Near-optimum decoding of product codes: block turbo codes

This paper describes an iterative decoding algorithm for any product code built using linear block codes. It is based on soft-input/soft-output decoders for decoding the component codes so that near-optimum performance is obtained at each iteration. This soft-input/soft-output decoder is a Chase decoder which delivers soft outputs instead of binary decisions. The soft output of the decoder is an estimation of the log-likelihood ratio (LLR) of the binary decisions given by the Chase decoder. The theoretical justifications of this algorithm are developed and the method used for computing the soft output is fully described. The iterative decoding of product codes is also known as the block turbo code (BTC) because the concept is quite similar to turbo codes based on iterative decoding of concatenated recursive convolutional codes. The performance of different Bose-Chaudhuri-Hocquenghem (BCH)-BTCs are given for the Gaussian and the Rayleigh channel. Performance on the Gaussian channel indicates that data transmission at 0.8 dB of Shannon's limit or more than 98% (R/C>0.98) of channel capacity can be achieved with high-code-rate BTC using only four iterations. For the Rayleigh channel, the slope of the bit-error rate (BER) curve is as steep as for the Gaussian channel without using channel state information     

衰落信道下卷积码的软判决译码

本文将交织、信道输出软信息、信道特征软信息相结合,研究Rayleigh衰落信道下卷积码的Viterbi软判决译码,在利用和不利用信道状态信息(CSI)两种情况下给出软判决的支路度量计算公式和性能仿真结果,计算了卷积码的性能上界;研究了解调器输出量化门限(量化级数目、量化间距)对译码性能的影响.结果与硬判决译码及AWGN信道的相关结论进行了比较.     

A sequential soft-decision decoder for Reed-Solomon codes appliedto encoded PSK in Rayleigh-fading channels

A soft-decision stack algorithm with a variable-bias-term branch metric and accurate channel state information estimate is applied to a Reed-Solomon-encoded phase-shift keying (PSK) system in the presence of memoryless Rayleigh fading. To compensate for the variable decoding delay inherent in sequential decoding algorithms, a time-out mechanism is used by the inner decoder: if a time-out occurs before complete decoding of a given block, the decoder declares an erasure. An erasures-and-errors correction decoding algorithm is implemented at the outer decoder to recover any incorrect or incompletely decoded inner code words. Simulation results show that significant improvement over uncoded modulation can be achieved with this approach with moderate cost in decoding complexity     

空时分组编码CDMA系统的性能分析

空时分组编码 ( STBC)可有效的应用于无线系统中 ,提高系统的容量。 STBC采用最大似然译码算法 ,译码过程中需要信道信息。本文利用导频辅助的方式获得信道信息 ,分析了Rayleigh信道下随着移动台速度的变化 STBC- CDMA系统的误码率性能     

Novel Viterbi decoder VLSI implementation and its performance

An advanced, high-speed, and universal-coding-rate Viterbi decoder VLSI implementation is presented. Two novel circuit design schemes have been proposed: scarce state transition (SST) decoding and direct high-coding-rate convolutional code generation and variable-rate decoding. SST makes it possible to omit the final decision circuit and to reduce the required path memory length without degrading error probability performance. Moreover, the power consumption of the SST Viterbi decoder is significantly reduced when implemented as a CMOS device. These features overcome the speed limits of high-speed and high-coding-gain Viterbi decoder VLSIs in the rate one-half mode imposed by the thermal limitation. The other Viterbi decoding scheme makes it possible to realize a simple and variable coding-rate forward-error-correction circuit by changing only the branch metric calculation ROM tables. By employing these schemes, high-speed (25-Mb/s) and universal-coding-rate Viterbi decoder VLSIs have been developed     

快速生成QAM比特置信度软判决度量的算法

在现代通信系统中,为了保证高的信道解码增益,信道解码器均采用软输入技术。传统的软判决度量大多是基于最小欧氏距离准则生成,该文提出一种基于比特置信度快速生成QAM软判决度量的算法,通过将比特置信度引入到QAM软判决度量的计算中来减少计算的复杂性。相比基于最小欧氏距离的软判决度量生成算法,该文提出的方法在保证信道解码器性能的前提下,减少了生成软判决度量的运算量。应用于中国数字电视地面传输标准DTMB系统的仿真结果表明,该文提出的软判决度量生成算法虽然降低了计算量,但性能几乎没有任何损失,具有良好的性能和可实现性。     

一种M-FSK信号的能量度量Viterbi软译码算法性能分析

Viterbi译码算法广泛应用于无线数字通信系统,一般采用比特对数似然信息(LLR)作为译码器的输入。针对M-FSK信号,该文提出一种采用信号解调得到的M维能量信息,直接作为译码器分支度量值,并给出了相应的Viterbi译码算法。在加性高斯白噪声(AWGN)和瑞利(Rayleigh)衰落信道下对所提算法的BER性能进行了理论推导,得到了闭合表达式。通过仿真验证了理论推导的正确性,与常规Viterbi算法相比,所提算法避免了比特LLR和分支度量值的计算,降低了算法复杂度和减少了信息损失,提高了M-FSK信号软解调Viterbi译码算法的BER性能,是一种更适用于工程实现的M-FSK信号的Viterbi译码算法。     

一种基于FPGA的Viterbi译码器的研究与设计

针对通信系统中传统维特比(Viterbi)译码器结构复杂、译码延时大、资源消耗大的问题,提出了一种新的基于FPGA的Viterbi译码器设计。结合(2,1,7)卷积编码器和Viterbi译码器的工作原理,设计出译码器的核心组成模块,具体采用3比特软判决译码,用曼哈顿距离计算分支度量,32个碟型加比选子单元并行运算,完成幸存路径和幸存信息的计算。幸存路径管理模块采用Viterbi截短译码算法,回溯操作分成写数据、回溯读和译码读,以改进的流水线进行并行译码操作,译码延时和储存空间分别降低至和。     

Soft decision decoding of block codes using received signalenvelope in digital mobile radio

The codeword error rate (WER) performance of noncoherent frequency-shift keying with soft decision decoding of block codes using Chase's second algorithm (1972) is investigated in a Rayleigh fading channel. The received signal envelope is sampled and used as channel measurement information. The theoretical upper and lower bounds of the WER are derived, assuming independent Rayleigh envelope samples in a received block. When the Golay (23, 12, 7) code is used, soft decision decoding with 6-bit error correction capability (3-bit error and 3-bit erasure) requires an average signal-to-noise power ratio about 5 dB lower than that for minimum distance decoding with 3-bit error correction to obtain a WER=10^-3. The effects of bit interleaving on the WER performance when fading envelope variation is slow compared to the bit rate are investigated through computer simulations     

Quantization loss in convolutional decoding

The loss in quantizing coded symbols in the additive white Gaussian noise (AWGN) channel with binary phase-shift keying (BPSK) or quadrature phase-shift keying (QPSK) modulation is discussed. A quantization scheme and branch metric calculation method are presented. For the uniformly quantized AWGN channel, cutoff rate is used to determine the step size and the smallest number of quantization bits needed for a given bit-signal-to-noise ratio (E_b/N₀) loss. A nine-level quantizer is presented, along with 3-b branch metrics for a rate-1/2 code, which causes an E_b/N₀ loss of only 0.14 dB. These results also apply to soft-decision decoding of block codes. A tight upper bound is derived for the range of path metrics in a Viterbi decoder. The calculations are verified by simulations of several convolutional codes, including the memory-14, rate-1/4 or -1/6 codes used by the big Viterbi decoders at JPL     

Modification of branch metric calculation to improve iterative SOVA decoding of turbo codes

It is known that the performance of a SOVA (soft output Viterbi algorithm) turbo decoder can be improved, as the extrinsic information that is produced at its output is over-optimistic. A new parameter associated with the branch metrics calculation in the standard Viterbi algorithm is introduced that affects the turbo code performance. Different parameter values show a simulation improvement in the AWGN channel as well as in an uncorrelated Rayleigh fading channel. By choosing the best value of this parameter, a coding gain improvement of 0.25 dB at BER of 10/sup -5/ is achieved compared to existing schemes.     

Channel coding for satellite mobile channels

The deployment of channel coding and interleaving to enhance the bit-error performance of a satellite mobile radio channel is addressed for speech and data transmissions. Different convolutional codes (CC) using Viterbi decoding with soft decision are examined with inter-block interleaving. Reed-Solomon (RS) codes with Berlekamp-Massey hard decision decoding or soft decision trellis decoding combined with block interleaving are also investigated. A concatenated arrangement employing RS and CC coding as the outer and inner coders, respectively, is used for transmissions via minimum shift keying (MSK) over Gaussian and Rayleigh fading channels. For an interblock interleaving period of 2880 bits, a concatenated arrangement of an RS(48,36). over the Galois field GF(256) and punctured PCC(3,1,7) yielding an overall coding rate of 1/2, provides a coding gain of 42dB for a BER of 10^?6, and an uncorrectable error detection probability of 1–10^?9.     

A coded 16 QAM scheme for fast fading mobile radio channels

An adaptive Viterbi algorithm, derived from a dynamic estimate of the fading channel is used for the decoding of a convolutional coded 16 QAM system in a mobile environment. The estimates are obtained by a sequence of known pilot symbols embedded in the data stream, and perform compensation for Rayleigh fading. The likelihood criterion in the Viterbi decoder is also modified by these channel estimates through a metric weighting function. We demonstrate through computer simulations, that our new technique achieves a BER improvement of 7-10 dB at P_e =10^-3 in a fast flat Rayleigh fading environment compared to an uncoded system. The BER performance of our new technique in a co-channel interference (CCI) controlled environment is also studied, and the results show that it may achieve a 40% to 85% improvement in capacity over the standard modem scheme for the new US digital cellular system, π/4-QPSK     

Forward Error Correction Coding for Fading Compensation in Mobile Satellite Channels

Fading in mobile satellite communications severely degrades the performance of data transmission. The channel is modeled with nonfrequency selective Rice and Rayleigh fading. Also, stored channel simulation is used for hardware data transmission. FEC coding with Viterbi decoding of convolutional codes, and Berlekamp-Massey decoding of Reed-Solomon codes, are used to compensate for the fading. In addition to interleaving, channel state and erasure information improve the performance of the decoder. The BER after decoding is calculated for specific codes on several channels and for different transmission schemes. Using very simple channel state and erasure information gives 2-7 dB additional coding gain. These gains have been verified by hardware data transmission on synthetic fading channels and stored mobile satellite channels.     

1000 BASE-T收发器中的Viterbi译码算法研究

采用4维8状态网格编码和Viterbi译码相结合的方法，理论上可以获得6dB的编码增益，用于补偿采用PAM-5编码所带来的噪声容限损失。文章给出了针对4维8状态网格编码的Viterbi译码算法的译码过程，并就译码深度、量化精度和溢出处理方法对译码器性能的影响进行了算法仿真，确定出适合1000 BASE-T收发器应用的译码器参数。     

Single carrier digital terrestrial television broadcasting

A transmission system for digital terrestrial television broadcasting has been designed. This system is based on the European cable system but uses stronger error correction and better equalization. The stronger error correction is a concatenation of Reed Solomon coding RS [204,188,17] and convolutional coding with R_conv=1/2, 2/3, 3/4, 5/6 and 7/8. The algorithm which is used for convolutional decoding is the Viterbi algorithm. To provide the Viterbi decoder with soft decision information, every symbol bit will be expanded with two soft decision (reliability) bits. The modulation scheme of the terrestrial transmission system is 64-QAM square root raised cosine filtered with a roll off factor α=0.15. The mapping of the symbols into the 64-QAM constellation is a Gray-mapping over the complete I,Q-plane. In this paper the performances of the terrestrial transmission system are simulated and analyzed     

一种基于滑窗回溯多标准Viterbi译码器

为满足当前通信系统中存在的多种通信标准要求,提出了一种基于滑窗回溯的多标准Viterbi译码器。与其他Viterbi译码器相比,该译码器在支持任意长度序列译码的基础上,实现了1/2、1/3和1/4三种不同码率的配置,并适配5~9五种可变约束长度。此外,该译码器还具有软判决和硬判决两种判决模式,其中软判决采用8 bit有符号数量化。在对路径度量防溢出及幸存路径管理等模块进行优化后,该译码器能够在不显著增加延迟的前提下,具有更优异的工作性能。实验结果表明,该译码器可以根据设置的参数适用多种通信标准,并得到更好的误码性能。     

Near-optimal decoding for coded and power-controlled DS-CDMA downlink

We first present the traditional decoding approach that employs the common pilot-channel-based maximal ratio combining and the Viterbi or iterative decoding cannot achieve the optimal error-rate performance for downlink direct-sequence code-division multiple-access (CDMA) signals when a fast power control technique is applied together with a convolutional or turbo coding. Then, as an efficient method to realize a nearly optimal decoding, we propose a branch metric power readjustment (BMPR) technique, where the downlink power control command generated by the mobile station is used not only to adjust the base station power in the transmitter side, but also to readjust the decoder input branch metric power in the receiver side. Numerical results show that the BMPR technique applied to the IMT-2000 wideband-CDMA system can improve the transmit power utilization by up to 0.4 dB for the block-error rate of 10/sup -2/.     

Performance analysis of stack decoding on block coded modulation schemes using tree diagram

The channel encoder adds redundancy in a structured way to provide error control capability. Modulator converts the symbol sequences from the channel encoder into waveforms which are then transmitted over the channel. Usually channel coder and modulator are implemented independently one after the other. But in a band limited channel better coding gains without sacrificing signal power are achieved when coding is combined with modulation. Block Coded Modulation (BCM) is such a scheme that results from the combination of linear block codes and modulation. In this paper we are proposing a stack decoding of rate 2/3 and rate 1/2 BCM schemes using tree structure and performance is compared with the Viterbi decoding that uses trellis representation. Simulation result shows that at reasonable bit error rate stack decoder performance is just 0.2 to 0.5 dB inferior to that of Viterbi decoding. Since stack decoding is a near optimum decoding scheme and whose decoding procedure is adaptable to noise level, we can consider this method in place of Viterbi decoding which is optimum and its decoding complexity grows exponentially with large code lengths.     

Systolic array processing of the Viterbi algorithm

Results on efficient forms of decoding convolutional codes based on the Viterbi algorithm by using systolic arrays are presented. Various properties of convolutional codes are discussed. A technique called strongly connected trellis decoding is introduced to increase the efficient utilization of all the systolic array processors. Issues dealing with the composite branch metric generation, survivor updating, overall system architecture, throughput rate, and computational overhead ratio are also investigated. The scheme is applicable to both hard and soft decoding of any rate b/n convolutional code. It is shown that as the length of the code becomes large, the systolic Viterbi decoder maintains a regular and general interconnection structure as well as moderate throughput rate gain over the sequential Viterbi decoder