The tracking problem in identification of certain classes of time-varying nonlinear systems is addressed. In particular, a Hammerstein type system which consists of a nonlinear part, given on a state space description, followed by a time-varying linear part is considered. A recursive prediction error method, RPEM combined with a method for on-line adjustment of the forgetting factor is proposed. This algorithm does not require estimation of the statistics of the noise and the dynamics of the true system. It is shown how the proposed scheme can be used for identification of certain nonlinear time-varying acoustic echo paths. Thus, the suggested algorithm is applicable to for instance, conference telephony and mobile telephone handsfree.

Channel codes where the redundancy is obtained not from parity symbols, but from expanding the channel signal-set, are addressed. They were initially proposed by G. Ungerboeck (1982) using a convolutional code. Here, a block coding approach is given. Rate m/(m+1) coded 2/sup m+1/-ary phase-shift keying (PSK) is considered. The expanded signal-set is given the structure of a finite field. The code is defined by a square nonsingular circulant generator matrix over the field. Binary data are mapped on a dataword, of the same length as the codewords, over an additive subgroup of the field. The codes using trellises are described, and then the Viterbi algorithm for decoding is applied. The asymptotic coding gain ranges from 1.8 to 6.0 dB for QPSK going from blocklength 3 to 12. For 8-PSK, the gain is from 0.7 to 3.0 dB with blocklength 4 to 8. With only four states in the trellis, codes of any length for QPSK and 8-PSK are constructed, each having an asymptotic coding gain of 3.0 dB. Simulation results are presented. It is found that the bit-error rate performance at moderate signal-to-noise ratios is sensitive to the number of nearest and next-nearest neighbors.>

A common problem in many situations is to identify changes in the statistics of a stochastic process. This paper is concerned with detection of sudden changes in spectral properties. Several detection variables based on the estimated parameters and on the residual signal after inverse filtering have been compared by means of computer simulations. The signals studied were generated by a true AR-process.

With DPCM, it is advantageous to adapt the quantizer characteristic to the signal. We have studied several schemes where a gain constant is controlled by either forward or backward estimation. With forward estimation, the gain is calculated on a two-dimensional block of data, and we have studied how the form and size of the block affects performance. With backward estimation, the Jayant algorithm has been extended from one to two dimensions by letting the change in gain constant depend upon prediction errors from neighboring elements on the present and previous line. Simulations are performed on a sequence of pictures from a monochrome videophone scene with very active movement. The improvement in mean square error with adaptive control is between 2 and 5 dB compared to the performance with a uniform fixed quantizer. The subjective improvement is substantial.

A recursively updated lattice filter has been used for detection of non-stationarities in stochastic processes. Detection of these may be based either on the residual or the filtercoefficients. A decision variable defined from the filter-coefficients has been found promising in application of the algorithm to seismic signals and to electroencephalograms.

The object of this work has been to study encoding of monochrome pictures with a rate of about 1 bit per picture element (pel). Differential pulse code modulation, DPCM, has been chosen to make the system reasonably simple. This motivates the choice of a fixed three-dimensional predictor made separable in time and space. It essentially amounts to encoding the frame difference using a two dimensional predictor. To improve performance, the quantizer is made adaptive and the encoding is combined with delayed decision. A three-level quantizer is being used with an adaptive scheme that works with either forward or backward estimation. The output from the DPCM unit is redundant and we have adopted entropy coding to further reduce the bit rate. The entropy measure is also used to adjust the quantizer parameters to achieve the desired bit rate of 1 bit/pel. Encoding experiments were carried out on a complex videophone scene by means of computer simulations.

Data transmission with combined amplitude and phase modulation is considered with signal design carried out in a four-dimensional space of two amplitude and two phase variables. The energy for each signal is fixed. Quaternions are used to represent signal vectors and an algebra for quaternions is introduced which allows distance between signal vectors and equivalence between signal codes to be defined. It is also used to characterize the structure of codes. Code construction is based on regular four-dimensional polytopes and particular interest is focused on group codes with 8, 24, 48 and 120 elements. Two classes of phase modulated signals have interest as reference codes. Code evaluation is carried out by calculation of the distance distribution and the error probability assuming opitmum coherent detection. The group codes are found to be between 1.3 and 3.4 dB better than the best phase modulated codes. By using a suitable representation for a signal code it may be realized by using a few amplitude and several phase values.

This concise paper is concerned with the problem of improved delta-coding by using delayed decision instead of bit-bit-by-bit decision. It is found that delayed encoding allows a fairly general predictor to be used without causing instability problems. Simulations indicate that considerable improvement can be achieved by matching the feedback filter to the input process. Delayed encoding requires a search algorithm for making the decisions. Some proposals of algorithms that are efficient from a computational point of view are presented. Particular interest is attached to a highly truncated version of the Viterbi algorithm, which seems very promising.

Communications research in Sweden covers the following subjects: digital PAM, equalization of data channels, digital line links, modulation and transmission analysis, signal measurements and detection, time variable and nonlinear filters, group codes, source approximation, sequential decoding, and shift register sequences.

A class of adaptive schemes for delta modulation is considered whereby the decision about step size is a function of the present and the lastksymbols. Such schemes are studied by computer simulations using speech-like signals through evaluation of SNR. Occasional large overshoots appear in the reconstructed signal after the integrater, and to avoid such events it is proposed to store a few signal samples and decide on the proper bit stream taking into account the adaptive logic. Two quadratic criteria have been tried, and improvements of a few decibels have been established with six stored signal samples and a sampling rate of 48 and 24 kHz. Results indicate that other criteria functions may achieve still higher values of SNR.

A system transmits data as phase-modulated signals over a noisy channel. In each ofrsubintervals the carrier phase has one ofppossible values wherepis a prime number. The firstkphase coordinates are specified by the information source while the otherr-kcoordinates are derived through a linear coding scheme in a polynomial field ofM = p^{k}elements. The receiver contains a phase detector and a decoder that operates algebraically on quantized phase values using a polynomial representation. It explores the fact that a correctable error must contain at least one member of a small set of error polynomials. The probability of a decoding failure and the required amount of computation is studied in detail whenp = 3. The average amount of computation is small for codes of moderate length but at a certain critical length it starts to increase exponentially. Numerical results on the probability of a detection failure is available whenp = 3and5forM < 1000. They show a degradation in SNR of more than3dB compared to an ideal detector.

A new class of codes is defined and analyzed when applied to a communication system that sends data over a bandlimited Gaussian channel. A code word is defined as a sequence ofr-phase values and transmitted either modulated on a carrier or transformed inton = 2rsamples on a baseband channel. An algebraic procedure is used to generate the phase sequence from a set ofpequidistant angles. The baseband model is analyzed in detail and the performance is evaluated by first assuming an ideal detector and computing an error-probability bound. Takingp = 61,73, and97, codes are shown to exist that perform close to the theoretical limit. The algebraic structure of these codes much simplifies the numerical analysis. A second receiver is defined that extracts phase values out of the received waveform and then performs a suitable quantization. The degradation of this detector appears to be moderate for low information rates when evaluated forp = 61. A carrier phase-modulated system is also defined and evaluated with a performance quite similar to the baseband model.

A class of shift-register codes is studied for correction of multiple errors. The defining matrix will satisfy an irreducible polynomial equation with coefficients 0 or 1. The errors are classified in terms of error cycles and a simple procedure is suggested to determine if error cycles are distinguishable. To facilitate the analyses, another classification of errors is introduced leaving the number of erroneous digits (weight) invariant. A number of specific codes have been investigated either for correction of error bursts or correction of all multiple errors of certain weights. Burst lengths 2, 3, 4, 5 and 6 are tried, mainly with as long codes as are theoretically possible. Codes are found for burst lengths 2, 3 and 4. The degree of the polynomial varies from 6 to 18 giving a wide range of code lengths. With single and double adjacent errors, a sufficient condition is given for the existence of a code of maximal theoretical length. Correction of all single and double errors in a code of length2^p + 1is studied in some detail. As a special case of triple error correction, the Golay code of length 23 also is analyzed. Finally these and other known examples of shift-register codes are compared with the result of an exhaustive search for suitable polynomials of degrees 8, 9, 10 and 11.

With application to radar and data transmission, a game situation is studied where one player selects a suitable receiving filter, and the other a function describing the noise power density under restriction of a fixed total amount of power. The payoff function is a signal to noise ratio. The information the players have about each others' choice defines two extreme situations of practical interest. The fundamental relation of game theory holds for pure strategies.