Performance of Block-Coding Systems When Transmitting Through a Ary Discrete Channel in the Presence of White Gaussian Noise

Abstract

The basic problem of transmitting digital (PCM) data with the least signal to noise ratio per bit of information is considered if the data is encoded into code words consisting of a finite number of symbols where each symbol belongs to an alphabet of N elements. For quantitative results the error probability of the decoded data has been taken as equal to or below one out of 10⁵ bits of information in the case where the transmitted symbols are corrupted by additive white Gaussian noise and are detected "symbol per symbol" by correlation methods. Mainly coherent detection is considered. After the derivation by a geometrical method of the upper bounds (based upon random coding) of the minimum signal to noise ratio per bit, the performance of several constructive code methods are compared with these bounds. The amount of hardware and the number of operations required respectively for encoding and for decoding the most promising class of codes (binary and N-ary Bose-Chaudhuri codes) are indicated. Considerations are given to synchronous demodulation requirements using a "Costas" phase lock loop type of demodulator.