Asymptotic performance comparison of concatenated (turbo) codes over GF(4)

In this paper, we investigate and compare the asymptotic performance of concatenated convolutional coding schemes over GF(4) over additive white Gaussian noise (AWON) channels. Both parallel concatenated codes (PCC) and serial concatenated codes (SCC) are considered. We construct such codes using optimal non-binary 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, which suite a wide spectrum of communications applications. For all of these code rates, we find the minimum distance and the corresponding 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 considerably outperform their counterpart PCC codes at a much lower complexity. Inspired by the superiority of SCC codes, we also discuss a mathematical approach for analysing such codes, leading to a more comprehensive analysis and allowing for further improvement in performance by giving insights on designing a proper interleaver that is capable of eliminating the dominant error patterns.