Low-Complexity Hybrid Algorithm for Decoding Convolutional Codes

The Viterbi algorithm is one of the most commonly used methods for decoding convolutional codes, which outputs a maximum-likelihood codeword for the input sequence. However, the complexity of the Viterbi algorithm is high when the constraint length is large. To address this issue, we propose a hybrid algorithm that contains at most two stages for decoding convolutional codes in this paper. In the first stage, the normalized min-sum algorithm (NMSA) with a small number of iterations is applied. If the output of the NMSA is not a codeword, the scarce-state-transition (SST) Viterbi algorithm is invoked for the second stage of decoding. We provide a method for constructing the input vector of the SST Viterbi algorithm, from which a truncating method is further presented for complexity reduction. Simulation results on two rate-l/2 convolutional codes show that the proposed hybrid algorithm has little performance degradation compared with the Viterbi algorithm. Meanwhile, the complexity of the proposed hybrid algorithm is reduced, especially in the high signal-to-noise ratio region.