Early Terminating Viterbi Decoding of Reed-Muller Code

The trellis-based decoding of Reed-Muller code (RM) has superior error performance amongst the RM decoding algorithms. However, the problem of the associated complexity limits its hardware implementation. The trellis complexity of the Reed-Muller codes, as any linear block codes, can be measured in terms of the state and branch complexities. To reduce the associated complexity of the trellis-based decoding, two major successful improvements have been introduced to the trellis structure of Reed-Muller code; sectionalization of a trellis, and parallel decomposition into sub-trellis. This work focuses on the decomposed implementation of the Reed-Muller trellis code into parallel identically sub-trellis (isomorphic) without any cross connection. We will introduce a novel complexity reduction approach to these decomposed RM code that can early terminate the decoding process of the conventional Viterbi algorithm (VA). The proposed early terminating Viterbi algorithm (ETVA) can eliminate 50% of the sub-trellises while maintaining the same error performance of the conventional VA. The gained results are of special interest for power limited space communication applications.