Turbo Decoding Using the Sectionalized Minimal Trellis of the Constituent Code: Performance-Complexity Trade-Off

The performance and complexity of turbo decoding using rate k/n constituent codes are investigated. The conventional, minimal and sectionalized trellis modules of the constituent convolutional codes are utilized. The performance metric is the bit error rate (BER), while complexity is analyzed based on the number of multiplications, summations and comparisons required by the max-log-MAP decoding algorithm. Our results show that the performance depends on how the systematic bits are grouped in a trellis module. The best performance is achieved when the k systematic bits are grouped together in the same section of the module, so that the log-likelihood ratio (LLR) of the k-bit vector is calculated at once. This is a characteristic of the conventional trellis module and of some of the sectionalizations of the minimal trellis module. Moreover, we show that it is possible to considerably reduce the decoding complexity with respect to the conventional trellis if a particular sectionalization of the minimal trellis module is utilized. In some cases, this sectionalization is found within the best performing group, while in some other cases a small performance loss can be traded off for a large complexity reduction.