Minimal Code(Error)-Trellis Module Construction for Rate-k/n Convolutional Codes: Extension of Yamada-Harashima-Miyakawa's Construction

Yamada, Harashima, and Miyakawa proposed to use a trellis constructed based on a syndrome former for the purpose of Viterbi decoding of rate-(n − 1)/n convolutional codes. In this paper, we extend their code-trellis construction to general rate-k/n convolutional codes. We show that the extended construction is equivalent to the one proposed by Sidorenko and Zyablov. Moreover, we show that the proposed method can also be applied to an error-trellis construction with minor modification. key words: convolutional codes, syndrome former, minimal code(error)trellis module, trellis complexity