Density evolution analysis of braided convolutional codes on the erasure channel

Braided convolutional codes (BCCs) are a class of spatially coupled turbo-like codes with a structure that is similar to product codes or generalized LDPC codes. We derive explicit input/output transfer functions of the component convolutional decoders for the binary erasure channel (BEC). These are then used to formulate exact density evolution equations for blockwise BCCs under belief propagation (BP) decoding with optimal component APP decoders. Thresholds are computed for the coupled and uncoupled case, which is equivalent to tailbiting. Due to the relatively high rate of the component codes a significant threshold improvement by spatial coupling can be observed.