Hiroshi Kamabe

Floating codes with good average performance

Floating codes are codes for multi-level flash memories. There are two main properties which those codes have, the worst-case block erasure period and the average block erasure period. Codes with large average block erasure period can be constructed from the Gray code. First it is shown that a construction method for the floating codes can be interpreted by using labelled graphs. Floating codes are proposed for cases (a) n = 5 and k = 4,1 = 2, q > 2; (b) n = 8, k = 4, I = 2, q> 2, where n is the number of cells in a block, k the number of information variables, I the number of levels of information variables and q the number of levels of cells. It is shown that if input data do not distribute uniformly, then the frequency of block erasure is low when the proposed code is used.

Integrated interleaving error correcting code and high-dimensional parity codes

The integrated interleaving error correcting scheme is a coding scheme for combining codes with different error correcting capabilities. This method is applied to channels in which a data sequence is interleaved, e.g., magnetic recording channels. We propose a decoding method which enhances the error correcting capability of the scheme. By using the method, we can correct more errors which occur in retrieved data sequences.

On construction of codes for DNA computers

We describe similarities between constraints of codes for DNA computers and constraints which appear in digital magnetic recording. We apply coding techniques developed for digital recording systems to problems on DNA sequences for DNA computers.

Two-dimensional codes for second order spectral null constraints

A two-dimensional code for a second order spectral null constraint is given and it is shown that the rate of the code is asymptotically equal to 1.

Insertion rate and optimization of redundancy of constrained systems with unconstrained positions

It was recently shown that the code rate of a simple coding scheme is better than a previously established maxentropic bound for the Wijngaarden-Immink reversed modulation and error control scheme(W-I coding scheme). This paper analyzes code rates of coding schemes for a given insertion rate of the W-I coding scheme using finite state transition diagrams. A new coding scheme is proposed and a new bound for the code rate of the W-I coding scheme is derived. It is proved that the new bound is better than the maxentropic bound when the insertion rate is 1/2.

Encoding algorithms for 2 dimensional run-length-limited constraints

Lower bounds of the capacities of 2-dimensional run-length-limited (RLL) constraints is studied in this paper. We also present a coding algorithm for encoding data sequences into two-dimensional binary arrays satisfying a (1,2)-RLL constraint along both horizontal and vertical directions.

Constructions of multiple error correcting WOM-Code

WOM-codes are constrained codes for memory devices whose state transition is irreversible. If we use the code, n-bit data can be written more than once on write-once cells of length greater than n. Error correcting WOM-codes have also been proposed. In this paper, a method for constructing multiple error correcting WOM-codes by modifying and simplifying the previously proposed error correcting WOM-code is presented. Codes constructed with our method have better code rates for some cases than the previously proposed code for some cases and no restrictions on the number of correctable errors. A single-symbol and a two-symbols error correcting code are also proposed.

Outfix-free and intercode constraints for DNA sequences

DNA sequences can be regarded as sequences consisting of 4 symbols A (adenine), C (cytosine), G (guanine), and T (thymine). Many constraints for the DNA sequences are studied because when the DNA sequences are used as fundamental ingredients for computation or processing information, the DNA sequences should satisfy constraints so that molecular biological processes are done with small error probabilities. We explain constraints of the DNA sequences for hybridization. We also show some results on outfix-free and intercode constraints for DNA sequences.

Constraints for DNA sequences by formal language and its capacity

DNA sequences can be regarded as sequences consisting of 4 symbols A (adenine), C (cytosine), G (guanine), and T (thymine). Many constraints for the DNA sequences are studied because when the DNA sequences are used as fundamental ingredients for computation or processing information, the DNA sequences should satisfy constraints so that molecular biological processes are done with small error probabilities. We explain constraints of the DNA sequences for hybridization. We also show some results on the capacity of the constraints.

Encoding Algorithms for 2 Dimensional Weak Run-Length-Limited Constraints

Weakly constrained codes were introduced for constructing efficient encoding algorithms with low complexities, that is, encoding algorithm which can be implemented with smaller circuits and less memories. In this paper we introduce 2-dimensional(2-D) weak input constraints for 2-D storage media. We propose coding rules for 2-D weak run-length-limited constraints. Simulation results show that these rules almost strictly obey given constraints. We can prove these results theoretically for some constraints.