Existence Condition for Tail-Biting Convolutional Codes(Regular Section)

概要

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We investigated the truncated convolutional code with the characteristics of a block code for block-based communication systems. Three truncation methods (direct truncation, tail-terminating, and tail-biting method) were introduced by other researchers. Each of the three methods has a weakness: the direct truncation method decreases the minimum distance, the tail-terminating method uses tail bits, and the tail-biting method can only be applied by using a complicated decoder. Although the tail-biting method gives a better BER performance than the other two methods, we cannot apply the tail-biting method in all situations. Occasionally, the tail-biting convolutional code does not exist. Wang et al. presented two necessary conditions for the existence of the tail-biting convolutional code of the rate-1/2 recursive systematic convolutional code. In this paper, we analyze the encoder of the convolutional code as a linear time invariant system, and present two theorems and six corollaries on the existence of the tail-biting convolutional code. These existence conditions are adaptable to all convolutional codes. In the communication system using the truncated convolutional code, these results are applicable to determining the truncation method.
社団法人電子情報通信学会の論文
2002-11-01