低、信噪比较高下性能曲线下降平缓,并且难以进行大计算量的仿真。使用输入信息序列片段长度递增筛选法,逐步筛选出所有产生自由距码字的信息帧,从而得出Turbo码完整的自由距特性,并用来估计极低误码率下的性能,该方法有效地减小了完整枚举法的计算量,且保证了精确性。     

Rayleigh衰落信道中多级编码调制的不等错误保护

本文研究了Rayleigh衰落信道中以信道容量规则为设计准则的多级编码调制系统的不等错误保护性能的实现及其改进.在详细分析了多级编码调制的不等错误保护原理的基础上,设计了一种针对8ASK调制的非均匀信号星座.理论分析与计算机仿真均表明,非均匀信号星座的设计能够增强多级编码调制系统的不等错误保护能力,在不展宽频带的前提下有效地提高Rayleigh衰落环境下数字通信系统的传输质量.     

On the Probability of Undetected Error for the Maximum Distance Separable Codes

In this paper we investigate the performance of maximum-distance-separable codes with symbols fromGF(q)when they are used for pure error detection or for simultaneous error correction and detection over aq-input andq-output discret memoryless channel with symbol error probability ε. First we show that the probability of undetected error for an MDS code used for pure error detection is upper bounded byq^{-r}and decreases monotonically as εdecreases from(q - 1)/qto 0, whereris the number of parity-check symbols of the code. Then we show that the probability of undetected error for an MDS code used for correctingtor fewer symbol errors is upper bounded byq^{-r} Summin{i=0}max{t}(min{i} max{n})(q - 1)^{i}and decreases monotonically as ε decreases from(q - 1)/qto 0. These results show that the MDS codes are effective for both pure error detection and simultaneous error correction and detection.     

A Tightened Upper Bound on the Error Probability of Binary Convolutional Codes with Viterbi Decoding

Tighter upper bounds on the error event and the bit error probabilities, respectively, for maximum-likelihood decoding of binary convolutional codes on the binary symmetric channel are derived from upper bounds previously published by Viterbi [1]. The measured bit error rateP_bfor a constraint length 3 decoder has been plotted versus the channel transition probabilitypand shows close agreement with the improved bound on the bit error probability.