Sequential Decoding of Convolutional Codes for Rayleigh Fading Channels

The performance of sequential decoding of long constraint length convolutional codes is evaluated for Rayleigh fading channels. Sequential decoding is not practical below a certain theoretical signal-to-noise ratio, and these theoretical limits are calculated for a number of modulation methods and code rates. As an example, with BPSK modulation, soft decisions and code rate 1/2, the theoretical signal-to-noise ratio per information bit is 5.7 dB. Above this limit the bit error rate can be made arbitrarily small by increasing the constraint length at no significant complexity cost. Furthermore, it is shown that with carefully chosen quantization steps, 8 level uniform quantization gives a negligible loss also for sequential decoding on a Rayleigh fading channel. Simulation results using 8 level quantization correspond well with the theoretical performance bounds. Also, the performance on a correlated channel with finite interleaving has been obtained. With an interleaver depth of 50×50 and a normalized doppler frequency equal to 0.01 we are only 0.5 dB away from the performance with perfect interleaving. Finally, bit error rate results show this scheme to compete well with Turbo codes.     

Error performance of interleaved trellis-coded PSK modulations incorrelated Rayleigh fading channels

The authors derive an exact and easily computed expression for the pairwise error event probability of interleaved coded PSK modulations transmitted over channels with correlated Rayleigh flat fading and additive white Gaussian noise. Both coherent and differential detection are considered. In the case of coded DPSK, it is found that full interleaving does not necessarily provide the best error performance, especially when the fading is relatively fast and when the autocorrelation function of the channel fading process exhibits an oscillating behavior. For coherent detection or for differential detection in channels with relatively slow fading, increasing the interleaving depth always improves the error performance. In these cases, an interleaving depth equivalent to one-fifth to one-quarter the duration of a fade cycle is almost as good as full interleaving     

Variable rate adaptive modulation for DS-CDMA

An adaptive coding scheme is introduced for a discrete sequence code-division multiple-access system. The system uses noncoherent M-ary orthogonal modulation with RAKE receiver and power control. Both a fast fading channel and a combined fast fading, shadowing and power control channel are considered. Analytical bounds and simulations are done to evaluate the performance of the system. It is found that there is significant improvement in the average throughput and the bit-error-rate performance in the adaptive coding scheme. The amount of improvement drops with the increase of diversity branches used. More importantly, it is found that adaptive coding scheme is relatively robust to shadowing, while fix-rate codes are ineffective in the shadowing environment. Finally, adaptive coding scheme is found to be robust to mobile speed, feedback delay, and finite interleaving depth     

一种采用交织┐RS码纠错技术的自适应流星突发通信系统及性能分析

本文从便于实施的角度提出将一种交织－ＲＳ码纠错技术用于自适应流星突发（Ｍｅｔｅｏｒ－Ｂｕｒｓｔ）通信。为得到较佳的自适应纠错策略，将用最优化方法搜索出在给定条件下使分组成功译码概率达到最大时的最佳交织深度和最佳码长。从几种不同差错控制方案的比较来看，采用分段编码和交织技术能有效地改善ＭＢ通信系统的性能。本文还对数值结果进行分析并得出一些有用的结论     

Error performance of MPSK trellis-coded modulation overnonindependent Rician fading channels

This paper presents new upper bounds on the pairwise error probability (PEP) of trellis-coded modulation (TCM) schemes over nonindependent Rician fading channels. Cases considered are coherent and pilot-tone-aided detection and differential detection of trellis-coded multilevel phase-shift keying (TC-MPSK) systems. The average bit-error probability P_b can be approximated by truncating the union bound. This method does not necessarily lead to an upper bound on P_b, and, hence, the approximation must be used with simulation results. In addition, for Rayleigh fading channels with an exponential autocovariance function, bounds resembling those for memoryless channels have been derived. The bounds are substantially more accurate than Chernoff bounds and hence allow for accurate estimation of system performance when the assumption of ideal interleaving is relaxed     

Analysis of coded noncoherent transmission in DS-CDMA mobilesatellite communications

The paper analyzes possible transmission schemes for satellite personal communication systems adopting low/medium-Earth orbit (LEO/MEO) constellations and direct-sequence code division multiple access (DS-CDMA) in the presence of fading and shadowing, the statistics of which are functions of the satellite elevation angle. In particular, the performance of M-ary Walsh-Hadamard orthogonal (MWHO) convolutionally coded DS-CDMA over a Rice-log-normal fading channel is analyzed in depth, and compared to the simpler coded differential BPSK (DBPSK) scheme. Optimization of the performance/complexity tradeoff in the metric computation for soft inputs to the Viterbi (1979) decoder is addressed. Upper bounds on the error probability without or with satellite diversity and equal gain combining are evaluated considering different coding rates. The effect of correlated fading is also taken into account via simulation. Among the various results, it is shown that the optimal coding rate is a function of the satellite elevation angle and of the diversity order, that the loss for using DBPSK instead of MWHO is in the range 1-1.4 dB, and that interleaving depth is a critical parameter     

Chip‐interleaving direct sequence spread spectrum system over Rician multipath fading channels

Chip interleaving (CI) is a unique technique to exploit time diversity in direct sequence spread spectrum (DS/SS)‐based systems operating in fading environments. In order to facilitate design of CI systems in various fading situations, we present a performance analysis for CI DS/SS system over Rician multipath time‐varying fading channels. We derive the analytical bit error rate (BER) expression for CI DS/SS to allow fast and accurate evaluation of BER performance based on the interleaving depth selected, spreading codes employed, and the time correlation function of the channel. We then discuss some ideal cases by using the analytical results to reveal some of the insights presented in the performance analysis. For the purpose of comparison, we also obtain the BER expression for conventional DS/SS system as a special case of CI system with an interleaving depth of one. Using numerical examples, we verify the analytical results with computer simulations and illustrate the BER performance behavior of CI DS/SS system with varying interleaving depth for all possible combinations of two sets of spreading codes of different type and two different time correlation functions of the channel. Copyright © 2011 John Wiley & Sons, Ltd.     

Trellis code design for periodic interleavers

A standard technique for correlated fading combines trellis codes designed for independent fading with interleaving that makes correlated fading appear to be independent for symbols within the Viterbi traceback depth. When the fading correlation is persistent and delay constraints preclude deep interleaving, some correlation remains among symbols within the traceback depth. Incorporating this post-interleaver correlation improves the trellis code design. This article presents such a trellis code design technique for periodic interleavers. Bit error rate simulations demonstrate that the new design technique can provide a dramatic performance improvement when fading or interference is severe and persistent     

A performance analysis of trellis-coded modulation schemes overRician fading channels

This paper presents a saddle point approximation (SAP) method to compute the pairwise error probability (PEP) of trellis-coded modulation (TCM) schemes over Rician fading channels. The approximation is applicable under several conditions, such as finite and ideal interleaving, ideal coherent and pilot-tone aided detection, and differential detection. The accuracy of this approximation is demonstrated by comparison to the results of numerical integration. When ideal interleaving is assumed, an asymptotic approximation for the PEP of ideal coherent, pilot-tone aided or differentially detected TCM is derived. This asymptotic approximation of the PEP is in a product form and much tighter than the ordinary Chernoff bound on the PEP. Also, based on the SAP, the effect of finite interleaving depth on the error performance of TCM schemes over Rician and shadowed Rician channels is studied     

Bit-Interleaving in Fast FH/SSMA Systems with M-FSK Modulation

The effects of bit-interleaving on the performance of convolutional codes and turbo codes in fast frequency- hop/spread-spectrum multiple-access systems with M-FSK modulation are investigated. It is observed that bit-interleaving induces two counter-acting forces on decoder performance. On the one hand, bit-interleaving disperses consecutive error bits caused by a noisy M-ary signal and makes the errors more correctable. On the other hand, the same measure makes it difficult for the decoder to make use of the bit dependency information. Both theoretical upper bounds and simulation results show that bit- interleaving degrades the performance of soft-decision decoded convolutional codes and turbo codes.     

一种面向RS码的卷积交织与解交织器的设计

采用了构造计数器来生成SRAM的读写地址的方法,设计了一种符合DVB-C标准,面向RS（204,188）码的卷积交织和解交织器．交织深度为12,单元深度为17。这种卷积交织和解交织器结构简单,性能良好,由于采用了单端口RAM,所以比一般的采用双端口RAM的设计节省了30％的电路面积。     

Bandwidth efficient concatenated coding schemes for fading channels

Concatenated codes consisting of trellis inner codes and Reed-Solomon outer codes are considered to achieve large coding gains with small bandwidth expansion in the presence of frequency-nonselective slow Rician fading. Both errors-only and errors-erasures decoding algorithms for outer codes are applied. New upper bounds on bit error probability performance in the presence of fading are obtained and compared with simulation results for zero channel memory. The effect of interleaving in eliminating channel memory is investigated. The performance gains that are achieved by the coding scheme relative to the reference uncoded systems are illustrated via some examples     

Concatenated coding performance for FSK modulation ontime-correlated Rician fading channels

We present an analytical method for evaluating the performance of noninterleaved concatenated codes over channels modeled as a nonfrequency selective correlated Rician fading channel with a known power spectral density. The main idea is to model the communication system from the modulator input to the demodulator output as a finite state channel (FSC) model, and apply powerful enumeration techniques to such a discrete channel in order to gain useful information on the system performance. The concatenated scheme makes use of two codes; Reed-Solomon codes are employed for the outer code, and binary block codes are used as the inner code. Next, the method is extended to study the effect on the performance when an interleaving with finite depth is incorporated into the communication system. A comparison between symbol and bit interleaving is made. Finally, we study the potential gain produced when channel information is passed on to the outer decoder in the form of an erasure symbol. In all cases, analytical expressions for the probability of the number of error symbols produced by the FSC model were obtained in terms of a coefficient in a formal power series. This is an interesting alternative approach with respect to computer simulations     

比特交织编码调制技术分析

为了在不降低频带利用率和功率利用率的情况下以设备的复杂化来换取编码增益,提出了一种将编码和调制方式结合在一起的比特交织编码调制(Bit Interleaved Coded Modulation,BICM)技术。该技术针对网格编码调制(TrellisCoded Modulation,TCM)灵活性差和衰落信道中性能差的缺点,在理想交织时将编码器和调制器分离设计,具有高度的灵活性,并可以得到近似网格编码调制的性能,并且对衰落信道具有很好的鲁棒性。介绍了比特交织编码调制的构成模式、关键技术,包括信道编码、比特交织和调制,给出了BCIM理论分析,并对不同的交织深度、交织方法和高阶调制等进行了性能仿真分析。仿真结果表明比特交织编码调制可以取得良好的误码率性能。     

Interleaving schemes for multidimensional cluster errors

We present two-dimensional and three-dimensional interleaving techniques for correcting two- and three-dimensional bursts (or clusters) of errors, where a cluster of errors is characterized by its area or volume. Correction of multidimensional error clusters is required in holographic storage, an emerging application of considerable importance. Our main contribution is the construction of efficient two-dimensional and three-dimensional interleaving schemes. The proposed schemes are based on t-interleaved arrays of integers, defined by the property that every connected component of area or volume t consists of distinct integers. In the two-dimensional case, our constructions are optimal: they have the lowest possible interleaving degree. That is, the resulting t-interleaved arrays contain the smallest possible number of distinct integers, hence minimizing the number of codewords required in an interleaving scheme. In general, we observe that the interleaving problem can be interpreted as a graph-coloring problem, and introduce the useful special class of lattice interleavers. We employ a result of Minkowski, dating back to 1904, to establish both upper and lower bounds on the interleaving degree of lattice interleavers in three dimensions. For the case t≡0 mod 6, the upper and lower bounds coincide, and the Minkowski lattice directly yields an optimal lattice interleaver. For t≠0 mod 6, we construct efficient lattice interleavers using approximations of the Minkowski lattice     

分布式STBC-OFDM交织深度优化

该文在分布式发射天线场景下,考虑多径瑞利衰落信道,针对每个天线上分别采用交织分组子载波功率扩展的STBC-OFDM链路,提出了一种交织深度优化方法:根据分布式信道的多径数和多径时延,以最小化成对错误概率上界为目标,设置交织子载波分组的交织深度。在两发一收STBC, BPSK调制,由M.1225步行测试信道A, B组成的分布式场景下仿真,结果表明:当误比特率为10-5时,与传统方法相比,该文方法有1.5 dB的功率节省。     

A Chaotic Interleaving Scheme for the Continuous Phase Modulation Based Single-Carrier Frequency-Domain Equalization System

In this paper, we propose a chaotic interleaving scheme for the continuous phase modulation based single-carrier frequency-domain equalization (CPM-SC-FDE) system. Chaotic interleaving is used in this scheme to generate permuted versions from the sample sequences to be transmitted, with low correlation among their samples, and hence a better bit error rate (BER) performance can be obtained. The proposed CPM-SC-FDE system with chaotic interleaving combines the advantages of the frequency diversity, the low complexity, and the high power efficiency of the CPM-SC-FDE system and the performance improvements due to chaotic interleaving. The BER performance of the CPM-SC-FDE system with and without chaotic interleaving is evaluated by computer simulations. Also, a comparison between the proposed chaotic interleaving and the conventional block interleaving is performed. Simulation results show that, the proposed chaotic interleaving scheme can greatly improve the performance of the CPM-SC-FDE system. Furthermore, the results show that this scheme outperforms the conventional block interleaving scheme in the CPM-SC-FDE system. The results also show that, the proposed CPM-SC-FDE system with chaotic interleaving provides a good trade-off between system performance and bandwidth efficiency.     

A double byte interleaving scheme for ADSL modems

We present a new way of operation for the convolutional interleaver of an asynchronous digital subscriber line (ADSL) modem, exploiting the single latency path through the modem. A combined buffer is added after the Reed-Solomon (RS) coders in order to support the parallel way of operation. On the other hand, the combined buffer increases the correcting capabilities of the structure in case the fast path through the modem used, as it serves as an interleaver with a depth of two. The interleaving process is of the double byte kind. The proposed structure offers a performance equivalent to that achieved by a conventional interleaver with a depth of interleaving of double size, reducing thus significantly the delay caused by the interleaver. The gains achieved range from 50% to even a 100%     

Design and analysis of transmitter diversity using intentionalfrequency offset for wireless communications

Coded modulation (usually with interleaving) is used in fading channel communications to achieve a good error performance. The major benefit from using coded modulation in fading channels is achieved if each code symbol of a codeword (or coded sequence) suffers statistically different fading (preferably independent fading). However, in many applications of mobile communications (e.g., in a metropolitan environment), a low vehicle speed (and hence, a small Doppler spread, f _D) is very common. With a small Doppler spread, ideal or close-to-ideal interleaving is no longer feasible and all code symbols of a codeword would suffer highly correlated fading especially in stationary fading (f_D≈0). Coded modulations will thus suffer seriously degraded performance. Previous performance analyses based on ideal interleaving are not accurate when a small Doppler spread is encountered and the much used union bound error probability analysis is loose for small Doppler spreads. To rectify this situation, this paper presents an improved performance analysis of coded modulations with correlated fading and pilot-symbol-assisted modulation (PSAM). Transmitter diversity can generate the necessary time-varying fading to maintain the effectiveness of a coded signaling scheme which this paper examines in detail using an intentional frequency offset between antennas. This work found that proper selections of the intentional frequency offset and interleaving depth can lead to good performance with traditional coded modulations (if enough antennas are used) using essentially the same simple demodulation structure as used in the traditional single-antenna PSAM     

Comprehensive evaluation of chip interleaving effect on turbo‐coded DS‐SS in a Rayleigh fading channel with antenna diversity reception

In this paper, we present a comprehensive performance evaluation of chip interleaving effect on turbo coded direct sequence spread spectrum (DS‐SS) system in a frequency non‐selective Rayleigh fading channel with antenna diversity reception. At the transmitter, chip interleaver scrambles the SF (spreading factor) chips associated with a data symbol and transforms the transmission channel into a highly time‐selective or highly memoryless channel at the chip level. The use of chip interleaving is equivalent to using SF‐antenna diversity reception with correlated fading among the branches and with reduced average received signal power per antenna by a factor of SF. We theoretically analyze how chip interleaving alters the received signal statistics. Then, the effect of the various parameters, viz. interleaver size, interleaving depth, information sequence length, spreading factor and the fading maximum Doppler frequency, are also evaluated. It is found that the bit error rate (BER) performance improves with increasing spreading factor and increasing frame length. Chip interleaving is found to be effective in the presence of receive antenna diversity as well. Copyright © 2005 John Wiley & Sons, Ltd.