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

Abstract

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.

Low Complexity Generalized Punctured Convolutional Codes for OFDM-CDMA based Mobile Radio Communications

“…Hence, using the minimal trellis in the Viterbi decoding, some paths may be eliminated in minimal trellis compared to trellis with n-bit branches. The first error events in the minimal trellis are in general different from those found in the trellis with n-bit branches [13]. This shows that there is a definite difference, but very small, between the first error event probability of decoding using the minimal trellis and that of decoding using the trellis with n-bit branches.…”