A hybrid automatic repeat request (ARQ) system (HARQ-II) with parity retransmission for error correction, which combines ARQ and forward error correction is discussed, and the successful application of these codes to HARG-II is illustrated. A method of constructing the codes whereby conventional BCH codes can be changed into separable codes is proposed. A scheme is presented that has the advantages that, the code lengths are always made equal and that even in parity retransmission new information symbols can be sent along with the necessary parity-check symbols. The performance of the proposed schemes on the binary symmetric channel is discussed. The numerical results show that they outperform conventional schemes.>

By modifying product codes, a new coding scheme and its decoding method are proposed. Compared to a product codeA, the first stage codeA_{1}of the new codeA_{M}is constructed in the same way as that of the codeAexcept that it has at least one subcode, while the second stage codesA_{2}^{(j)}of the codeA_{M}are a set of codes With the same length and different rates. The new coding scheme has a smaller upper bound on the probability of decoding error than the original product coding scheme for any given nonzero rate less than the capacity of a binary symmetric channel. An example is given for which the rate is increased compared With the original product code, at a fixed probability of decoding error, for a relatively short code length.

The asymptotic performance of variance-mismatched vector quantizers is presented. It is demonstrated by both asymptotic analysis and computer simulations that well-designed vector quantizers are inherently more invulnerable to mismatch than are conventional scalar quantizers. A generalized exponential density function is considered as a statistical model of sources. As an example, the asymptotic performance is derived and applied to the memoryless Laplacian source with the squared-error distortion measure.

Double symbol error rates ofM-ary differentially coherent phase shift keying (DPSK) systems in a satellite-aircraft multipath channel are evaluated. A joint probability density function (pdf) of two consecutive differential phase errors in the DPSK outputs is newly derived. Numerically calculated results are shown in figures for binary, quaternary, and octonary DPSK systems. It is further shown that the analytical values agree well with the data observed by ATS-5 experimental tests.

We interpret Reed-Muller codes in terms of superimposition and present a new decoding algorithm for Reed-Muller codes. Before presenting this algorithm, we propose a decoding algorithm for a class of simple iterated codes (SI codes) that will play an important role in our new decoding algorithm. Finally, we compare our algorithm with the conventional algorithm for the cyclic Reed-Muller codes from the standpoint of decoding delay.

The lower bound m the error exponent for the generalized version of concatenated codes is shown to be improved at low rates for binary-input memoryless channels.

New coding and decoding schemes based on concatenated codes are proposed. The new coding schemes are potentially superior to Forney's original concatenation scheme in the sense that for discrete memoryless channels the former has a smaller upper bound on the probability of decoding error for the same order of decoding complexity.

Binary block codes are constructed that are capable of correcting successive timing errors such as the deletion or insertion ofsbits(s\leq D)within a single additive burst of errors of lengthbor less(b=f+g+2D), wherefandDare the design parameters that specify the length of correctable successive timing errors andgis the length of the correctable additive burst. A decoding algorithm is given and the efficiency of these codes is discussed.

A family of codes of lengthn=q^{s+l}over GF(q), with2s \leq qare presented which are constructed by superimposing concatenated codes on a concatenated code. The raterand the distance ratio\deltaof the new codes satisfy the relationr=1-\delta+\delta \ln (\delta)for sufficiently large values ofnandq/s. The new codes are superior to the comparable Bose-Chaudhuri-Hocquenghem (BCH) codes, fors\geq 3, in the sense that they contain more codewords. An asymptotically good code constructed using these new codes has a distance ratio greater than those of other asymptotically good codes known to the authors for rates smaller than 0.007.

Error control techniques in the various digital data transmission systems can be divided into three classes, i.e., classes of forward error correction (FEC), automatic repeat request (ARQ), and FEC embedded within ARQ (Hybrid). We exactly analyze and compare the performances of these error control techniques in both independenterror and dependent-error channels. It is shown that among the various error control techniques the Go-Back-2 ARQ system offers the best performances over a wide range of the channel error rate, i.e.,P_{e} \lsim 10^{-4}, regardless of the type of the channel. The various numerical results are shown graphically along with the discussions.

The average error probabilities and outage rates of error probability for theM-phase CPSK signal through the Nakagami'sm-distributed fading channel are exactly evaluated both for nondiversity reception and for diversity reception. The probability density functions of the composite phase of fading signal and noise and those of the diversity-combined signal envelopes are newly derived in this paper. The results are generally obtained including the digital phase modulation component, the fading figure as a measure of fading depth, the average carrier-to-noise power ratio, the power correlation coefficient between two diversity branches, etc. The diversity improvements are also verified. Additionally some useful approximate formulas are briefly shown. This study will add a newly widened view to the considerations of system performances and designs for digital radio communications via fading channels.

A new class of asymptotically good codes is constructed by iteratively superimposing Justesen codes on a Justesen code. The lower bound for the new codes lies above the Zyahlov bound for rater, 0.31 < r < 1.

A simple Markov chain model for differentially encoded CPSK Channels faciliates the calculation of the probability of the occurrence of several most probable error patterns in a given codeword. Several error correcting codes which can efficiently correct several most-probable error patterns are proposed and their error performances are analyzed.

Finite-state Markov chain models are proposed to represent the process of the occurrence of errors in differential phase-shift-keying (DPSK) systems and also in coherent phase-shift-keying (CPSK) systems with differential coding-and-decoding schemes. A simple and general formula is derived for the probabilityP(m,n)of the occurrence of m errors in a sequence ofndigits which is the fundamental error statistic required to evaluate random-error-correcting codes applied to these channels.

This paper provides a general analysis of the transmission characteristics of a coherent PSK signal, where anM-ary coherent signal is transmitted via a repeater system composed of a cascade ofNbandpass hard limiters. The probability density function of a composite phase of the signal and noise over the system is newly derived to obtain an error probability. In addition, the comparison with the repeater system composed of a cascade ofNlinear amplifiers is made to clarify the features of the transmission characteristics. It is found that the probability density function of the composite phase over the system is symmetric about each input carrier-to-noise power ratio (CNR), and it reduces to some well-known results. It is also shown that for a reasonably large input CNR in each stage, the presence of the bandpass hard limiter (BPHL) provides some improvement, but that for small input CNR it causes degradation in performance.

We present new classes of binary codes that are constructed on the basis of concatenated codes and product codes. We discuss the random-error-correction capabilities of these codes. Some examples of the codes for the correction of random errors are given which have at least as many codewords as the best codes previously known (to the authors) with the same minimum distance and same number of check symbols. The burst-error-correction capabilities of the codes are also discussed. Several examples of the codes for the correction of both random errors and burst errors are given. A decoding algorithm for the codes is also described.

An erasures-and-errors decoding algorithm for Goppa codes is presented. Given the Goppa polynomial and the modified syndrome polynomial, a modified key equation is solved using Euclid's algorithm to determine the error locator polynomial and the errata evaluator polynomial.

It is shown that Goppa codes with Goppa polynomial\{g(z)\}^{q}have the parameters: lengthn \leq q^{m} - s_{o}, number of check symbolsn - k \leq m (q - 1) (\deg g), and minimum distanced \geq q (\deg g) + 1, whereqis a prime power,mis an integer,g(z )is an arbitrary polynomial overGF(q^{m}), and so is the number of roots ofg(z)which belong toGF(q^{m}). It is also shown that all binary Goppa codes of lengthn \leq 2^{m} - s_{o}satisfy the relationn - k \leq m (d - 1)/2. A new class of binary codes withn \leq 2^{ m} + ms _{0}, n - k \leq m (\deg g) + s_{0}, andd \leq 2(\deg g) + 1is constructed, as well as another class of binary codes with slightly different parameters. Some of those codes are proved superior to the best codes previously known. Finally, a decoding algorithm is given for the codes constructed which uses Euclid's algorithm.

In this correspondence, we present a new class of binary codes that are constructed on the basis of BCH codes. Some examples of these codes are given, having more codewords than the best codes previously known (to the authors) with the same minimum distance and number of check symbols. A decoding algorithm for the codes is also described.

In this correspondence, we construct a new class of binary codes by exploiting the symmetry properties of the parity check matrix of the Srivastava codes. The construction is a generalization of Goppa's construction [1]. A number of the binary codes constructed are proved equal, or superior, to the best codes previously known.

Signal-to-noise ratios (SNR's) at the output of the squarelaw detector are determined as the functions of modulation degree and bandwidth ratio of the modulating signal and the noise carrier, when the input is an amplitude-modulated noise carrier.

Signal interaction is analyzed when the composite signal of a simultaneously amplitude- and angle-modulated wave, a nonmodulated sinusoidal wave, and a noise is added to a half-wave linear mixer. If a certain mixing condition is satisfied, a half-wave linear mixer operates like an ideal bandpass limiter with frequency conversion function. The limiter action is also verified by experiment.

An analysis is presented on the output signal-to-noise ratios for the FM correlation systems having an FM detector in each input channel of a conventional correlator. The input consists of a frequency-modulated signal combined additively with stationary narrow-band Gaussian random noise. A general expression is derived for the output signal-to-noise ratio. A detailed calculation is made for the output signal-to-noise ratios when each input signal is a carrier frequency-modulated by a Gaussian random process and the integrating filter is of RC low pass. The dependence of the output signal-to-noise ratios on several parameters is discussed.

By the term "FM correlation system," we mean the analog correlation system that consists of two channels, each containing an FM detector. Expressions are derived for the output of the FM correlation system for the following cases. Each channel input to be correlated is a conventional FM signal plus Gaussian noise; and each input is an amplitude-limited or a nonlimited narrow-band Gaussian random signal plus Gaussian noise. The effect of the input carrier-to-noise power ratios is made clear. The features of the FM correlation system are shown in comparison with a conventional correlation system. In addition, a detailed analysis of the effect of the envelopes of the narrow-band Gaussian random signals on the output is presented.