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.

This paper presents an extension of the database query language SQL to include queries against a database with natural language annotations. The proposed scheme is based on Concept Coupling Model, a language model for handling natural language sentence structures. Integration of the language model with the conventional relational data model provides a unified environment for manipulating information sources comprised of relational tables and natural language texts.

In this paper, we show that a priori probabilities of information bits can be incorporated into metrics for syndrome decoding. Then it is confirmed that soft-in/soft-out decoding is also possible for syndrome decoding in the same way as for Viterbi decoding. The derived results again show that the two decoding algorithms are dual to each other.