The Computation of Error Probability for Digital Transmission

In a large class of digital transmission systems, a succession of amplitude modulated pulses is sent over a channel to the receiver. The signal suffers two main types of distortion: additive noise and intersymbol interference ( I S I ) . The latter arises from dispersion in the channel, and is a noise-like process due to the overlapping of m a n y neighboring pulses. 1 T h e number of these neighboring pulses, or "interferers," depends on the system impulse response, and can be rather large for systems with restricted bandwidth. To properly analyze a system one must compute its probability of error due to the noise and intersymbol interference. The effect of the additive noise is simple to analyze, but that of the LSI is extremely difficult to find due to the complicated nature of its probability density function ( p d f ) . The complexity of the pdf grows exponentially with the number of interferers, and for more than about 12 interferers the computation of error probability has long seemed impossible. 2055