Performance and bounds for repeat tree codes

The Repeat Accumulate (RA) codes introduced in [1] are Serial Concatenated Codes (SCC) consisting of a repetition code and an accumulator which are connected through an interleave. It has the advantage of low encoding complexity and good performance. On the other hand, Concatenated Tree (CT) codes introduced in [2] are Parallel Concatenated Codes (PCC) and also show good performance with low encoding and decoding complexity. The constituent code of CT codes has a tree structure which consists of nonrecursive information bits as well as recursive information bits. In this paper, we present a new code which is constructed based on the RA codes but shows much better performance and better thresholds (i.e., higher noise level or lower signal-to-noise ratio). The main contribution of this paper is putting nonrecursive information bits as well as recursive information bits in the accumulating part of RA codes. The enhanced performance is shown by computer simulation and the asymptotic performance in the water fall region is shown by density evolution. We also show the upper bound on the performance of the RT code for a specific interleaver using the simple tight bound and specific input-output weight distributions that are obtained by the sample based MLE (Maximum Likelihood Estimator).