Soft-decision and erasure decoding in fast frequency-hoppingsystems with convolutional, turbo, and Reed-Solomon codes

In this contribution we present an exhaustive treatment of various coding and decoding techniques for use in fast frequency-hopping/multiple frequency shift keying multiple-access systems. One of the main goals is to show how reliability information on each received bit can be derived to enable soft-decision decoding. Convolutional codes as well as turbo codes are considered applying soft-decision, erasure, and hard-decision decoding. Their performance is compared to that of previously proposed Reed-Solomon with either errors-only or errors-and-erasures decoding. A mobile radio environment yielding a frequency-selective fading channel is assumed. It is shown that the application of turbo codes and convolutional codes with soft decision decoding can allow for a comparable number of simultaneously transmitting users to Reed-Solomon codes with errors-and-erasures decoding. Furthermore, the advantage of soft decisions is shown, which can be applied to a widely and growing range of channel codes. The pertinent technique of calculating soft decisions is described in the paper     

Comparison of Convolutional and Turbo Coding for Broadband FWA Systems

It has been demonstrated that turbo codes substantially outperform other codes, e.g., convolutional codes, both in the non-fading additive white Gaussian noise (AWGN) channel as well as multiple-transmit and multiple-receive antenna fading channels. Moreover, it has also been reported that turbo codes perform very well in fast fading channels, but perform somewhat poorly on slow and block fading channels of which the broadband fixed wireless access (FWA) channel is an example. In this paper, we thoroughly compare the performance of turbo-coded and convolutional-coded broadband FWA systems both with and without antenna diversity under the condition of identical complexity for a variety of decoding algorithms. In particular, we derive mathematical expressions to characterize the complexity of turbo decoding based on state-of-the-art Log-MAP and Max-Log-MAP algorithms as well as convolutional decoding based on the Viterbi algorithm in terms of the number of equivalent addition operations. Simulation results show that turbo codes do not offer any performance advantage over convolutional codes in FWA systems without antenna diversity or FWA systems with limited antenna diversity. Indeed, turbo codes only outperform convolutional codes in FWA systems having significant antenna diversity.     

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     

Space-time turbo codes with full antenna diversity

In attempting to find a spectrally and power efficient channel code which is able to exploit maximum diversity from a wireless channel whenever available, we investigate the possibility of constructing a full antenna diversity space-time turbo code. As a result, both three-antenna and two-antenna (punctured) constructions are shown to be possible and very easy to find. To check the decodability and performance of the proposed codes, we derive non-binary soft-decoding algorithms. The performance of these codes are then simulated and compared with two existing space-time convolutional codes (one has minimum worst-case symbol-error probability; the other has maximal minimum free distance) having similar decoding complexity. As the simulation results show, the proposed space-time turbo codes give similar or slightly better performance than the convolutional codes under extremely slow fading. When fading is fast, the better distance spectra of the turbo codes help seize the temporal diversity. Thus, the performance advantage of the turbo codes becomes evident. In particular, 10^-5 bit-error rate and 10^-3 frame-error rate can be achieved at less than 6-dB E_b/N₀ with 1 b/s/Hz and binary phase-shift keying modulation. The practical issue of obtaining the critical channel state information (CSI) is also considered by applying an iteratively filtered pilot symbol-assisted modulation technique. The penalty when the CSI is not given a priori is about 2-3 dB     

Concatenated coding for DS/CDMA transmission in wirelesscommunications

We investigate the use of forward-error correction (FEC) as well as concatenated coding for reliable data transmission in asynchronous direct-sequence code-division multiple-access communications over frequency-selective Rayleigh fading channels. The FEC scheme combines antenna diversity with low complexity concatenated codes which consist of a Reed-Solomon outer code and a convolutional inner code. Under this concatenated coding scheme, we analyze the average bit-error rate performance and capacity tradeoffs between various system parameters under a fixed total bandwidth expansion and concatenated codes constraint requirements     

LDPC-COFDM系统在多径衰落信道下的性能分析

将正交频分复用(OFDM)技术应用于多径衰落信道下的高速数据传输是一个极富吸引力的方案,包括卷积码、RS码、Turbo码在内的多种纠错编码都曾被应用在OFDM系统中.最近,一种新的编码方案--低密度奇偶校验码(LDPC)引起了人们的注意.LDPC具有低的解码复杂度和逼近香农限的性能.文中仿真分析了LDPC-COFDM(编码正交频分复用)系统的性能,并与Turbo码系统进行了对比,结果表明该系统在多径衰落信道下显示出更为优越的性能.     

Assembled space-time turbo trellis codes

A novel full rate space-time turbo trellis code, referred to as an assembled space-time turbo trellis code (ASTTTC), is presented in this paper. For this scheme, input information binary sequences are first encoded using two parallel concatenated convolutional encoders. The encoder outputs are split into four parallel streams and each of them is modulated by a QPSK modulator. The modulated symbols are assembled by a predefined linear function rather than punctured as in the standard schemes. This results in a lower code rate and a higher coding gain over time-varying fading channels. An extended two-dimensional (2-D) log-MAP (maximum a posteriori probability) decoding algorithm, which simultaneously calculates two a posteriori probabilities (APP), is developed to decode the proposed scheme. Simulation results show that, under the same conditions, the proposed code considerably outperforms the conventional space-time turbo codes over time-varying fading channels.     

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     

Differential detection of turbo codes for Rayleigh fast-fadingchannels

The performance of turbo codes using differentially detected quadrature phase-shift keying (QPSK) signals transmitted over Rayleigh fast-fading channels is investigated. So far in the open technical literature dealing with turbo codes only slow fading has been considered. Our research has shown that the use of a simple differential detector in conjunction with turbo codes can generally outperform convolutional codes in terms of the bit-and block-error rates for fading rates with a BT product up to 0.1. However, to achieve significant performance improvements, large block sizes must be employed, particularly at slower fading rates     

Comparative study of turbo equalization schemes usingconvolutional, convolutional turbo, and block-turbo codes

Turbo equalizers have been shown to be successful in mitigating the effects of inter-symbol interference introduced by partial response modems and by dispersive channels for code rates of R⩽ 1/2. We comparatively studied the performance of a range of binary phase-shift keying turbo equalizers employing block-turbo codes, namely Bose-Chaudhuri-Hocquenghen (1960, 1959) turbo codes, convolutional codes, and convolutional turbo codes having high code rates, such as R=3/4 and R=5/6, over a dispersive five-path Gaussian channel and an equally weighted symbol-spaced five-path Rayleigh fading channel. These turbo equalization schemes were combined with an iterative channel estimation scheme in order to characterize a realistic scenario. The simulation results demonstrated that the turbo-equalized system using convolutional turbo codes was the most robust system for all code rates investigated     

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     

Performance analysis of convolutionally coded systems over quasi-static fading channels

This paper presents an improved upper bound on the performance of convolutionally coded systems over quasi-static fading channels (QSFC). The bound uses a combination of a classical union bound when the fading channel is in a high signal-to-noise ratio (SNR) state together with a new upper bound for the low SNR state. This new bounding approach is applied to both BPSK convolutional and turbo codes, as well as serially concatenated BPSK convolutional/turbo and space-time block codes. The new analytical technique produces bounds which are usually about 1 dB tighter than existing bounds. Finally, based on the proposed bound, we introduce an improved design criterion for convolutionally coded systems in slow flat fading channels. Simulation results are included to confirm the improved ability of the proposed criterion to search for convolutional codes with good performance over a QSFC.     

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。     

Low-Complexity High-Rate Reed--Solomon Block Turbo Codes

This letter considers high-rate block turbo codes (BTC) obtained by concatenation of two single-error-correcting Reed-Solomon (RS) constituent codes. Simulation results show that these codes perform within 1 dB of the theoretical limit for binary transmission over additive white Gaussian noise with a low-complexity decoder. A comparison with Bose-Chaudhuri-Hocquenghem BTCs of similar code rate reveals that RS BTCs have interesting advantages in terms of memory size and decoder complexity for very-high-data-rate decoding architectures.     

Low rate convolutional and turbo codes based on non‐linear cyclic codes

Low rate convolutional and turbo codes that output non‐linear cyclic (NLC) codewords of length n = 2^m, m being a positive integer, are described. These codes have a very low coding rate, which makes them especially suitable for spread spectrum systems where they can be used for simultaneously achieving error correction and bandwidth expansion. Due to the cyclic properties and codeword length of the component codes, branch metrics can be efficiently computed using the fast Fourier transform (FFT), enabling simple implementation of the encoder and decoder. Among the possible NLC base codes, special attention is given to the Tomlinson, Cercas, Hughes (TCH) codes family due to their good autocorrelation properties. It is shown by simulation that the turbo codes schemes studied usually perform better than traditional turbo codes (in this paper the universal mobile telecommunications system (UMTS), rate 1/3 turbo code was used as a reference). This improvement is accomplished at the cost of bandwidth expansion. One of the advantages of the presented solutions over other low rate codes is their ability to improve the synchronization process at the receiver due to the good autocorrelation properties of the available NLC codes (especially TCH codes). A comparison of performance between the UMTS uplink connection and an equivalent system using the proposed codes for a multiuser scenario in a multipath fading channel is presented showing the possibility of capacity increase when using these codes. Copyright © 2006 John Wiley & Sons, Ltd.     

Transmission of nonuniform memoryless sources via nonsystematic turbo codes

We investigate the joint source-channel coding problem of transmitting nonuniform memoryless sources over binary phase-shift keying-modulated additive white Gaussian noise and Rayleigh fading channels via turbo codes. In contrast to previous work, recursive nonsystematic convolutional encoders are proposed as the constituent encoders for heavily biased sources. We prove that under certain conditions, and when the length of the input source sequence tends to infinity, the encoder state distribution and the marginal output distribution of each constituent recursive convolutional encoder become asymptotically uniform, regardless of the degree of source nonuniformity. We also give a conjecture (which is empirically validated) on the condition for the higher order distribution of the encoder output to be asymptotically uniform, irrespective of the source distribution. Consequently, these conditions serve as design criteria for the choice of good encoder structures. As a result, the outputs of our selected nonsystematic turbo codes are suitably matched to the channel input, since a uniformly distributed input maximizes the channel mutual information, and hence, achieves capacity. Simulation results show substantial gains by the nonsystematic codes over previously designed systematic turbo codes; furthermore, their performance is within 0.74-1.17 dB from the Shannon limit. Finally, we compare our joint source-channel coding system with two tandem schemes which employ a fourth-order Huffman code (performing near-optimal data compression) and a turbo code that either gives excellent waterfall bit-error rate (BER) performance or good error-floor performance. At the same overall transmission rate, our system offers robust and superior performance at low BERs (< 10/sup -4/), while its complexity is lower.     

Effectiveness of Convolutional Codes in WCMDA Systems Supporting High Data Rate Users

This article studies the effects of applying convolutional codes to a wideband code-division multiple access (WCDMA) system that supports multirate users. The system is modeled following the WCDMA standards and the channel introduces noise, frequency-selective fading, and MAI. Rate one-half convolutional codes suggested in the third-generation (3G) standards are studied; we find that the error-correcting capabilities provided by these codes are insufficient for supporting very high data rate users. Possible solutions to this problem include employing turbo codes or multiple frequency band transmission.     

Space-time codes and concatenated channel codes for wirelesscommunications

Following a brief historical perspective on channel coding, an introduction to space-time block codes is given. The various space-time codes considered are then concatenated with a range of channel codecs, such as convolutional and block-based turbo codes as well as conventional and turbo trellis codes. The associated estimated complexity issues and memory requirements are also considered. These discussions are followed by a performance study of various space-time and channel-coded transceivers. Our aim is first to identify a space-time code/channel code combination constituting a good engineering tradeoff in terms of its effective throughput, bit-error-rate performance, and estimated complexity. Specifically, the issue of bit-to-symbol mapping is addressed in the context of convolutional codes (CCs) and convolutional coding as well as Bose-Chaudhuri-Hocquenghem coding-based turbo codes in conjunction with an attractive unity-rate space-time code and multilevel modulation is detailed. It is concluded that over the nondispersive or narrow-band fading channels, the best performance versus complexity tradeoff is constituted by Alamouti's twin-antenna block space-time code concatenated with turbo convolutional codes. Further comparisons with space-time trellis codes result in similar conclusions     

Turbo codes for noncoherent FH-SS with partial band interference

Turbo codes are investigated in a slow frequency-hopped spread spectrum (FH-SS) system with partial band jamming. In addition, full-band thermal noise is present. The channel model is that of a partial-band jammer in which a fraction of the frequency band is jammed and the remaining fraction is unjammed. This paper focuses on the implementation and performance of a modified turbo decoder for this model. We refer to the knowledge that each transmitted bit is jammed as channel state information. We consider cases of known or unknown channel state and variable number of bits per hop. Our approach is to modify the calculation of branch transition probabilities inherent in the original turbo decoder. For the cases with no side information and multiple bits per hop, we iteratively calculate channel state estimates. Analytical bounds are derived and simulation is performed for noncoherent demodulation. The performance of turbo codes is compared with a Reed-Solomon and a concatenated code comprised of a convolutional inner code and Reed-Solomon outer code     

Design and performance of turbo Gallager codes

The most powerful channel-coding schemes, namely, those based on turbo codes and low-density parity-check (LDPC) Gallager codes, have in common the principle of iterative decoding. However, the relative coding structures and decoding algorithms are substantially different. This paper shows that recently proposed novel coding structures bridge the gap between these two schemes. In fact, with properly chosen component convolutional codes, a turbo code can be successfully decoded by means of the decoding algorithm used for LDPC codes, i.e., the belief-propagation algorithm working on the code Tanner graph. These new turbo codes are here nicknamed "turbo Gallager codes." Besides being interesting from a conceptual viewpoint, these schemes are important on the practical side because they can be decoded in a fully parallel manner. In addition to the encoding complexity advantage of turbo codes, the low decoding complexity allows the design of very efficient channel-coding schemes.