On multiple interference error bounds

This letter presents upper and lower bounds for the error rate for (effectively) PAM signalling in the presence of thermal noise, cochannel interference, and intersymbol interference. To accomplish this, two known bounds and one new lower bound are used. For a class of examples from the literature, these simple bounds were found to provide an error-rate estimate accurate to 1 db in system SNR. Computational experiments indicate that this level of accuracy can be achieved when the system's eye is open by at least a factor of two.     

Near optimum error correcting coding and decoding: turbo-codes

This paper presents a new family of convolutional codes, nicknamed turbo-codes, built from a particular concatenation of two recursive systematic codes, linked together by nonuniform interleaving. Decoding calls on iterative processing in which each component decoder takes advantage of the work of the other at the previous step, with the aid of the original concept of extrinsic information. For sufficiently large interleaving sizes, the correcting performance of turbo-codes, investigated by simulation, appears to be close to the theoretical limit predicted by Shannon     

Distance upper bounds and true minimum distance results for turbo-codes designed with DRP interleavers

This paper presents a number of distance upper bounds for Turbo-codes designed with dithered relative prime (drp) interleavers. These bounds help determine how much dither should be applied and which input data patterns to test when designing high-distance interleavers with different lengths. Using a block length of only 640 data bits, true minimum distances of 30, 42 and 53 have been achieved for rate 1/3 Turbo-codes with 4, 8 and 16-state constituent codes, respectively. Simulated error rate results for a block length of 1504 data bits (188 bytes,mpeg packet) show excellent flare performance.     

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     

On the tightness of two error bounds for decision feedback equalizers

A new upper bound on the probability of error for decision feedback equalizers that is valid for serially independent and dependent stationary noise processes was presented by P. Kabaila (1987). It is shown that a bound of D.L. Duttweiler et al. (1974) is tighter than the bound of Kabaila when the noise component shows no serial dependence and with equalization over the full channel response length.<>     

New upper bounds on error exponents

We derive new upper bounds on the error exponents for the maximum-likelihood decoding and error detecting in the binary symmetric channels. This is an improvement on the best earlier known bounds by Shannon-Gallager-Berlekamp (1967) and McEliece-Omura (1977). For the probability of undetected error the new bounds are better than the bounds by Levenshtein (1978, 1989) and the bound by Abdel-Ghaffar (see ibid., vol.43, p.1489-502, 1997). Moreover, we further extend the range of rates where the undetected error exponent is known to be exact. The new bounds are based on an analysis of possible distance distributions of the codes along with some inequalities relating the distance distributions to the error probabilities     

Sharp error bounds for intersymbol interference

Sharp upper and lower bounds of the Chebyshev type are established for the probability of error due to intersymbol interference and additive Gaussian noise in a digital communication system. The results are in relatively closed form, and the only statistical knowledge assumed about the interference is the peak eye opening and the variance. The bounds apply to correlated and uncorrelated signals and for any signal to noise ratio.     

Dependence of the error performance of turbo-codes on theinterleaver structure in short frame transmission systems

The dependence of both bit and frame error performance, respectively, of the novel parallel concatenated recursive systematic codes, termed turbo-codes, on the interleaver structure is investigated in frame transmission systems with frames containing 192 bits required for speech transmission in a possible future mobile radio system     

Tight bounds on Rician-type error probabilities and someapplications

Consider the classic problem of evaluating the probability that one Rician random variable exceeds another, possibly correlated, Rician random variable. This probability is given by Stein (1964) in terms of the Marcum's Q-function, which requires numerical integration on the computer for its evaluation. To facilitate application in many digital communication problems, we derive here tight upper and lower bounds on this probability. The bounds are motivated by a classic result in communication theory, namely, the error probability performance of binary orthogonal signaling over the Gaussian channel with unknown carrier phase. Various applications of the bounds are reported, including the evaluation of the bit error probabilities of MDPSK and MPSK with differential detection and generalized differential detection, respectively. The bounds prove to be tight in all cases. Further applications will be reported in the future     

Group structure of turbo-codes

The author discusses the group property of turbo-codes when considered as a periodic linear system. It is shown that the interleaving procedure provides a homomorphism between different encoded sequences and thereby breaks the low weight sequences by a factor of, at most, 1/2^r, where r is the constraint length of the code     

Intersymbol-interference error bounds for hard-limited satellite channels

Upper and lower bounds on the probability of error for binary p.s.k. signals received over a hard-limited satellite channel in the presence of intersymbol interference are derived. Comparison with previously derived numerical results computed for a hard-limited channel containing a Chebyshev filter indicates that the bounds are reaionably tight.     

Quantization error bounds for hybrid control systems

A useful quantization error bound is obtained for hybrid digital-analog control systems. The error is bounded by a time-varying function that becomes zero if the digital computer has no time or ordinate quantization error. The error bound may either converge or diverge depending on the magnitudes involved. The analysis is valid for a hybrid computerization of a linear time-varying system. Sharp results for the constant coefficient case are presented.     

Tight error bounds for asynchronous multicarrier CDMA and theirapplication

Upper and lower bounds on the average bit error rate for binary phase-shift keying (BPSK), asynchronous multicarrier (MC)-CDMA communications using coherent detection are derived. The bounds can be made very tight by adjusting a parameter in the computation and this is demonstrated by numerical examples. Based on the derived bounds it is shown by numerical examples that the performance of asynchronous MC-CDMA using Zadoff-Chu sequences is better than that using Walsh codes     

A note on asymmetric turbo-codes

Little attention has been devoted in the literature to turbo-codes with nonidentical component codes. However, in order to optimize the performance of parallel concatenated schemes with respect to both the so called “error-floor” and the “waterfall” regions, the idea has certain advantages     

Bi-directional SOVA decoding for turbo-codes

In this letter, we present a bi directional SOVA-based decoding scheme for turbo-codes, which combines the soft-outputs provided by both forward and backward SOVA decodings. Importantly, we explain why this bi-directional decoding improves SOVA decoding. The simulation results show that bi-directional SOVA can achieve about the same performance as the Max-Log-MAP algorithm in turbo decoding     

Combined source-channel coding using turbo-codes

The authors present a new approach to combined source-channel coding based on using the reliability information available from the turbo-code channel decoder. Numerical results are presented for the transmission of the DCT coefficients of still images showing a noticeable improvement with respect to an ordinary, as well as a channel optimised quantiser     

Simulated cardinal series errors versus truncation error bounds

It is shown through simulations that the cardinal series yields larger truncation errors than a sampling expansion utilizing a convergence factor for certain cases of interest.     

Lower bounds on the mean square estimation error

A general class of lower bounds on the mean square error (mse) in random parameter estimation is formulated. These bounds are generated using functions of the parameter and the data that are orthogonal to the data. A particular choice in the class yields a new lower bound which is superior to both the Cramer-Rao and Bobrovsky-Zakai lower bounds.