An algorithm for reversible data compression based on predictive coding is presented. From the input data, a sequence of integer-valued residuals is generated by a linear or nonlinear operation. The size of the alphabet for residuals is reduced by performing a modular operation on its symbols. The reconstruction process recovers the original data exactly. The modular operation results in a smaller-size codebook and prevents data expansion when the source is not matched to the code. For the encoder designed for compression of ECG (electrocardiogram) signals studied in an example, the encoded data volume was 78% larger than the input data volume when the input signal was white noise with a uniform amplitude distribution. For modular prediction, the expansion was reduced to 45%. The modular operation also reduces the entropy of the residuals, which theoretically should result in a higher degree of data compression, but this seems to be of little practical significance.>

A multiuser system employing on-off FSK modulation in conjunction with frequency hopping is examined for digital transmission. The receiver consists of a bank of bandpass noncoherent detectors followed by a message decoder. An analysis is presented for a transmission channel characterized by Rayleigh fading and additive Gaussian noise. The main source of impairment is interference between users. An upper limit on the number of simultaneous system users for acceptable transmission quality is derived. An example of a system with (one-way) bandwidth of 20 MHz and transmission rate of 32 kbits/s per user shows a maximum of 169 users at an average SNR on the channel of 25 dB and a bit error probability not exceeding 10-3. The effect of applying error correcting codes to the system is evaluated. It is shown how Reed-Solomon codes can be used to generate both user identification and message coding. Such coding increases the number of users the system can accommodate in the example above to 212. Convolutional codes are shown to be even more effective. Such a code of constraint length 2 results in 285 simultaneous users in the example, which is an increase of 70 percent over an uncoded system. The drawback of coding is an increased complexity of the receiver. The amount of computation needed for the decoding of block and convolutional codes is estimated.

A modified algorithm for an adaptive quantizer is proposed. The algorithm is of the backward estimating type and no additional information needs to be transmitted to the receiver. An analysis in terms of central step size behavior and mistracking caused by transmission errors is presented. In addition, the signal-to-distortion ratio is estimated by computer simulations. It is shown by an example that the new algorithm can result in a system with an extended dynamic range and the same approximate transmission error performance as a conventional robust algorithm.

A necessary and sufficient condition is presented for an input signal alphabet to optimize the random coding exponent for a time-discrete channel with signals restricted in amplitude. It is applied to the white noise Gaussian channel for signals in one and two dimensions. By use of this theorem the best input signal quantizafion is determined by numerical optimization. Results are presented on the number of amplitude or envelope levels needed to maximize the error bound parameter R0at different signal-to-noise ratios. For one-dimensional (baseband) signals a binary antipodal configuration is optimum, in the sense of maximizing R0, for signal-to-noise ratios below 6.9 dB. For two-dimensional (passband) signals with limited envelope, phase modulation is shown to be optimum for signal-to-noise ratios below 7.35 dB.

This paper deals with soft decision as a means to bridge the gap in performance between a receiver using hard decision symbol estimation followed by an algebraic decoder and a maximum-likelihood receiver. A measure of the reliability of the code symbol estimates is introduced to facilitate the decoding process. The decoding operation studied erases the least reliable received symbols and then applies an algorithm capable of correcting errors and erasures. This procedure, termed successive-erasure decoding (SED), was introduced by G. D. Forney in connection with general minimum-distance decoding (GMD). It is studied for binary and nonbinary transmission using polyphase signals on the additive white Gaussian noise (AWGN) channel. The exponential behavior of the error probability at high signal-to-noise ratio (SNR) is calculated and is supplemented by computer simulations. The results indicate that soft decision by successive erasures for binary transmission has properties not present in the nonbinary case. In the binary case the procedure is asymptotically optimum for increasing SNR's. On the nonbinary channel, however, the procedure is only capable of bridging part of the gap in performance between maximum-likelihood decoding (MLD) and hard decision decoding (HDD).

This correspondence points out that theN-orthogonal codes of Reed and \footnote[1]{Scholtz} are equivalent to time-shifted phase-modulated signals. This leads to a simple geometric derivation of the probability of error and also directly determines the minimum distance of the code.