Partially Information Coupled Duo-Binary Turbo Codes

Partially information coupled turbo codes (PIC-TCs) is a class of spatially coupled turbo codes that can approach the BEC capacity while keeping the encoding and decoding architectures of the underlying component codes unchanged. However, PIC-TCs have significant rate loss compared to its component rate-$\frac{1}{3}$ turbo code, and the rate loss increases with the coupling ratio. To absorb the rate loss, in this paper, we propose the partially information coupled duo-binary turbo codes (PIC-dTCs). Given a rate-$\frac{1}{3}$ turbo code as the benchmark, we construct a duo-binary turbo code by introducing one extra input to the benchmark code. Then, parts of the information sequence from the original input are coupled to the extra input of the succeeding code blocks. By looking into the graph model of PIC-dTC ensembles, we derive the exact density evolution equations of the PIC-dTC ensembles, and compute their belief propagation decoding thresholds on the binary erasure channel. Simulation results verify the correctness of our theoretical analysis, and also show significant error performance improvement over the uncoupled rate-$\frac{1}{3}$ turbo codes and existing designs of spatially coupled turbo codes.