This paper describes about unified belief propagation (BP) algorithm and how it helps in decoding in tailbiting convolutional and turbo codes.  For all convolutional code classes and turbo codes, BP algorithm provides an effective general methodology for devising low-complexity iterative decoding algorithms. If a small performance has taken place during decoding turbo codes with BP instead of MAP, then this will be offset by the lower complexity of the BP algorithm. 

Overview: 

Prerequisites like generator matrix and parity check matrix are required to apply BP algorithm on tail-biting convolutional code by a Tanner graph for decoding.  In order to replace the traditional decoders of turbo codes with the BP decoder, there is a need to obtain the turbo code party-check matrix. As the BP decoder is less complex than traditional decoder and also due to enables a unified decoding approach, the loss in BER performance is acceptable.  When compares MAP and SOVA decoders, BP algorithm yields the lowest implementation complexity over all the required operations.  BP algorithm for turbo codes is about 1.7 dB worse at a BER value of 10−2, than that of traditional decoders for turbo codes. 

Conclusions: 

The usage of BP algorithm is determined in this paper and also describes the feasibility of decoding arbitrary tailbiting convolutional and turbo codes. This algorithm helps to speeds up the error correction convergence and decreases the decoding computational complexity in WiMAX systems. Besides, based on forward-only algorithm, BP algorithm performs a non-trellis.

BP decoder for turbo codes in a combined architecture is having more benefits based on the efficient reuse of computational hardware and memory resources of the two separate decoders. As traditional turbo decoders having a higher complexity, there is a high loss in performance with BP. In fact, the low decoding complexity of BP decoder brings end-to-end efficiency as both encoding and decoding takes place with low hardware complexity.