Some Properties of Homogenous Trellis-Constrained Codes

We consider Homogenous Trellis-Constrained Codes (HTCC), a generalization of Turbo-codes where all bits are constrained. No efficient decoding algorithm is known for these codes, so our results are primarily of theoretical interest.
We propose a technique to derive an upper bound for the maximum-likelihood (ML) decoding of BSC errors. Our tech- nique is based on the weight distributions of the constituent codes and it can also be used when a specific number of errors e is known. We observe that with an ML-decoder some HTCC codes exhibit an error correcting performance close to that of random codes. For those codes we also observe a significant performance gap between ML-decoding and practical decoding based on belief-propagation.