Masato Tajima

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

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.

Relation between encoder and syndrome former variables and symbol reliability estimation using a syndrome trellis

We derive a linear correspondence between the variables of an encoder and those of a corresponding syndrome former. Using the derived correspondence, we show that the log-likelihood ratio of an information bit conditioned on a received sequence can be equally calculated using the syndrome trellis. It is shown that the proposed method also applies to recursive systematic convolutional codes which are typical constituent codes for turbo codes. Moreover, we show that soft-in syndrome decoding considering a priori probabilities of information bits is possible in the same way as for Viterbi decoding based on the code trellis. Hence, the proposed method can be applied to iterative decoding such as turbo decoding. We also show that the proposed method is effective for high-rate codes by making use of trellis modification.

On the equivalence between scarce-state-transition viterbi decoding and syndrome decoding of convolutional codes

In this paper, we show that Scarce State Transition (SST) Viterbi decoding is equivalent to syndrome decoding by transforming the code trellis module for the main decoder in an SST Viterbi de- coder to a syndrom6 trellis module.

Simultaneous code/error-trellis reduction for convolutional codes using shifted code/error-subsequences

In this paper, we show that the code-trellis and the error-trellis for a convolutional code can be reduced simultaneously, if reduction is possible. Assume that the error-trellis can be reduced by shifting particular error-subsequences. In this case, if the identical shifts occur in the corresponding subsequences of each code path, then the code-trellis can also be reduced. First, we obtain pairs of transformations which generate the identical shifts both in the subsequences of the code-path and in those of the error-path. Next, by applying these transformations to the generator matrix and the parity-check matrix, we show that reduction of these matrices is accomplished simultaneously, if it is possible. Moreover, it is shown that the two associated trellises are also reduced simultaneously.

State-Complexity Reduction for Convolutional Codes Using Trellis-Module Integration

Assume that G(D) is a k0×n0 canonical generator matrix. Let G(L)(D) be the generator matrix obtained by integrating L consecutive trellis-modules associated with G(D). We also consider a modified version of G(L)(D) using a column permutation. Then take notice of the corresponding minimal trellis-module T(L). In this paper, we show that there is a case where the minimum number of states over all levels in T(L) is less than the minimum attained for the minimal trellis-module associated with G(D). In this case, combining with a shifted sectionalization of the trellis, we can construct a trellis-module with further reduced number of states. We actually present such an example. We also clarify the mechanism of state-space reduction. That is, we show that trellis-module integration combined with an appropriate column permutation and a shifted sectionalization of the trellis is equivalent to shifting some particular bits of the original code bits by L time units.

Symbol reliability estimation using the bidirectional Viterbi algorithm with a code trellis and a syndrome trellis for QLI codes

In this paper, we show that in the case of quick look-in (QLI) codes, the symbol reliability values are obtained by applying the bidirectional Viterbi algorithm (BIVA) either to the code trellis or to the corresponding syndrome trellis.

Language model and sentence structure manipulations for natural language application systems

This paper presents a language model and its application to sentence structure manipulations for various natural language applications including human-computer communications. Building a working natural language dialog systems requires the integration of solutions to many of the important subproblems of natural language processing. In order to materialize any of these subproblems, handling of natural language expressions plays a central role; natural language manipulation facilities are indispensable for any natural language dialog systems. Concept Compound Manipulation Language (CCML) proposed in this paper is intended to provide a practical means to manipulate sentences by means of formal uniform operations.

Symbol reliability estimation using code trellis degeneration for QLI codes

We clarify the relation between trellis degeneration (TDG) and symbol reliability estimation using the bidirectional Viterbi algorithm (BIVA) for the case of quick look-in (QLI) codes.

Code trellis degeneration using SST (scarce state transition) Viterbi decoding of QLI codes

We show that code trellis degeneration can be realized for SST (scarce state transition) Viterbi decoding of quick look-in (QLI) codes. We consider an AWGN channel with biphase modulation.

Bidirectional Viterbi decoding algorithm with repeat request and estimation of unreliable region

A bidirectional Viterbi decoding algorithm for framed information with repeat request which is an extended version of the Yamamoto-Itoh scheme (1980) is presented. A method to estimate the unreliable region in a received frame using the proposed algorithm is also presented.