Iterative Viterbi decoding, trellis shaping, and multilevelstructure for high-rate parity-concatenated TCM

We define and apply a new algorithm called the iterative Viterbi decoding algorithm (IVA) to decode a high-rate parity-concatenated TCM system in which a trellis code is used as the inner code and a simple parity-check code is used as the outer code. With trellis shaping, the IVA can achieve a performance 1.25 dB away from the Shannon limit at a BER of 3×10^-5 with low complexity. By augmenting the system with a binary BCH code, the error floor can be reduced to 10^-9 with very little additional cost