Iterative decoding of turbo codes based on factor graphs

Turbo codes and low-density parity-check (LDPC) codes both have their advantages and can achieve the Shannon limited performance. The constituent recursive systematic convolutional (RSC) codes in turbo codes are more structural and this lends the encoding problem easier with a shift-register circuit. While the encoding of LDPC codes is performed via matrix multiplication, and this is more complex than it appears for capacity-approaching LDPC codes. On the other hand, the soft-input soft-output BCJR algorithm, or the sub-optimal version of it, used for turbo-decoding is rather complex while sum-product algorithm used for LDPC decoding lends itself to parallel implementation and is computationally simpler. Combining the turbo codes encoding and LDPC decoding, a new scheme based on factor graphs and sum-product algorithm is developed, it can reduce the decoding complexity of turbo codes greatly, and also has some guides in the designing of interleaver and the choosing of RSC constituent codes. Simulation shows the correctness of the scheme.