The Effect of a Precoder on Serially Concatenated Coding Systems with an ISI Channel

The performance of a serially concatenated system which includes a channel with memory preceded by a precoder as a rate one inner coder is presented. The effect of different precoders on the maximum Like-lihood bit error performance is analyzed. the precoder weight gain, which explains the good bit error rateperformance, is identified through a union bound analysis. Precoders are divided into two groups based onan analysis of the Euclidean distance and its multiplicity, and each precoder group shows a distinct bit error rate curve behavior. It is shown that the bit error rate curves for two precoder groups cross over each other. Convolutional codes and block codes are considered as outer codes in simulations on various ISI Channels. Several important design considerations for the choice of precoders are derived based on the analysis and these are confirmed through simulations with an iterative decoding algorithm.