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     

Variable-bit-rate speech transmission using punctured convolutionalcodes

Rate (n-1)/n punctured convolutional codes are very effective in conjunction with embedded differential pulse code modulation (EDPCM) in variable-bit-rate speech transmission. The authors investigate the performance of this variable-bit-rate EDPCM system in terms of probability of bit error and audio signal-to-noise ratio (SNR) versus channel SNR in an additive white Gaussian noise and Rayleigh fading channel using soft-decision decoding for specific sets of code generators of punctured convolutional codes. The results show that different sets of code generators affect the performance in terms of both the probability of bit error and the audio SNR. Improvements were obtained in the cases of Gaussian nonfading and Rayleigh fading channels using soft-decision decoding     

Coded modulation for a coherent DS-CDMA system employing an MMSE receiver in a fading channel

Previous results have shown that high rate codes tend to yield a lower average bit-error rate than low rate codes when employing a minimum mean-square error (MMSE) receiver for a direct-sequence code-division multiple-access (CDMA) system in either an additive white Gaussian noise channel or a flat Rayleigh fading channel. we consider the use of larger signal constellations with both trellis-coded modulation and bit-interleaved coded modulation (BICM) to determine if further gains can be achieved in either the Rayleigh or Ricean fading channel. The average bit-error probability is derived for both coding schemes using the general Ricean fading channel model, based upon the common assumptions of infinite interleaving, perfect channel state information, and optimal MMSE receiver coefficients. New bounds are presented for BICM with 8-PSK and 16-QAM symbols, which take advantage of the symmetries inherent in the signal constellations with Gray code mapping. In addition, simulation results are presented which show the important effect a finite interleaving delay constraint has on the comparison of various codes. The results show that there are cases when coded modulation does yield a significant improvement in performance for a CDMA system using an MMSE receiver, compared to standard convolutional coding. However, the best coding strategy depends upon several factors, including the nature of the fading process (Rayleigh or Ricean), the operating signal-to-noise ratio, the interleaving delay constraint, the time-variability of the channel, the number of users in the system, and the severity of the near-far problem.     

Iterative decoding of space-time differentially coded unitary matrix modulation

Noncoherent communication over the Rayleigh flat fading channel with multiple transmit and receive antennas is investigated. Codes achieving bit error rate (BER) lower than 10/sup -4/ at bit energy over the noise spectral density ratio (E/sub b//N/sub 0/) of 0.8 to 2.8 dB from the capacity limit were found with coding rates of 0.5 to 2.25 bits per channel use. The codes are serial concatenation of a turbo code and a unitary matrix differential modulation code. The receiver is based on a high-performance joint iterative decoding of the turbo code and the modulation code. Information-theoretic arguments are harnessed to form guidelines for code design and to evaluate performance of the iterative decoder.     

Block-coded modulation and multiple block-coded modulation withViterbi decoding for fading channels

This paper describes how block-coded modulation (BCM) and multiple BCM (MBCM) with Viterbi decoding can be designed for use in Rayleigh fading and severe Rician fading channels. New codes are developed by modifying known codes to increase the minimum symbol distance, which is one of the distances that has a strong effect on the bit error rate (BER) performance under fading channels. Combined with anti-fading techniques such as fading compensation, interleaving, and branch weighting, the new codes significantly improve BER performance. Computer simulations were used to confirm the code performance     

An Adaptive Hybrid ARQ Scheme

A hybrid ARQ in which the transmitter adaptively selects an FEC code according to the channel condition is presented and analyzed. The code is selected according to the past transmissions and acknowledgements by an algorithm which is a generalization of that in [1]. The throughput is obtained as a function of the frame error rate for a general system employing the adaptive hybrid ARQ with acknowledgements that arrive instantly on an error-free return channel. The throughput is obtained as a function of the signal-to-noise ratio for an example quad rate system employing convolutional codes with non-coherent frequency shift keying over the uncorrelated Rayleigh fading channel. This allows the best choice for the parameters of the algorithm to be made. In the case that the channel bit errors are independent, the generalization offers performance improvement of less than 10% over that in [1]. But when the channel errors are bursty, as in the case of Rayleigh fading with finite bit interleaving, the generalization offers throughput improvement as high as 24%. We go on to consider incorporating code combining with the adaptive scheme to form an adaptive memory hybrid ARQ. Simulation of a system using complementary punctured convolutional codes with 4 code rates shows that 2-level code combining can extend the adaptive scheme's useful throughput into the low SNR region by approximately 4 dB.     

Probabilistic construction of large constraint length trellis codesfor sequential decoding

Probabilistic algorithms are given for constructing good large constraint length trellis codes for use with sequential decoding that can achieve the channel cutoff rate bound at a bit error rate (BER) of 10^-5-10^-6. The algorithms are motivated by the random coding principle that an arbitrary selection of code symbols will produce a good code with high probability. One algorithm begins by choosing a relatively small set of codes randomly. The error performance of each of these codes is evaluated using sequential decoding and the code with the best performance among the chosen set is retained. Another algorithm treats the code construction as a combinatorial optimization problem and uses simulated annealing to direct the code search. Trellis codes for 8 PSK and 16 QAM constellations with constraint lengths v up to 20 are obtained. Simulation results with sequential decoding show that these codes reach the channel cutoff rate bound at a BER of 10^-5-10^-6 and achieve 5.0-6.35 dB real coding gains over uncoded systems with the same spectral efficiency and up to 2.0 dB real coding gains over 64 state trellis codes using Viterbi decoding     

Multistage recursive interleaver for turbo codes in DS-CDMA mobileradio

A multistage recursive block interleaver (MIL) is proposed for the turbo code internal interleaver. Unlike conventional block interleavers, the MIL repeats permutations of rows and columns in a recursive manner until reaching the final interleaving length. The bit error rate (BER) and frame error rate (FER) performance with turbo coding and MIL under frequency-selective Rayleigh fading are evaluated by computer simulation for direct-sequence code-division multiple-access mobile radio. The performance of rate-1/3 turbo codes with MIL is compared with pseudorandom and S-random interleavers assuming a spreading chip rate of 4.096 Mcps and an information bit rate of 32 kbps. When the interleaving length is 3068 bits, turbo coding with MIL outperforms the pseudorandom interleaver by 0.4 dB at an average BER of 10^-6 on a fading channel using the ITU-R defined Vehicular-B power-delay profile with the maximum Doppler frequency of f_D = 80 Hz. The results also show that turbo coding with MIL provides superior performance to convolutional and Reed-Solomon concatenated coding; the gain over concatenated coding is as much as 0.6 dB     

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

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Performance of phase-invariant trellis coding for differentially-encoded coherent M-PSK signals on Rayleigh fading channels

Rate(n-1)/n phase-invariant trellis coding with unquantised maximum-likelihood Viterbi decoding for differentially-encoded coherent M-ary (M-2/sup n/) PSK signals on Rayleigh fading channels is considered. The simulated bit error probability performance of the trellis-coded modulation is presented for four- and eight-state linear and nonlinear codes for constraint lengths 3 and 4, respectively, with coding gains of at least 2.5 dB at a bit error rate of 10/sup -3/.<>     

Combined MMSE interference suppression and turbo coding for acoherent DS-CDMA system

The performance of a turbo-coded code division multiaccess system with a minimum mean-square error (MMSE) receiver for interference suppression is analyzed on a Rayleigh fading channel. In order to accurately estimate the performance of the turbo coding, two improvements are proposed on the conventional union bounds: the information of the minimum distance of a particular turbo interleaver is used to modify the average weight spectra, and the tangential bound is extended to the Rayleigh fading channel. Theoretical results are derived based on the optimum tap weights of the MMSE receiver and maximum-likelihood decoding. Simulation results incorporating iterative decoding, RLS adaptation, and the effects of finite interleaving are also presented. The results show that in the majority of the scenarios that we are concerned with, the MMSE receiver with a rate-1/2 turbo code will outperform a rate-1/4 turbo code. They also show that, for a bit error rate lower than 10^-3, the capacity of the system is increased by using turbo codes over convolutional codes, even with small block sizes     

Rice衰落下RS码级联空时分组码系统的性能分析

从理论上给出一种Rice衰落条件下Reed-Solomon码级联空时分组码系统的差错性能分析方法,并推导给出级联码误比特率上界的数学表达式。理论分析和仿真结果表明,随着信噪比的增加,级联码系统的性能曲线迅速变好,获得了很高的编码增益。在误比特率为10-4时,与Reed-Solomon码的级联可以使衰落条件下空时分组码的性能提高大约5 dB。     

Multilevel trellis coded modulations for the Rayleigh fadingchannel

The authors present coded 8-phase-shift-keyed (8-PSK) modulations for the Rayleigh fading channel. The schemes are based on multilevel trellis-coded-modulation constructions and utilize maximum free Hamming distance binary convolutional codes as building blocks. A suboptimal multistage decoder that utilizes interstage interleaving and iterative decoding is proposed and evaluated. Examples are constructed to show that the proposed schemes outperform the best modified codes of the Ungerboeck type due to significantly higher implicit time diversity, yielding seven branches of built-in time diversity, whereas the Ungerboeck code yields four branches of time diversity for a 64-state system. The transmission delay is higher, however. The new schemes can provide three levels of unequal error protection when 8-PSK or 8-differential-phase-shift-keying (8-DPSK) modulations are used. They provide 10-14-dB channel signal-to-noise ratio gain over uncoded 4-DPSK at a bit error rate of 10^-3 for a modest decoding complexity     

一种面向物联网的轻量级增强型长距离物理层设计方法

为了提高LoRa在衰落信道下的误码率性能,该文设计了一种轻量级的增强型长距离(EnLoRa)物理层。首先,采用循环码移位键控(CCSK)作为纠错码,级联对角矩阵交织和啁啾扩频(CSS)调制技术,构造了一种新的比特交织编码调制(BICM)结构。然后,基于该结构,提出了一种基于比特对数似然比信息的软CSS解调和软译码算法,并将译码输出后的外信息作为先验信息反馈至解调模块,进行迭代译码。仿真结果表明,与相同码率的LoRa系统对比,EnLoRa系统在高斯信道下的编码增益提高了0.8 dB,在瑞利信道下的编码增益提高了7 dB。在此基础之上,通过多次迭代译码,还可以获得最大2.5 dB的额外收益。时间复杂度增加不到10%,空间复杂度增幅可忽略不计。该方法可望进一步降低物联网节点的功耗,在室内、市区和工业等复杂多径场景具有较大的应用价值。     

Ordered statistics decoding of linear block codes on frequencynonselective multipath channels

This paper investigates the performance of ordered statistics decoding (OSD) of linear block codes with binary differential phase-shift-keying (2DPSK) transmission on frequency nonselective multipath channels. First, the wireless channel is modeled as a frequency nonselective, slow fading environment without intersymbol interference. Second, block interleaving is embedded to decorrelate the successive received symbols so that the performance of OSD, designed essentially for memoryless channels, is retained. Third, we derive the log-likelihood ratio of received symbols based on 2DPSK modulation. Fourth, we derive the statistics of received symbols and the statistics of received symbols after ordering. Further, we analyze the system error performance for sufficient degree of interleaving. Specifically, we derive the asymptotic bit error rate (BER) of OSD at high SNRs using the first-order approximation, finally, we conduct experiments at various channel characteristics and interleaving degrees for (128, 61, 22) extended BCH code and (24, 12, 8) extended Golay code. Results show that the error performance improves tremendously with increased interleaving degree     

改进交织的单层极化码高阶编码调制系统

极化码作为一种新型编码方式,被采纳为5G通信中的短码方案。本文将极化码应用到比特交织编码调制（Bit-Interleaved Coded Modulation,BICM）系统,优化交织器的设计,提出了一种新型交织算法。相比于现有的交织算法,新型交织算法的提出是基于比特信道可靠性衡量参数,将高可靠性的比特信道与低可靠性的比特信道交错设计,按照高可靠性信道对低可靠性信道辅助译码的方式,提高极化码的纠错性能。由于新型交织算法只存在于比特信道可靠度参数的简单排序,在复杂度上没有明显增加。仿真结果表明:新型交织算法具有优异的性能,当误码率为10-5,码长为256时,采用新型交织算法的极化码BICM系统与LDPC码的BICM系统相比大约有1.51 dB的增益。      

SVD iterative detection of turbo-coded multiantenna unitary differential modulation

A new suboptimal demodulator based on a singular value decomposition for estimation of unitary matrices is introduced. Noncoherent communication over the Rayleigh flat fading channel with multiple transmit and receive antennas, where no channel state information is available at the receiver is investigated. Codes achieving bit-error rate (BER) lower than 10/sup -4/ at bit energy over the noise spectral density ratio (E/sub b//N/sub 0/) of 1.6-1.9 dB from code restricted capacity limit were found. At higher data rates, computation of code restricted capacity is impractical. Therefore, the mutual information upper bound of the capacity attaining isotropically random unitary transmit matrices was used. The codes achieve BER lower than 10/sup -4/ at E/sub b//N/sub 0/ of 3.2-6 dB from this bound, with coding rates of 1.125-5.06 bits per channel use, and different modulation decoding complexities. The codes comprise a serial concatenation of turbo code and a unitary matrix differential modulation code. The receiver employs the high-performance coupled iterative decoding of the turbo code and the modulation code. Information theoretic arguments are harnessed to form guidelines for code design and to evaluate performance of the iterative decoder.     

Fast turbo codes with space‐time block codes in fast fading channels

In this paper, space‐time block coding has been used in conjunction with Turbo codes to provide good diversity and coding gains. A new method of dividing turbo encoder and decoder into several parallel encoding and decoding blocks is considered. These blocks work simultaneously and yield a faster coding scheme in comparison to classical Turbo codes. The system concatenates fast Turbo coding as an outer code with Alamouti's G2 space‐time block coding scheme as an inner code, achieving benefits associated with both techniques including acceptable diversity and coding gain as well as short coding delay. In this paper, fast fading Rayleigh and Rician channels are considered for discussion. For Rayleigh fading channels, a fixed frame size and channel memory length of 5000 and 10, respectively, the coding gain is 7.5 dB and bit error rate (BER) of 10^?4 is achieved at 7 dB. For the same frame size and channel memory length, Rician fading channel yields the same BER at about 4.5 dB. Copyright © 2013 John Wiley & Sons, Ltd.     

一种基于增强奇偶校验码级联极化码的新型编译码方法

极化码作为一种纠错码,具有较好的编译码性能,已成为5G短码控制信道的标准编码方案。但在码长较短时,其性能不够优异。提出一种基于增强奇偶校验码级联极化码的新型编译码方法,在原有的奇偶校验位后设立增强校验位,对校验方程中信道可靠度较低的信息位进行双重校验,辅助奇偶校验码在译码过程中对路径进行修剪,以此提高路径选择的可靠性。仿真结果表明,在相同信道、相同码率码长下,本文提出的新型编译码方法比循环冗余校验(cyclic redundancy check,CRC)码级联极化码、奇偶校验(parity check,PC)码级联极化码误码性能更优异。在高斯信道下,当码长为128、码率为1/2、误码率为10-3时,本文提出的基于增强PC码级联的极化码比PC码级联的极化码获得了约0.3 dB增益,与CRC辅助的极化码相比获得了约0.4 dB增益。     

Performance of RS coded M-ary modulation with and without symbol overlapping

In this paper, we present analytical bit error probability results for M-ary modulation concatenated with Reed Solomon (RS) codes. The analysis of bit error probability is nontrivial as the number of bits per symbol for the RS codes may not be an integer multiple of the number of bits per symbol for a modulation symbol. We propose a Markov chain technique which allows analytical evaluation of the bit error probability for such cases. The performance of RS coding with coherent biorthogonal, coherent/non-coherent orthogonal modulation over an additive white Gaussian noise (AWGN) channel is evaluated. Simulation of the bit error probability of RS code concatenated with a Nordstrom Robinson (NR) code as an inner code is performed and compared with the case of biorthogonal modulation. From the results, we notice that a stronger inner code gives better bit error probability. In addition, the throughput of the coded system with biorthogonal modulation over an AWGN channel is discussed. For a Rayleigh flat fading and block fading channel, we analyze the bit error probability of RS codes concatenated with biorthogonal modulation. From the result, we notice that a stronger outer code gives a better bit error probability for the case of Rayleigh flat fading channel.