On the Equivalence Between Scarce-State-Transition Viterbi Decoding and Syndrome Decoding of Convolutional Codes (Coding Theory)

概要

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It is known that Viterbi decoding based on the code trellis and syndrome decoding based on the syndrome trellis (i. e., error trellis) are equivalent. In this paper, we show that Scarce State Transition (SST) Viterbi decoding of convolutional codes is equivalent to syndrome decoding. First, we derive fundamental relations between the hard-decision input to the main decoder and the encoded data for the main decoder. Then using these relations, we show that the code trellis module for the main decoder in an SST Viterbi decoder can be reduced to a syndrome trellis module. This fact shows that SST Viterbi decoding based on the code trellis is equivalent to syndrome decoding based on the syndrome trellis. We also calculate the SST Viterbi decoding metrics for general convolutional codes assuming an AWGN channel model. It is shown that the derived metrics are equal to those of conventional Viterbi decoding. This fact shows that SST Viterbi decoding is equivalent to conventional Viterbi decoding, and consequently to syndrome decoding.
社団法人電子情報通信学会の論文
2003-08-01