Simulation of error sources in digital channels

A general approach to error-source simulation in digital channels is discussed. It is shown that the stochastic sequential machine (SSM) model is general enough to describe error-source statistics in digital communication channels. The SSM model is capable of describing both the correlation between errors in a channel (bursts of errors) and the correlation between errors in different channels (crosstalk). Physical causes of error burstiness in satellite channels are considered, and it is shown that the SSM model can account for differential encoding, scrambling, forward error correction, intersymbol interference, nonlinear signal distortion, adjacent channel interference, modem defects, etc. SSM models of the satellite channel with differential and convolutional codes are simulated. The results of simulation agree with the experimental data for the actual channels. Analytical methods for determining the performance characteristics of SSM-modeled systems are developed     

Burst error correction in high-speed digital mobile radio communications

In high-speed digital mobile radio communication, transmission performance is severely degraded by frequency-selective fading caused by the delay time spread of multipath propagation. Forward error correction (FEC) is one of the most effective techniques to improve transmission quality. The authors evaluate the effect of FEC on burst errors under frequency-selective fading. The FEC effect with diversity reception and interleaving is also investigated.<>     

Bursty error model for digital transmission channels

A simple statistical model is proposed which simulates errors on digital transmission channels and accommodates the tendency for errors to occur in bursts. The model only needs three parameters to be simulated, all of which can be measured from live channels of interest     

Burst error performance encountered in digital land mobile radio channel

Burst error characteristics are studied by using a Rayleigh and Nakagami-Rice fading simulator. Burst error length distribution estimated with fade duration is described. Thus burst length shortening by means of dual frequency diversity is a promising candidate in order to introduce safely forward error correction (FEC) coding into digital land mobile communication systems.     

Burst error statistics of simulated Viterbi decoded BPSK on fadingand scintillating channels

The author presents and analyzes burst error statistics of a soft-decision Viterbi decoder when the transmitted signal is encoded with the 313 (3, 1/2) or 31123 (5, 1/2) convolutional codes, modulated via coherent binary phase-shift keying (BPSK) for the additive white Gaussian noise (AWGN) channel, and subjected to slow and nonselective scintillation/fading modeled by the Nakagami-m distribution. These statistics were generated by Monte-Carlo simulations, and presented in terms of burst error length average and quantile (90 and 99%) statistics versus SNR (E_b/N₀) parameterized by the fading intensity parameter m. The results indicate how Viterbi decoder burst error statistics vary with the fading/scintillation intensity m for Nakagami-m channels, and, consequently, provide information important to the design of interleaved or noninterleaved concatenated coding schemes for such channel environments     

Jitter and error performance analysis of trellis coded M-PSK overpartial response fading channels

For the first time, a partial response fading channel is introduced. The new channel model acts in a similar way to partial response signalling (PRS) with a Rayleigh probability density function. Emphasis is given to jitter and error performances of M-PSK schemes in the proposed channel with ideal channel state information, but with no side information existing on the phase noise process. Analytical upper bounds are derived using the Chernoff bounding technique, combined with the modified generating functional approach. Simulation studies confirming analytically obtained curves are carried out     

Tight bounds on the error probability of coded modulation schemesin Rayleigh fading channels

This paper presents a tight upper bound on the bit error performance of coded modulation schemes in Rayleigh fading channels. Upper and lower bounds on the pairwise error probability are first derived. The upper bound is then expressed in a product form to be used with the transfer function bounding technique. This upper bound has the same simplicity as the union-Chernoff bound while providing closer results to the exact expression. Examples for the case of four-state and eight-state TCM 8PSK schemes are also given to illustrate the tightness and the application of this upper bound     

On multidimensional coded modulations having uniform error propertyfor generalized decoding and flat-fading channels

We consider the problem of uniform error property (UEP) for a coded modulation with constant energy multidimensional symbols, transmitted over the additive white Gaussian noise (AWGN) or fading channels and received by a broad class of decoders. This class includes coherent, partially coherent, double differential, and noncoherent decoders, decoders designed for fading channels, decoders using one or multiple-symbol observations, and many more. These decoders are described as special cases of a general decoder model. This decoder operates by maximizing an arbitrary likelihood function that its arguments are front-end correlator (matched-filter) outputs, A group code structure that guarantees UEP is developed by using the theory of geometrically uniform codes and applying it to the general decoder. These codes are defined over groups (commonly nonbinary) with isometric mapping to channel symbols. We show the code construction for the specific case of Lth-dimensional M-ary phase-shift keying (MPSK). An additional interesting property of these general uniform error codes is related to the case of noncoherent decoding. We show that when using codes of this family, if a code is noncoherently catastrophic, then it is also rotationally invariant. Then, the use of preceding of the input such that the code becomes rotationally transparent will also make it noncatastrophic     

Bit error probability of distributed Turbo coded relay systems over quasi-static Rayleigh fading channels

As is known, distributed Turbo coding (DTC) performs close to the theoretic outage probability bound of a relay channel when correct decoding is assumed at the relay. However, decoding error is inevitable in practical fading channels due to the error-prone feature of radio channels, and the decoding error propagation in DTC scheme will severely degrade the error performance of the relay system. As a result, it is necessary to evaluate the error performance of the DTC scheme in multi-hop relaying wireless systems in practical fading channels. Moreover, the theoretical method of analysis provides an effective tool for obtaining the error performance besides lengthy simulations. In this article, the concept of equivalent signal-to-noise ratio (SNR) of the two-hop relay channel and the method of computing equivalent SNR are developed, and then the upper bound on the bit error probability (BEP) of DTC relay systems is analyzed by use of Turbo code's distance spectrum, the concept of uniform interleaver, the limit-before-averaging technique, and the union bound method. Both theoretical analysis and numerical simulation are implemented for relay systems with DTC scheme over quasi-static Rayleigh fading channels. The results show that the upper bound approaches the simulation results in the medium to high SNR region.     

Markov characterization of digital fading mobile VHF channels

We apply techniques for the modeling of error sequences on digital communication channels to results of experiments undertaken on mobile VHF channels. The experiments were carried out using four different modulation schemes at some of the different standardized signaling rates. The modulation schemes used were: FSK @ 300 baud, DPSK @ 1200 baud, QPSK @ 1200 baud, and 8-ary PSK @ 1600 baud, and in each case, subcarrier modulation was used. The experiments were undertaken for urban as well as freeway environments. Fritchman-partitioned Markov chain models were derived throughout, and from the models, block error probability distributions were derived. These block error probability distributions or P(m,n) give the probability that a block of n bits will contain exactly m errors. We present P(⩾m,n) for 7-, 15-, 31-, 63-, 127-, and 255-b blocks, for the above-mentioned modulation schemes, in the mobile VHF environments mentioned. P(⩾m,n) denotes the probability that at least m errors will occur in a block of n bits. Furthermore, the P(⩾m,n) information presented here, should give some indication of the performance to be expected from block error-correcting schemes     

Bounds on the pairwise error probability of coded DS/SSMAcommunication systems in Rayleigh fading channels

Arbitrarily tight upper and lower bounds on the pairwise error probability (PEP) of a trellis-coded or convolutional-coded direct-sequence spread-spectrum multiple-access (DS/SSMA) communication system over a Rayleigh fading channel are derived. A new set of probability density functions (PDFs) and cumulative distribution functions (CDFs) of the multiple-access interference (MAI) statistic is derived, and a modified bounding technique is proposed to obtain the bounds. The upper bounds and lower bounds together specify the accuracy of the resulting estimation of the PEP, and give an indication of the system error performance. Several suboptimum decoding schemes are proposed and their performances are compared to that of the optimum decoding scheme by the average pairwise error probability (APEP) values. The approach can be used to accurately study the multiple-access capability of the coded DS/SSMA system without numerical integrations     

Improved performance of coded digital FM

The performance of convolutionally encoded narrow-band digital FM with Viterbi decoding was considered in some detail by Simon (1983) for a noncoherent limiter/discriminator (L/D) with integrate and dump (I&D) bit detection. Employing a new threshold receiver which averages the output of the I&D detector with the output of a sample and hold (S&H) detector, a 3-dB improvement over Simon's results for the bit error probability with FM clicks is shown to be achievable. At low error rates, the performance of this new receiver is, moreover, comparable to that obtained when the clicks are exactly removed by Simon's hypothetical “genie”     

Adaptive coded modulation for fading channels

We apply coset codes to adaptive modulation in fading channels. Adaptive modulation is a powerful technique to improve the energy efficiency and increase the data rate over a fading channel. Coset codes are a natural choice to use with adaptive modulation since the channel coding and modulation designs are separable. Therefore, trellis and lattice codes designed for additive white Gaussian noise (AWGN) channels can be superimposed on adaptive modulation for fading channels, with the same approximate coding gains. We first describe the methodology for combining coset codes with a general class of adaptive modulation techniques. We then apply this methodology to a spectrally efficient adaptive M-ary quadrature amplitude modulation (MQAM) to obtain trellis-coded adaptive MQAM. We present analytical and simulation results for this design which show an effective coding gain of 3 dB relative to uncoded adaptive MQAM for a simple four-state trellis code, and an effective 3.6-dB coding gain for an eight-state trellis code. More complex trellis codes are shown to achieve higher gains. We also compare the performance of trellis-coded adaptive MQAM to that of coded modulation with built-in time diversity and fixed-rate modulation. The adaptive method exhibits a power savings of up to 20 dB     

Hidden Markov models for burst error characterization in indoorradio channels

Many digital communication channels exhibit statistical dependencies among errors. The design of error control schemes for such channels and their performance evaluation is simplified if appropriate generative models of the overall communication link are available. This paper presents a new class of generative models based on the interconnection of hidden Markov submodels parameterized by the Baum-Welch algorithm. The method has some resemblance to the well-studied problem of speech recognition of isolated words; however, in our approach, instead of dealing with words, one deals with error bursts, and the final goal is to generate bursts rather than to recognize words. The proposed model is particularly suitable for simulating error profiles with long bursts, as is often the case in indoor radio channels, where the error-free gaps inside a burst are heavily nonrenewal. The merits of the method are corroborated by applying the technique to two particular examples of indoor code-division multiple-access (CDMA) radio links     

Burst error generator using flip-flop metastability

A novel burst error generator for communications systems testing is presented which is based on the phenomenon of metastability observed in flip-flops. Bursts can be created with predetermined bit error ratios by means of an external control voltage. The errors appear to follow a double Poisson distribution, characteristic of the Neyman type A contagious process     

Spectral analysis of variable-length coded digital signals

Spectral analysis is performed for a digital message produced by a variable-length encoder driven by a stationary memoryless source. In particular, closed form expressions are derived for both the continuous and the discrete part of the spectral density. The continuous part turns out to be a rational function ofz=exp (j2pi fT),whereTis the symbol period, whereas the discrete part exhibits in general spectral lines at multiple integers of(lambda_{0}T)^{-1}, wherelambda_{0}is the greatest common divisor of the codeword lengths. As an application of the theory explicit formulas are derived for the spectra of BnZS and HDBncodes.     

Use of error patterns in coded communication systems

In digital communication systems, receivers often have trouble in deriving the correct bit synchronisation from transitionless received signals. The letter shows that transitionless signals can come from four sources, and that this problem can be easily eliminated by injecting a detectable error pattern into the transmitted coded signal.     

Analysis of error performance on Turbo coded FDPIM

Due to variable symbol length of digital pulse interval modulation(DPIM),it is difficult to analyze the error performances of Turbo coded DPIM.To solve this problem,a fixed-length digital pulse interval modulation(FDPIM) method is provided.The FDPIM modulation structure is introduced.The packet error rates of uncoded FDPIM are analyzed and compared with that of DPIM.Bit error rates of Turbo coded FDPIM are simulated based on three kinds of analytical models under weak turbulence channel.The results show that packet error rate of uncoded FDPIM is inferior to that of uncoded DPIM.However,FDPIM is easy to be implemented and easy to be combined.with Turbo code for soft-decision because of its fixed length.Besides,the introduction of Turbo code in this modulation can decrease the average power about 10 dBm,which means that it can improve the error performance of the system effectively.     

Analysis of error performance on Turbo coded FDPIM

Due to variable symbol length of digital pulse interval modulation（DPIM）, it is difficult to analyze the error performances of Turbo coded DPIM. To solve this problem, a fixed-length digital pulse interval modulation（FDPIM） method is provided. The FDPIM modulation structure is introduced. The packet error rates of uncoded FDPIM are analyzed and compared with that of DPIM. Bit error rates of Turbo coded FDPIM are simulated based on three kinds of analytical models under weak turbulence channel. The results show that packet error rate of uncoded FDPIM is inferior to that of uncoded DPIM. However, FDPIM is easy to be implemented and easy to be combined, with Turbo code for soft-decision because of its fixed length. Besides, the introduction of Turbo code in this modulation can decrease the average power about 10 dBm, which means that it can improve the error performance of the system effectively.