On the application of BP decoding to convolutional and turbo codes

We investigate a new approach to decode convolutional and turbo codes by means of the belief propagation (BP) decoder used for low-density parity-check (LDPC) codes. In addition, we introduce a general representation scheme for convolutional codes through parity check matrices. Also, the parity check matrices of turbo codes are derived by treating turbo codes as parallel concatenated convolutional codes. Indeed, the BP algorithm provides a very attractive general methodology for devising low complexity iterative decoding algorithms for all convolutional code classes as well as turbo codes. However, preliminary results show that BP decoding of turbo codes performs slightly worse than conventional maximum a posteriori (MAP) and soft output Viterbi algorithm (SOVA) algorithms which already are in use in turbo code decoders. Since these traditional turbo decoders have a higher complexity, the observed loss in performance with BP is more than compensated by a drastically lower implementation complexity. Moreover, given the encoding simplicity of turbo codes with respect to generic LDPC codes, the low decoding complexity brings about end-to-end efficiency.