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We consider the decoding of convolutional codes using an error trellis constructed based on a submatrix of a given check matrix. In the proposed method, the syndromesubsequence computed using the remaining submatrix is utilized as auxiliary information for decoding. Then the ML error path is correctly decoded using the degenerate error trellis. We also show that the decoding complexity of the proposed method is basically identical with that of the conventional one based on the original error trellis. Next, we apply the method to check matrices with monomial entries proposed by Tanner et al. By choosing any row of the check matrix as the submatrix for errortrellis construction, a 1-state error trellis is obtained. Noting the fact that a likelihood-concentration on the all-zero state and the states with many 0's occurs in the error trellis, we present a simplified decoding method based on a 1-state error trellis, from which decoding-complexity reduction is realized.

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.

An algorithm for generating a multi-level NAND logic circuit is proposed. In the algorithm, (a) to cover true (1) cell, permissible cubes described by the product of the affirmative literals are generated; and (b) if false (0) cell is found in the generated cube, new permissible cubes excluding the false cell are added. Procedures (a) and (b) are repeated until no true cell exists together with false cell in the permissible cube. The finally obtained cubes are converted into a NAND gate circuit. The circuit generation is carried out only by the mouse operations and the circuit can easily be displayed on a screen.

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