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/.<>     

Bandwidth efficient coding for fading channels: code constructionand performance analysis

The authors apply a general method of bounding the event error probability of TCM (trellis-coded modulation) schemes to fading channels and use the effective length and the minimum-squared-product distance to replace the minimum-free-squared-Euclidean distance as code design parameters for Rayleigh and Rician fading channels with a substantial multipath component. They present 8-PSK (phase-shift-keying) trellis codes specifically constructed for fading channels that outperform equivalent codes designed for the AWGN (additive white Gaussian noise) channel when v⩾5. For quasiregular trellis codes there exists an efficient algorithm for evaluating event error probability, and numerical results which demonstrate the importance of the effective length as a code design parameter for fading channels with or without side information have been obtained. This is consistent with the case for binary signaling, where the Hamming distance remains the best code design parameter for fading channels. The authors show that the use of Reed-Solomon block codes with expanded signal sets becomes interesting only for large value of E_s/N₀, where they begin to outperform trellis codes     

TCMP-a modulation and coding strategy for Rician fading channels

The authors describe TCMP, a novel modulation strategy for Rician fading channels that multiplexes a time domain pilot sequence with trellis-coded data to permit coherent detection. This technique is shown to provide remarkably robust performance in the presence of fading. It is also shown that, when choosing trellis codes for fading channels, time diversity is of greater important than asymptotic coding gain. The motivation for studying this strategy is to find signaling schemes for transmitting data at a 4.8 kb/s rate over a mobile satellite channel with 5-kHz channel spacing     

Performance of interleaved trellis-coded differential 8-PSKmodulation over fading channels

The performance of trellis-coded differential octal phase-shift keying (coded 8-DPSK) with differentially coherent detection and soft-decision Viterbi decoding is investigated. A suitable receiver is presented whose signal processing is based on Nyquist signaling, requiring only one complex sample per modulation interval. Symbol synchronization and automatic frequency control are performed in a decision-directed way. Bit-error-rate (BER) performance over Gaussian, Rayleigh, and Rician channels is determined by means of computer simulations. The performance of coded 8-DPSK on the Gaussian channel is shown for a four-state convolutional trellis code. The unquantized outputs of up to three symbol detectors with delays of 1, 2, and 3 symbol periods are used for metric computation. The coding gain which includes losses due to timing and frequency synchronization errors is found to be 2.5 dB at BER=10^-5 with respect to uncoded 4-DPSK. Much larger gains are achieved for fading channels if interleaving is applied. Using an eight-state trellis code the performance is determined on Rayleigh and Rician channels for various Doppler spreads and interleaver sizes     

Nonlinear rotationally invariant trellis codes for multidimensionalmodulation

The concept of a general nonlinear parity-check equation was first proposed by Pietrobon et al. who used them to construct rotationally invariant trellis codes for two dimensional signal sets. This paper applies this technique to trellis-coded modulation (TCM) codes with multidimensional MPSK and MQAM constellations to construct nonlinear phase rotationally invariant multi-D codes. Based on this construction technique, a series of the best fully phase rotationally invariant multi-D trellis codes for a variety of signal constellations is obtained through a systematic code search program. The code search results show that most codes achieve the same asymptotic coding gain as the best linear, but nonphase rotationally invariant codes found by Pietrobon et al     

Constructing Space-Time Trellis Codes Using Orthogonal Designs

In this paper we consider the design of space-time trellis codes usingorthogonal designs. We derive a condition on the codewords to obtainthe maximum received signal energy and show that the codes based onorthogonal designs satisfy this condition.We consider in detail the design of a trellis code for two transmitantennas. The new code we develophas a higher diversity in fast fading and a higher coding gain in quasi-static fading when compared to otherexisting space-time codes. We also consider a turbo implementation ofthe new trellis code which results in very high diversity gains infast fading channels.     

Application of Coded Modulation to 1.544-Mbit/s Data-in-Voice Modems for FDM FM and SSB Analog Radio Systems

The technical issues relevant to providing high-quality digital service over analog radio using 1.544-Mbit/s DS-1 data-invoice modems operating through analog supergroup channels with 256-QAM modulation are reviewed. By means of a typical example, the desirability of increasing the fading margin when operating over FM radio systems is demonstrated. This motivates the consideration of coded modulation as a means of extending the threshold of the modem System, so that operation of the modem can be achieved in supergroup channels located higher in the radio baseband. It is found that trellis coded modulation provides better improvement of threshold performance than lattice coded modulation when the actual coding gain realized near the R0channel bound is used rather than the high signalto-noise-ratio (SNR)asymptotic coding gains. Using Ungerboeck's eight-state trellis code [3], a coding gain of approximately 2 dB is found for operation at 28 dB SNR (1 dB from the R0bound). Furthermore, it is found that even at this low operating SNR (where error events at the coded modulation receiver ouput can be long), high-rate, interleaved Reed-Solomon codes, used for burst noise protection at high SNR, still provide over 2 dB of additional coding gain.     

Improved Superorthogonal Codes Through Generalized Rotations

Concatenation of orthogonal space-time block codes (OSTBC) with an outer trellis has led to simple and powerful codes, known as superorthogonal codes or space-time block trellis-coded modulation. In this letter, we generalize these codes by finding new code supersets and corresponding set partitioning, resulting in improved coding gain. We provide design guidelines for the labeling of the generalized code trellises and demonstrate the gains by several example designs for two and four transmit antennas     

I-Q TCM: reliable communication over the Rayleigh fading channelclose to the cutoff rate

This paper presents some trellis codes that provide high coding gain to channels with slow, non frequency-selective Rayleigh fading. It is shown that the use of two encoders in parallel-used to specify the in-phase and quadrature components of the transmitted signal-results in greater minimum time diversity than the conventional design in which a single encoder is used. Using this approach-which we label “I-Q TCM”-codes with bandwidth efficiencies of 1, 2, and 3 bits/s/Hz are described for various constraint lengths. The performance of these codes is bounded analytically and approximated via simulation; the results show a large improvement in the bit error rate (BER) when compared with conventional trellis-coded modulation (TCM) schemes when perfect channel state information (CSI) is available to the receiver. Indeed, when this approach is applied to channels with independent Rayleigh fading, the resulting coding gain is close to that implied by the cutoff rate limit, even for only moderately complex systems. The proposed codes are also simulated under less ideal assumptions. For instance, results for a 1-bit/s/Hz IQ-TCM code without CSI show a significant gain over conventional coding. Finally, simulations over channels with correlated fading were undertaken; it is concluded that an interleaver span of 4ν yields performance close to what is achieved with ideal interleaving     

Space-time codes for high data rate wireless communication:performance criterion and code construction

We consider the design of channel codes for improving the data rate and/or the reliability of communications over fading channels using multiple transmit antennas. Data is encoded by a channel code and the encoded data is split into n streams that are simultaneously transmitted using n transmit antennas. The received signal at each receive antenna is a linear superposition of the n transmitted signals perturbed by noise. We derive performance criteria for designing such codes under the assumption that the fading is slow and frequency nonselective. Performance is shown to be determined by matrices constructed from pairs of distinct code sequences. The minimum rank among these matrices quantifies the diversity gain, while the minimum determinant of these matrices quantifies the coding gain. The results are then extended to fast fading channels. The design criteria are used to design trellis codes for high data rate wireless communication. The encoding/decoding complexity of these codes is comparable to trellis codes employed in practice over Gaussian channels. The codes constructed here provide the best tradeoff between data rate, diversity advantage, and trellis complexity. Simulation results are provided for 4 and 8 PSK signal sets with data rates of 2 and 3 bits/symbol, demonstrating excellent performance that is within 2-3 dB of the outage capacity for these channels using only 64 state encoders     

Multifrequency trellis coding with low delay for fading channels

An L-frequency trellis coding scheme designed for fading channels that provides diversity up to order L is described. L-frequency coding is advantageous over channel coding schemes that achieve implicit time-diversity through trellis coding in conjunction with time-interleaving because it requires negligible end-to-end delay. The authors derive an upper-bound for the probability of symbol error of the L-frequency code. Based on this upper-bound, they then deduce the design criteria for optimum L-frequency codes. A numerical approximation to this upper-bound and the design of a two-state and two four-state, two-frequency codes are presented. Through simulations, it was found that relative to the traditional dual frequency diversity approach, the two-state and four-state codes achieve 3- and 4-dB coding gains, respectively. This energy efficiency gain can be translated into a spectral efficiency gain. A brief discussion on the difference in code design techniques for the Gaussian channel and the fading channel is also presented     

Discrete multiple tone modulation with coset coding for thespectrally shaped channel

A discrete approach to multiple tone modulation is developed for digital communication channels with arbitrary intersymbol interference (ISI) and additive Gaussian noise. Multiple tone modulation is achieved through the concatenation of a finite block length modulator based on discrete Fourier transform (DFT) code vectors, and high gain coset or trellis codes. Symbol blocks from an inverse DFT (IDFT) are cyclically extended to generate ISI-free channel-output symbols that decompose the channel into a group of orthogonal and independent parallel subchannels. Asymptotic performance of this system is derived, and examples of asymptotic and finite block length coding gain performance for several channels are evaluated at different values of bits per sample. This discrete multiple tone technique is linear in both the modulation and the demodulation, and is free from the effects of error propagation that often afflict systems employing bandwidth-optimized decision feedback plus coset codes     

The design of trellis coded MPSK for fading channels: setpartitioning for optimum code design

A previous work on criteria for designing trellis-coded MPSK modulation to achieve minimum error probability performance on the Rician fading channel (see ibid., vol.36, no.9, p.1004-1012, Sep. 1988) is extended. It is demonstrated that allowing for multiple symbols per trellis branch, i.e., multiple trellis-coded modulation (MTCM), provides an additional degree of freedom for designing a code to meet the optimization on the fading channel. Diversities larger than those achievable with conventional trellis codes having the same number of trellis states are now attainable, it is under these conditions that MTCM achieves its full potential     

The design of trellis coded MPSK for fading channels: performancecriteria

It has been well established that the appropriate criterion for optimum trellis-coded modulation design on the additive white Gaussian noise channel is maximization of the free Euclidean distance. It is shown that when the trellis-coded modulation is used on a Rician fading channel with interleaving/deinterleaving, the design of the code of optimum performance is guided by other factors, in particular, the length of the shortest error-event path, and the product of branch distances (possibly normalized by the Euclidean distance of the path) along the path. Although maximum free distance (d_free) is still an important consideration, it plays a less significant role the more severe the fading is on the channel. These considerations lead to the definition of a new distance measure of optimization of trellis codes transmitted over Rician fading channels. If no interleaving/deinterleaving is used, then once again the design of the trellis code is guided by maximizing d_free      

Analysis and design of trellis codes optimized for a binarysymmetric Markov source with MAP detection

We consider the problem of transmitting a binary symmetric Markov source (BSMS), over the additive white Gaussian noise (AWGN) channel. The coding technique considered is trellis-coded modulation (TCM), where we utilize decoders which implement the maximum-likelihood (ML) and maximum a posteriori (MAP) criteria. Employing 8-PSK Ungerboeck codes on a BSMS with state transition probability 0.1, we first show that the MAP decoder realizes a 0.8-2.1-dB coding gain over the ML decoder. Motivated by these gains, we consider the design of trellis codes optimized for the BSMS/AWGN/MAP system. An approximate union bound is established for this system. Using this bound, we found codes which exhibit additional 0.4-1.1-dB gains over Ungerboeck codes. Finally, we compare the proposed TCM system with a tandem coding system. At normalized signal-to-noise ratio (SNR) of 10.8 dB and below, the proposed system significantly outperforms the tandem system     

Multidimensional M-PSK trellis codes for fading channels

This paper investigates the code search problem for trellis-coded multidimensional phase modulation for Rayleigh fading channels. New set partitionings for multiple phase-shift keying (M-PSK) are proposed using the effective code length (ECL) and the minimum product distance (PD) as the code design criteria. By using these set-partitionings rules, new multidimensional codes which are optimum for Rayleigh fading channels are constructed. The proposed codes compare favorably with the existing multidimensional trellis codes on fading channels in terms of bit error performance. The bit error performance is evaluated by simulation     

Space–Time Codes From Structured Lattices

We present constructions of space–time (ST) codes based on lattice coset coding. First, we focus on ST code constructions for the short block-length case, i.e., when the block length is equal to or slightly larger than the number of transmit antennas. We present constructions based on dense lattice packings and nested lattice (Voronoi) shaping. Our codes achieve the optimal diversity–multiplexing tradeoff (DMT) of quasi-static multiple-input multiple-output (MIMO) fading channels for any fading statistics, and perform very well also at practical, moderate values of signal-to-noise ratios (SNR). Then, we extend the construction to the case of large block lengths, by using trellis coset coding. We provide constructions of trellis coded modulation (TCM) schemes that are endowed with good packing and shaping properties. Both short-block and trellis constructions allow for a reduced complexity decoding algorithm based on minimum mean-squared error generalized decision feedback equalizer (MMSE-GDFE) lattice decoding and a combination of this with a Viterbi TCM decoder for the TCM case. Beyond the interesting algebraic structure, we exhibit codes whose performance is among the state-of-the art considering codes with similar encoding/decoding complexity.      

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.     

Trellis-coded differential unitary space-time modulation over flat fading channels

Coding and modulation for multiple-antenna systems have gained much attention in wireless communications. This paper investigates a noncoherent trellis-coded scheme based on differential unitary space-time modulation when neither the transmitter nor the receiver know the channel. In a time-varying flat Rayleigh fading environment, we derive differentially noncoherent decision metrics and obtain performance measures for systems with either an ideal interleaver or no interleaver. We demonstrate that with an ideal interleaver, the system performance is dominated by the minimum Hamming distance of the trellis code, while without an interleaver, the performance is dominated by the minimum free squared determinant distance (a novel generalization of the Euclidean distance) of the code. For both cases, code construction is described for Ungerboeck-type codes. Several examples that are based on diagonal cyclic group constellations and offer a good tradeoff between the coding advantage and trellis complexity are provided. Simulation results show that, by applying the soft-decision Viterbi decoder, the proposed scheme can achieve very good performance even with few receive antennas. Extensions to trellis-coded differential space-time block codes are also discussed.     

满速率串行级联空时分组MTCM编码方法研究

该文研究了级联空时编码系统在编码增益,分集增益和传输能量效率的限定下最大化传输速率的问题,提出了一种在保留TCM编码方法校验位冗余的同时,还可获得满速率串行级联空时分组TCM编码方法。新方法通过引入具有不同功率分集因子的正交发射码字矩阵,并给出新的译码算法,从而使得新的编码方法在获得满速率的同时还可以获得满分集增益。分析和MATLAB仿真结果表明,在相同的编码状态数下,新方法在编码增益上比现有的满速率超正交空时分组编码方法提高1dB左右。