On parallel and serial concatenated convolutional codes over GF(4)

We compare the asymptotic performance of parallel concatenated codes (PCCs) and serial concatenated codes (SCCs) over GF(4). We construct such codes using optimal nonbinary convolutional codes where optimality is in the sense of achieving the largest minimum distance for a fixed number of encoder states. Code rates of the form K₀/(K₀ + 1) for K₀ = 1, 8, and 64 are considered. For all of these code rates, we find the minimum distance and its multiplicity for both concatenated code systems. This is accomplished by feeding the encoder with all possible weight-two and weight-three input information patterns and monitoring, at the output of the encoder, the weight of the corresponding codewords and their multiplicity. Our analytical results indicate that the SCC codes outperform their counterpart PCC codes with much lower complexity.