Some Thoughts on the Equivalence of Systematic and Non-Systematic Convolutional Encoders∗

In this paper, we re-examine the notion of equivalent systematic and non-systematic convolutional encoders within the context of turbo coding. In particular, we argue that using equivalent systematic and non-systematic constituent encoders in a parallel concatenated system does not yield the same performance. In fact, the performance can differ greatly, depending on the effective free distance and the encoder mapping. Since non-systematic encoders typically have larger effective free distances than their systematic counterparts, they are better in the “error floor”, or low BER, region of the performance curve. On the other hand, since systematic encoders typically have better encoder mappings than non-systematic encoders, they are better in the “waterfall”, or high BER, region of the performance curve.