Trellis-coded constant-envelope modulations with linear receivers

We present two multilevel constant-envelope continuous-phase modulation (CPM) schemes with four-dimensional (4-D) trellis coding. The receiver is composed of a simple quadrature demodulator, followed by a symbol-rate sampler and a Viterbi decoder matched to the code trellis. The first modulation is a quaternary CPM scheme whose phase transitions over a symbol interval are those of π/4-shift quaternary phase-shift keying (QPSK). The demodulator filter is optimized so as to minimize the combined effect of intersymbol interference (ISI) and noise at the decision instants. We use Wei's (1987) 16-state 4-D trellis code, and redefine the set partitioning tree so as to maintain the same minimum distance between parallel transitions as in quadrature amplitude modulation (QAM) signal sets. The resulting modulation outperforms minimum-shift keying (MSK) by as much as 3.5 dB, in addition to reducing the 30-dB signal bandwidth by 20%. Next, we introduce an octonary (8-level) CPM scheme whose phase transitions are those of π/8-shift 8PSK. The same trellis code and receive filter optimization are also applied to this modulation which is shown to achieve better error rate performance than MSK, while saving some 60% of the transmitted signal bandwidth     

Coded 64-CAP ADSL in an impulse-noise environment-modeling ofimpulse noise and first simulation results

This paper presents the performance of various coding schemes for the asymmetrical digital subscriber line (ADSL) in an impulse-noise environment. Impulse noise is considered to be one of the most damaging impairments in the ADSL, in which compressed video signals are delivered to residential customers. The impulse noise used in this study was measured and collected in German telephone networks. Based on this measurement and the corresponding statistical modeling, a simulation model for impulse noise is proposed and its properties are outlined. The coding schemes considered here utilize burst-error correcting Reed-Solomon codes and/or random error correcting trellis codes as well as symbol interleaving between the two codes. It has been found through computer simulations that a proper concatenation of the two codes could increase the immunity against impulse noise compared to an uncoded scheme. Specifically, a concatenated code, using a 2-dimensional 8-state trellis code and a 4-error-correcting Reed-Solomon code with an interleaving depth of 18 symbols, was able to eliminate all the errors caused by the impulse noise used in the study. It has also been found that the trellis codes are not very effective against impulse noise, unless they are used in conjunction with Reed-Solomon codes and a proper symbol interleaving. Performance results of other coding configurations using Reed-Solomon codes with different error-correcting capabilities are also presented. In addition, we also show the performance results when simple array codes are used instead of the Reed-Solomon codes     

STTC码在QPSK通信系统中的应用与仿真

网格空时码是在时延分集的基础上与TCM编码结合而成的,是一种改进的传输分集方式,适用于多种无线信道环境。在无线通信中为了有效抑制噪音积累,选用QPSK调制,因为QPSK调制比QAM更适合噪音环境,QPSK调制具有理想的误差保护。网格空时码在QPSK调制传输系统中具有更好的纠错能力,具有低误码率与误帧率的优良性能。     

Turbo码和高频谱利用率调制技术

本文论述了Ｔｕｒｂｏ码的基本原理和译码器结构。介绍一种联合Ｔｕｒｂｏ码调制方案，并将之与格状编码调制方案进行比较。     

Enhanced space-time block coded systems by concatenating turbo product codes

The BER performance of a turbo product code (TPC) based space-time block coding (STBC) wireless system has been investigated. With the proposed system, both the good error correcting capability of TPC and the concurrent large diversity gain characteristic of STBC can be achieved. The BER upper bound has been derived taking BPSK modulation as an example. The simulation results show that the proposed system with the concatenated codes outperforms the one with only TPC or STBC and other reported schemes that concatenate STBC with convolutional Turbo codes or trellis codes.     

A comparison of two combining techniques for equal gain, trelliscoded diversity receivers

Trellis coded modulation is widely used for digital transmission over fading channels. Classical diversity techniques are also frequently employed to combat fading. In this paper two different strategies for equal gain combining are compared, One scheme is based on an interleaved code combining technique. The alternative scheme is based on averaged diversity combining. The well known transfer function bounding technique for trellis codes is used to obtain: expressions for the bit error rate performance of the two trellis coded diversity receivers over a slowly fading Rayleigh channel. The analysis of interleaved code combining is a straightforward modification of the analysis for multiple trellis coded modulation. The analysis of averaged diversity combining is accommodated through a more involved, novel modification of the branch labeling of the error state diagram. The analytic techniques presented in this paper are supported by simulation results using a TCM scheme based on QPSK modulation and a rate-l/2 linear convolution code     

Space-time MSK Codes for Quasi-Static Fading Channels

In this paper, 4-state and 8-state space-time trellis codes with full rate, full diversity and high coding gain are proposed for MSK modulation, based on a technique similar to the super-orthogonal space-time trellis code (SOSTTC) design. Since the phase continuity requirement of MSK is the main constraint in space-time MSK code design not all the signal matrices corresponding to the trellis branches are orthogonal. The paper shows that the SOSTTC design technique can be extended to nonorthogonal coding structures. The new space-time MSK codes have frame error performances very close to those of their space-time QPSK counterparts given in [1]     

Concatenated space-time block coding with trellis coded modulation in fading channels

Trellis coded modulation (TCM) is a bandwidth efficient transmission scheme that can achieve high coding gain by integrating coding and modulation. This paper presents an analytical expression for the error event probability of concatenated space-time block coding with TCM which reveals some dominant factors affecting the system performance over slow fading channels when perfect interleavers are used. This leads to establishing the design criteria for constructing the optimal trellis codes of such a concatenated system over slow flat fading channels. Through simulation, significant performance improvement is shown to be obtained by concatenating the interleaved streams of these codes with space-time block codes over fading channels. Simulation results also demonstrate that these trellis codes have better error performance than traditional codes designed for single-antenna Gaussian or fading channels. Performance results over quasi-static fading channels without interleaving are also compared in this paper. Furthermore, it is shown that concatenated space-time block coding with TCM (with/without interleaving) outperforms space-time trellis codes under the same spectral efficiency, trellis complexity, and signal constellation.     

Analysis of the pairwise error probability of noninterleaved codeson the Rayleigh-fading channel

The majority of previous analytical studies of signal-space coding techniques (includes trellis and block codes) on the Rayleigh-fading channel have assumed ideal interleaving. The effect of finite interleaving on the performance of different coding schemes has been studied only by simulation In this paper we first derive a maximum likelihood (ML) decoder for codewords transmitted over a noninterleaved Rayleigh flat fading channel, followed by an exact expression for the pairwise error event probability of such a decoder. It includes phase shift keying (PSK), quadrature amplitude modulation (QAM) signal sets, trellis coded modulation (TCM) and block coded modulation (BCM) schemes, as well as coherent (ideal channel state information) and partially coherent (e.g., differential, pilot tone, etc.) detection. We derive an exact expression for the pairwise event probability in the case of very slow fading-i.e., the fading experienced by all the symbols of the codeword is highly correlated. We also show that the interleaving depth required to optimize code performance for a particular minimum fading bandwidth can be approximated by the first zero of the fading channel's auto-correlation function     

Coded overlapped code division multiplexing system with Turbo product structure

Coded overlapped code division multiplexing system with Turbo product structure (TPC-OVCDM) is introduced, and trellis coded modulation (TCM) code is employed as error correcting code for uncoded overlapped code division multiplexing (OVCDM) system. In such a scheme, row code and column code are TCM and OVCDM spreading code, respectively. Data bits are only encoded directly by TCM and transformed into a matrix. Each column of this matrix is then permuted by symbol interleaver before being encoded by OVCDM spreading code. During iterative decoding process in the receiver, two constituent decoders use symbol by symbol BCJR algorithm in the log domain. The order of decoding two sub-codes is determined by the encoding order. The proportion of TCM coding and OVCDM coding affects system performance. For fixed coding structure and symbol interleaver, the performance of TPC-OVCDM systems of different proportions of additive white Gaussian noise (AWGN) channel have been simulated. The results show that TPC-OVCDM system of reasonable proportion can achieve significant coding gain, compared with uncoded OVCDM system under the condition of same spectral efficiency at bit error rate (BER) level of 10-5 .     

Low complexity concatenated coding schemes for digital satellite communications

A study of reduced complexity concatenated coding schemes, for commercial digital satellite systems with low-cost earth terminals, is reported. The study explored trade-offs between coding gain, overall rate and decoder complexity, and compared concatenated schemes with single codes. It concentrated on short block and constraint length inner codes, with soft decision decoding, concatenated with a range of Reed-Solomon outer codes. The dimension of the inner code was matched to the outer code symbol size, and appropriate interleaving between the inner and outer codes was used. Very useful coding gains were achieved with relatively high-rate, low-complexity schemes. For example, concatenating the soft decision decoded (9,8) single parity check inner code with the CCSDS recommended standard Reed-Solomon outer code gives a coding gain of 4.8dB at a bit error probability of 10^?5, with an overall rate of 0-78.     

An eight-dimensional 64-state trellis code for transmitting 4 bitsper 2-D symbol

An eight-dimensional, 64-state, 90° rotationally invariant trellis code for transmitting 4 bits/baud over a bandlimited channel is described. The 2-D constellation contains 20 points. The code achieves a 5.23-dB coding gain over the uncoded 4×4 QAM (quadrature amplitude modulation) constellation and a 1.23-dB gain over the standard CCITT V32 trellis code. Simulation results are presented that verify these coding gains. Simulation results showing symbol error probability versus signal/noise ratio and trellis depth are also presented     

QAM调制下基于卷积码与累加编码调制级联的纠错码性能研究

基于卷积码与累加编码的PPM调制级联码(SCPPM)在泊松信道光PPM调制下具有极优异的性能。文章将这种累加编码结构引入到QAM调制中,分析其性能。将卷积码+累加编码+QAM调制串行级联(SCAQAM)纠错方案与常规基于卷积码、并行级联卷积码(Turbo)以及低密度奇偶校验码(LDPC)的比特交织编码调制迭代译码(BICM-ID)系统进行比较,并进一步比较了SCAQAM系统的自然、格雷、反格雷星座映射方式。结果表明,在高阶QAM调制下,这种纠错结构具有极优异的误码性能。对于16QAM及64QAM调制,SCAQAM相对于另外几种纠错码结构的BICM-ID系统分别有约0.3和0.5 dB的性能提升,只有卷积码与累加码结合才更具性能优势。并且SCAQAM将累加后的比特流以反格雷方式映射具有更优异的性能。     

级联格状编码传输方案在数字HDTV中的应用研究

本文首先对地面广播信道的各种干扰进行分析。研究级联格状编码方案在ＨＤＴＶ中应用的设计要求。提出用于ＨＤＴＶ地面数字传输系统的级联８状态ＴＣＭ３２ＱＡＭ和ＲＳ码方案，并对其性能进行计算机模拟。最后分析ＨＤＴＶ的突然中断效应和数字传输系统性能的关系。     

On the probability of symbol error in Viterbi decoders

An upper bound is derived on the probability that at least one of a sequence of B consecutive bits at the output of a Viterbi (1979) decoder is in error. Such a bound is useful for the analysis of concatenated coding schemes employing an outer block code over GF(2^B) (typically a Reed-Solomon (RS) code), an inner convolutional code, and a symbol (GF(2^B)) interleaver separating the two codes. The bound demonstrates that in such coding schemes a symbol interleaver is preferable to a bit interleaver. It also suggests a new criterion for good inner convolutional codes     

Complexity Reduction in SISO Decoding of Block Codes

SISO decoding for block codes can be carried out based on a trellis representation of the code. However, the complexity entailed by such decoding is most often prohibitive and thus prevents practical implementation. This paper examines a new decoding scheme based on the soft-output Viterbi algorithm (SOVA) applied to a sectionalized trellis for linear block codes. The computational complexities of the new SOVA decoder and of the conventional SOVA decoder, based on a bit-level trellis, are theoretically analyzed and derived for different linear block codes. These results are used to obtain optimum sectionalizations of a trellis for SOVA. For comparisons, the optimum sectionalizations for Maximum A Posteriori (MAP) and Maximum Logarithm MAP (Max-Log-MAP) algorithms, and their corresponding computational complexities are included. The results confirm that the new SOVA decoder is the most computationally efficient SISO decoder, in comparisons to MAP and Max-Log-MAP algorithms. The simulation results of the bit error rate (BER) performance, assuming binary phase -- shift keying (BPSK) and additive white Gaussian noise (AWGN) channel, demonstrate that the performance of the new decoding scheme is not degraded. The BER performance of iterative SOVA decoding of serially concatenated block codes shows no difference in the quality of the soft outputs of the new decoding scheme and of the conventional SOVA.     

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.     

Joint Source and Channel Coding using Punctured Ring Convolutional Coded CPM

In this paper, a novel trellis source encoding scheme based on punctured ring convolutional codes is presented. Joint source and channel coding (JSCC) using trellis coded continuous phase modulation (CPM) with punctured convolutional codes over rings is investigated. The channels considered are the additive white gaussian noise (AWGN) channel and the Rayleigh fading channel. Optimal soft decoding for the proposed JSCC scheme is studied. The soft decoder is based on the a posteriori probability (APP) algorithm for trellis coded CPM with punctured ring convolutional codes. It is shown that these systems with soft decoding outperform the same systems with hard decoding especially when the systems operate at low to medium signal-to-noise ratio (SNR). Furthermore, adaptive JSCC approaches based on the proposed source coding scheme are investigated. Compared with JSCC schemes with fixed source coding rates, the proposed adaptive approaches can achieve much better performance in the high SNR region. The novelties of this work are the development of a trellis source encoding method based on punctured ring convolutional codes, the use of a soft decoder, the APP algorithm for the combined systems and the adaptive approaches to the JSCC problem.     

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.     

光通信中基于BCJR的BCH译码算法研究

首先从理论上分析了硬判决译码算法和软判决译码算法的性能然后对BCH(Bose,Ray-Chaudhuri,Hocquenghem)码的网格结构以及BCJR(Bahl,Cocke,Jelinek and Raviv)算法进行了详细地分析及推导。实验结果表明,在光信道环境中,在误比特率为10-5时,当仅提高最小汉明距离码率相同或者仅减小码率最小汉明距离相同时,BCJR算法相对于硬判决译码算法的编码增益分别在之前的编码增益基础上又增加了0.15dB和0.25dB。因此设计级联码方案时,应尽可能选择纠错能力较大的内码。此外也可以采用适当增加内码的冗余度相应减小外码的冗余度的方法,在获得更高的编码增益的同时保证整个系统的带宽利用率不变。