On computing undetected error probabilities on the Gilbert channel

Two methods for computing the probability of undetected error on the Gilbert (1960) channel are examined. First, using a method proposed by Kittel (1978), we study some standard cyclic redundancy codes and compare the results with those on the binary symmetric channel. Then we consider a general method of approximate code evaluation, proposed by Elliott, which involves P(m, n), the probability of m errors in a block of length n bits. A nonrecursive technique for computing P(m, n) on the Gilbert channel is described     

On the symbol error probability of maximum-selection diversityreception schemes over a Rayleigh fading channel

The symbol error probability of two selection schemes, namely, maximum signal-to-noise ratio (Mγ) selection and maximum output (MO) selection, for M-ary multidiversity reception over a Rayleigh fading channel are discussed. The symbol error probability of the MO scheme is lower than that of the Mγ scheme. The more diversity receptions that are used, the larger is the difference. A simple expression of crossover average signal-to-noise ratio (per bit) is presented as a guideline for increasing the number of diversity receptions     

Symbol error probability for guided scrambling over a recording channel

We derive expressions for the symbol error probabilities for a recording code concatenated with a Reed-Solomon (RS) code. The recording code is structured by a guided scrambling (GS) code for the direct current (DC) suppression in conjunction with a runlength-limited (RLL) code. As for the GS codes, convolutional GS and Galois field (GF) addition GS schemes are examined. As for the RLL codes, two types of RLL codes are investigated. One is a traditional RLL code where a bit length m of an RS symbol is an integer multiple of a bit length p of an RLL source symbol. The other is a new type of high-rate RLL code where p>m. We compute the RS symbol error rates when these RLL codes are combined with the two GS schemes.     

On error probabilities of DS-CDMA systems with arbitrary chipwaveforms

The error probabilities of asynchronous DS-CDMA systems using random signature sequences depend on the number of users, the processing gain and the chip waveforms employed. The exact calculation of the error probabilities is computationally difficult and therefore approximations and bounds are more commonly used. In this article, the improved Gaussian approximation proposed by Holtzman (1992) is extended to include arbitrary chip waveforms. Comparisons to the exact calculation and the standard Gaussian approximation are also made to evaluate the accuracy of the improved Gaussian approximation     

On the error probability of decision-feedback differential detection

We give a tight approximation for the bit-error rate (BER) of decision-feedback differential detection (DF-DD). The influence of error propagation is modeled by a Markov chain. A simple state reduction method is proposed to limit computational complexity. Our results show that error propagation strongly depends on the chosen feedback filter. In particular, the popular assumption that error propagation increases BER by a factor of two is not always justified.     

采用最小成对误码率设计准则的MISO干扰信道波束形成

本文针对MISO干扰信道的瞬时波束形成的设计问题开展研究.现有的研究都是基于最大速率和准则,没有考虑通信质量.本文以通信质量优先为出发点,基于最小成对误码率准则设计MISO干扰信道的瞬时波束形成向量,建立了问题模型并推导了求解方法.通过仿真实验对两种设计准则下的最优波束形成向量进行了比较,结果表明两种方法得到的最优波束...     

On the bit error probability of QAM modulation

This paper presents some closed-form bit error probability expressions for coherent demodulation of both Gray coded and differentially decoded Gray coded QAM modulations in nonfading and frequency nonselective Rayleigh fading channels. These results demonstrate that as QAM constellation sizes get larger the BEP degradation due to differential encoding and decoding becomes negligible.     

On the decoder error probability of block codes

By using coding and combinational techniques, an explicit formula is derived which enumerates the complete weight distribution of decodable words of block codes using partially known weight distributions. Also, an approximation formula for nonbinary block codes is obtained. These results give exact and approximate expressions for the decoder error probability P_E(u) of block codes     

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     

On the undetected error probability for binary codes

In this paper, the undetected error probability for binary codes is studied. First complementary codes are studied. Next, a new proof of Abdel-Ghaffar's (1997) lower bound on the undetected error probability is presented and some generalizations are given. Further, upper and lower bounds on the undetected error probability for binary constant weight codes are given, and asymptotic versions are studied.     

On symbol error probability bounds for ISI-like channels

Some issues with Forney's upper and lower bounds (1972) for the symbol error probability in systems with memory (e.g., intersymbol interference channels) have been pointed out in the literature. We expound on these issues. For the upper bound, we show that, although the most commonly cited proofs are not logically consistent, the bound is true for more general conditions. The reasoning leading to the lower bound is shown to be flawed and, in general,to lead to invalid lower bounds. We suggest a lower bound based on Mazo's bound (1975) as an alternative     

Average error probability for quadriphase modulated DS-SSMA communications through Nakagami fading channel

An asynchronous direct sequence spread spectrum multiple access system using quadrature phase shift keying modulation through Nakagami'sm-distributed fading channel is considered for nondiversity reception. Approximation to the average error probability is evaluated in two steps. Using the Gauss quadrature rule, the moments of the multiple interferences are used to evaluate the conditional probability conditioned on a fixed fading amplitude of the desired signal. The probability density function of the desired signal is Nakagami distributed. The average error probability which is the expected value of the conditional probability is evaluated by the trapezoidal integration method. This method provides a good approximation to the average error probability for a small to a fairly large number of users. Numerical results are presented for a set of Gold code of code length 127.     

On the probability of error in linear multiuser detection

The problem of determining the bit-error probability in linear multiuser detection analytically is considered. A number of upper and lower bounds are developed, some of which are very tight, and issues of asymptotic behavior, optimality, and Gaussian approximation are explored. Several special cases, including those of equi-energy and equi-correlated signals, are treated in some detail.     

On divergence and probability of error in pattern recognition

An upperbound on the probability of error in classifying a pattern using Bayesian decision criterion is obtained in terms of its divergence and it is shown that the maximization of the divergence of the pattern minimizes this upperbound. Furthermore, a relationship between the divergence of a pattern and its nearest neighbor classification risk is presented.     

On the error probability of coded frequency-hopped spread-spectrummultiple-access systems

A simple, exact calculation is presented of the probability distribution of the number of hits in a block of n symbols in a frequency-hopped, spread-spectrum, multiple-access communication system. While the sequence of hits is not Markovian, there is an underlying Markovian structure that allows the probability distribution of the number of hits to be calculated in a recursive fashion. Knowing the probability distribution of the number of hits makes it possible to calculate the probability of error for a system employing error correcting codes for several different types of receivers, including receivers with both errors and erasures. The numerical results show that both the approximation obtained by assuming the actual sequence of hits is Markovian and the approximation obtained by assuming the hits are independent are very good. When the number of frequency slots is not too small (less than five), calculations show that assuming the independence of hits gives an error probability accurate to within 1% of the actual error probability. Assuming the hits are Markovian gives error probabilities which are accurate to within 0.001%     

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     

Lateness probability of a retransmission scheme for error controlon a two-state Markov channel

In this paper, we study the performance of a simple retransmission-based error-control strategy for delay-constrained data communications over a bursty channel. Correlated errors are modeled as a two state Markov process. A retransmission algorithm is used to correct errors, and the probability that a packet is not successfully delivered within D slots of its arrival is computed. In the presence of a smoothing buffer at the receiver, this is the probability that the jitter experienced by a packet is too large to be absorbed by the buffer itself. The cases of zero and nonzero roundtrip delay are studied separately, as are the conditions of perfect and imperfect feedback. Our results relate the achievable quality of service and the amount of traffic that can be served to the packet-error process parameters, which in turn are induced by the physical layer specifications. This relationship between the traffic and the channel parameters can be useful in making admission control decisions and in assessing the effect of physical layer design on the performance of higher layer protocols     

Upper bound on the bit error probability of TCM overfrequency-selective Rayleigh fading channel

A new upper bound on the bit error probability using Chernoff's bound of trellis code modulation (TCM) is introduced. It can be applied to a frequency-selective Rayleigh fading channel. The bound indicates a new design criterion, which is the product of the intersymbol interference (ISI) distance     

Symbol error probability of two-dimensional signaling in Ricean fading with imperfect channel estimation

In this paper, a general analytical framework is developed for calculating the symbol error rate of two-dimensional (2-D) signaling in Ricean fading with imperfect channel estimation. We show that in the presence of channel estimation errors, the symbol error rate of arbitrary 2-D signaling in Ricean fading can be expressed as a two-fold proper integral with finite integration limits, which is suitable for numerical evaluation. This new analysis is applicable to any channel estimation scheme where the estimated and the actual channel gains are jointly complex-Gaussian. System parameters related to specific channel estimation schemes are optimized and the effect of Doppler frequency shift in the channel line-of-sight component on the error performance is investigated using our analysis.