Combinatorial analysis of the minimum distance of turbo codes

In this paper, new upper bounds on the maximum attainable minimum Hamming distance of turbo codes with arbitrary-including the best-interleavers are established using a combinatorial approach. These upper bounds depend on the interleaver length, the code rate, and the scramblers employed in the encoder. Examples of the new bounds for particular turbo codes are given and discussed. The new bounds are tighter than all existing ones and prove that the minimum Hamming distance of turbo codes cannot asymptotically grow at a rate more than the third root of the codeword length     

Interleaver design for turbo codes

The performance of a turbo code with short block length depends critically on the interleaver design. There are two major criteria in the design of an interleaver: the distance spectrum of the code and the correlation between the information input data and the soft output of each decoder corresponding to its parity bits. This paper describes a new interleaver design for turbo codes with short block length based on these two criteria. A deterministic interleaver suitable for turbo codes is also described. Simulation results compare the new interleaver design to different existing interleavers     

Exploiting UEP in QAM-based BICM: interleaver and code design

In this paper we formally analyze the interleaver and code design for QAM-based BICM transmissions using the binary reflected Gray code. We develop analytical bounds on the bit error rate and we use them to predict the performance of BICM when unequal error protection (UEP) is introduced by the constellation labeling. Based on these bounds the optimum design of interleaver and code is found, and numerical results for representative configurations are presented. When the new design is used, the improvements may reach 2 dB, and they are obtained without any increase on the transceiver?s complexity. We also introduce the concept of generalized optimum distance spectrum convolutional codes, which are the optimum codes for QAM-based BICM transmissions.     

Serial concatenation of interleaved codes: performance analysis,design, and iterative decoding

A serially concatenated code with interleaver consists of the cascade of an outer encoder, an interleaver permuting the outer codewords bits, and an inner encoder whose input words are the permuted outer codewords. The construction can be generalized to h cascaded encoders separated by h-1 interleavers. We obtain upper bounds to the average maximum-likelihood bit error probability of serially concatenated block and convolutional coding schemes. Then, we derive design guidelines for the outer and inner encoders that maximize the interleaver gain and the asymptotic slope of the error probability curves. Finally, we propose a new, low-complexity iterative decoding algorithm. Throughout the paper, extensive comparisons with parallel concatenated convolutional codes known as “turbo codes” are performed, showing that the new scheme can offer superior performance     

Turbo码的优选扩散交织器设计

该文提出了Turbo码交织器的一种新的设计方法,适用于任意长度的交织设计,称为优选扩散交织,文中阐述了它的设计原则与步骤,以及对16状态Turbo码交织器的设计分析,并对其性能进行了仿真。     

一种具有低相关特性的分块交织器的设计

Ｔｕｒｂｏｃｏｄｅｓ是近年信道编码理论研究的热点课题。交织器的设计问题是Ｔｕｒｂｏｃｏｄｅｓ研究中的主要问题之一。本文结合Ｔｕｒｂｏｃｏｄｅｓ在个人通信中的应用问题，对分块交织方法进行了研究，给出了一种新的交织器的设计方案，理论分析和计算机仿真证实了此方案在实现上和相关性上都具有良好的性能。同时，本文从理论上解释了在交织长度很大时，交织器的选择对Ｔｕｒｂｏｃｏｄｅｓ译码性能几乎没有影响的原因。     

Improved upper bounds on the ML decoding error probability ofparallel and serial concatenated turbo codes via their ensemble distancespectrum

The ensemble performance of parallel and serial concatenated turbo codes is considered, where the ensemble is generated by a uniform choice of the interleaver and of the component codes taken from the set of time-varying recursive systematic convolutional codes. Following the derivation of the input-output weight enumeration functions of the ensembles of random parallel and serial concatenated turbo codes, the tangential sphere upper bound is employed to provide improved upper bounds on the block and bit error probabilities of these ensembles of codes for the binary-input additive white Gaussian noise (AWGN) channel, based on coherent detection of equi-energy antipodal signals and maximum-likelihood decoding. The influence of the interleaver length and the memory length of the component codes is investigated. The improved bounding technique proposed here is compared to the conventional union bound and to a alternative bounding technique by Duman and Salehi (1998) which incorporates modified Gallager bounds. The advantage of the derived bounds is demonstrated for a variety of parallel and serial concatenated coding schemes with either fixed or random recursive systematic convolutional component codes, and it is especially pronounced in the region exceeding the cutoff rate, where the performance of turbo codes is most appealing. These upper bounds are also compared to simulation results of the iterative decoding algorithm     

无线光通信编码调制中交织器设计研究

交织设计是无线光比特交织编码调制通信系统抗衰落能力的一个影响因素。在构建系统模型基础上,给出了交织器优化设计的基本原则及其数学模型,对伪随机交织、S-随机交织和改进黄金分割交织的距离特性及其在弱湍流条件下的性能进行了仿真分析。结果表明,交织可有效提高编码调制的差错性能,对于给定交织方式,增加交织长度可获得更好改善,当交...     

Analysis, design, and iterative decoding of double seriallyconcatenated codes with interleavers

A double serially concatenated code with two interleavers consists of the cascade of an outer encoder, an interleaver permuting the outer codeword bits, a middle encoder, another interleaver permuting the middle codeword bits, and an inner encoder whose input words are the permuted middle codewords. The construction can be generalized to h cascaded encoders separated by h-1 interleavers, where h>3. We obtain upper bounds to the average maximum likelihood bit-error probability of double serially concatenated block and convolutional coding schemes. Then, we derive design guidelines for the outer, middle, and inner codes that maximize the interleaver gain and the asymptotic slope of the error probability curves. Finally, we propose a low-complexity iterative decoding algorithm. Comparisons with parallel concatenated convolutional codes, known as “turbo codes”, and with the proposed serially concatenated convolutional codes are also presented, showing that in some cases, the new schemes offer better performance     

Comparison of iterative decoder performance with union bounds for short frame turbo codes

We consider short frame turbo codes, suitable for delay-sensitive services such as conversational speech, or for encoding single ATM cells. We compare the uniform interleaver bound of Benedetto and Montorsi, and a union bound obtained by estimating the weight distribution due to the actual pseudo-random interleaver, with the simulated BER using an iterative decoder. We show that the uniform interleaver bound is significantly pessimistic at high SNR, where the random interleaver union bound is quite close. However, at lower SNR the ber exceeds the union bound, showing that it does not achieve ml decoding. We also consider half rate turbo codes formed by puncturing various proportions of the data and parity sequences, and adapt the uniform interleaver bounds for these codes. We show that while the union bounds predict better performance for data-punctured codes, in practice they perform better only at high snr and for limited proportions of data puncturing.     

On error bounds and turbo-codes

Turbo-codes have been hailed as the ultimate step toward achieving the capacity limit Shannon established some 50 years ago. We look at the performance of turbo-codes with respect to various information theoretic error bounds. This comparison suggests that, if (block, or) frame error rates are considered, careful interleaver design is necessary to ensure an error performance within a fraction of a decibel of the theoretical limit for large block sizes, while random interleavers perform well for block sizes smaller than about 2 K. If the bit error performance is considered, interleaver design seems to have only a minor effect, and the codes perform close to the limit for all block sizes considered     

Combined turbo codes and interleaver design

The impact of the distance spectrum and interleaver structure on the bit error probability of turbo codes is considered. A new turbo code design method for Gaussian channels is presented. The proposed method combines a search for good component codes with interleaver design. The optimal distance spectrum is used as the design criterion to construct good turbo component codes at low signal-to-noise ratios (SNRs). In addition, an interleaver design method is proposed. This design improves the code performance at high SNR. Search for good component codes at low SNR is combined with a code matched interleaver design. This results in new turbo codes with a superior error performance relative to the best known codes at both low and high SNR. The performance is verified by both analysis and simulation     

A new block interleaver and noniterative decision feedback decodingenhance performance of IS-95 CDMA uplink or similar M-ary system

This paper investigates the combination of a new block interleaver design and a noniterative decision feedback receiver/decoder for IS-95 code-division multiple-access (CDMA) uplink in additive white Gaussian noise and a Rayleigh fading multipath environment. The new interleaver design yields better performance than the currently used IS-95 interleaver, with E_b/N₀ improvements of 0.27 to 0.76 dB. At the same time, the new interleaver design improves the effectiveness of a noniterative decision feedback receiver/decoder herein presented. The performance of the proposed design is measured via computer simulation for both coherent and noncoherent detection. A mathematical justification is also given to show the reason why the performance is improved using the proposed design. Based on these results, it is concluded that the use of the new interleaver design with noniterative decision feedback decoding can improve the quality of service and/or capacity of a modified cellular IS-95 system or a system using a similar concatenation of convolutional coding, interleaving, and orthogonal Walsh modulation. Although the approach presented is applied to the uplink of IS-95, it can also be applied to similar M-ary systems     

Prunable Collision Free Random Interleaver Design

In this article we introduce a new collision free prunable random interleaver. The suggested interleaver is a joint structure involving rectangular and S-random interleaver. It comprises a general model for all kind of collision free prunable random interleavers. In addition, it can be designed for any number of parallel processors and any length of information sequence vector and can be considered also as a template for collision free prunable interleavers. The proposed interleaver can be used with all kind of turbo-like codes. The performance of the proposed interleaver is measured with parallel decodable serially concatenated convolutional codes (PDSCCCs) and compared to the PDSCCCs?? performance with collision full S-random interleaver.     

低信噪比下随机交织器识别

针对Turbo码随机交织器参数识别问题,充分利用信道截获数据的软判决信息,提出了一种基于对数符合度的交织映射关系识别算法。该算法从计算总的编码方程成立概率出发,定义了能很好衡量概率大小的对数符合度概念,极大地简化了计算复杂度,使得计算量仅与截获码块数目和交织长度的平方有关,计算方式仅为大小比较与符号提取;再利用正确交织位置能够使总的编码方程成立的概率达到最大这一特性,依次实现各个位置的交织关系的识别。与现有算法相比,所提算法识别性能稍差,但计算复杂度更低。仿真结果表明,在信噪比为0 dB、交织长度为200时,仅需要截获码块数目为500,其正确识别率就能达到100%。     

Turbo码有效自由距离d2上限的证明

Turbo码是一种新的纠错码,具有十分突出的纠错能力。Turbo码编码器由两个或两个以上的分量码编码器和交织器并行级联而成。S.Benedetto和G.Montersi(1996)中提出了设计Turbo码的新参数有效自由距离d2(Effective Free Distance)。D.Divsalar和R.J.McEliece(1996)给出了有效自由距离的两个上限,但未给出证明。本文从理论上对d2的两个上限进行证明。     

短帧Turbo码交织器的设计

本文给出一种分组交织器与最佳周期交织器相结合对数据进行交织的方案，可应用在短帧Turbo码交织器的设计中。通过对这种交织器的性能进行计算机模拟，本文得出在短帧Turbo码中该交织器的性能优于伪随机交织器和一般的分组交织器的性能。     

Decoding of the IS-95A uplink code

This letter considers the decoding of the IS-95(A) uplink code in an effort to assess its best achievable performance. Union bounds on the bit error probability for the IS-95(A) indicate that the interleaver affects significantly system performance. Computer simulation results for iterative decoding show that performance gains in the order of 0.6 dB can be obtained when the sequential interleaver is replaced by a pseudorandom interleaver of same size. Improving iterative decoding for this code while maintaining the original sequential interleaver, results only in minor performance gains over published results     

A novel all-fiber optical interleaver with flat-top passband

An all-fiber optical interleaver with almost rectangular wavelength response is developed by using a new configuration. The device consists of a 2/spl times/2 and a 3/spl times/3 directional fiber coupler. Based on the digital approximation method of Fourier series, the relationships among the splitting ratios of the couplers, the length difference of interference arms, and the intensity transmission spectrum are analyzed. The results indicate that a uniform flattop spectral response can be obtained by the configuration when the length difference of interference arms and the coupling coefficient of the couplers, with some certain values, are given. The passband and stopband of optical interleaver are improved remarkably. The coupling ratio of couplers and the proportion of the length differences can be controlled accurately in the course of fabricating the interleaver. A novel structure of an interleaver is fabricated by using the fused biconical taper technics in experiment. The experimental results are in good agreement with the analytical ones.