Tail biting circular trellis block codes (TBC)2 used along with iterative Maximum A-Posteriori (MAP) decoders achieve performance very close to the Shannon limit. A Low Density Parity Check (LDPC) code using a Sum Product Algorithm (SPA) decoder is also known to achieve comparable performance. In this work the performance of (TBC)2 encoder used with an SPA decoder is presented. The goal of this research is to compare the performance of (TBC)2 encoder with different iterative decoders.
In order to use the SPA for decoding, a parity check (H) matrix representation of the (TBC)2 is developed. It is shown that for small block lengths this H matrix achieves comparable performance. For larger block sizes the H matrix representation of the (TBC)2 encoder is found non-optimal for SPA decoding and the performance of the code is degraded.