Akiko Manada

A Comparative Study of Periods in a Periodic-Finite-Type Shift

Periodic-finite-type shifts (PFTs) form a class of sofic shifts that strictly contains the class of shifts of finite type (SFTs). In this paper, we study PFTs from the viewpoint of certain “periods” that can be associated with them. We define three kinds of periods (descriptive, sequential, and graphical) for PFTs and investigate the relationships between them. The results of our investigation indicate that there are no specific relationships between these periods, except for the fact that the descriptive period of an irreducible PFT always divides its graphical period. Furthermore, we compute the number of periodic sequences in PFTs of a certain type, from which we obtain expressions for their zeta functions.

A Grouping Based on Local Girths for the Group Shuffled Belief Propagation Decoding

Low-density parity-check codes have been known to exhibit good error correcting performance by using with the belief propagation (BP) decoding. The group shuffled BP decoding, which is a modification of the BP decoding, can exhibit a better performance than BP decoding by suitably grouping variable nodes in a Tanner graph. In this letter, we propose a new grouping of variable nodes based on local girths and evaluate its performance.

On coding schemes for wireless body area networks

Wireless body area networks (WBANs) have become increasingly practical in recent times, especially with the development of new standards for low-power, short-range electronic devices. Reliability of communications and power consumption are paramount to the widespread adoption of this technology. In this paper, we focus on lightweight coding schemes, for the erasure channel. Such coding schemes have low computational complexity and are very suitable for WBANs. We analyze the robustness of said schemes against packet erasure from the perspective of graph theory and linear algebra.

The zeta function of a periodic-finite-type shift

The class of periodic-finite-type shifts (PFTs) is a class of sofic shifts that strictly includes the class of shifts of finite type (SFTs), and the zeta function of a PFT is a generating function for the number of periodic sequences in the shift. In this paper, we derive a useful formula for the zeta function of a PFT. This formula allows the zeta function of a PFT to be computed more efficiently than the specialization of a formula known for a generic sofic shift.

On the period of a periodic-finite-type shift

Periodic-finite-type shifts (PFTpsilas) form a class of sofic shifts that strictly contains the class of shifts of finite type (SFTpsilas). In this paper, we investigate how the notion of ldquoperiodrdquo inherent in the definition of a PFT causes it to differ from an SFT, and how the period influences the properties of a PFT.

Graph Theoretical Analysis on Distributed Line Graphs for Peer-to-Peer Networks

Distributed line graphs were introduced by Zhang and Liu as an overlay for Peer-to-Peer networks. Distributed line graphs have some useful properties as a network topology, such as out-regular and small diameter, where the former implies that each user possesses a constant size of routing table and the latter means that a reasonably small number of hops is necessary to reach a target user. In this paper, we newly introduce distributed line sharp graphs, as an extension of distributed line graphs, so as to further expand the possibility of finding better network topologies and theoretically analyze their properties. The analysis on the distributed line sharp graphs is based on the analysis on distributed line graphs presented by Zhang and Liu. In particular, we further examine the diameter and the in-degree of a vertex, and improve the previous results together with detailed proofs. We also show that the diameter of a certain distributed line sharp graph is equal to the diameter of its corresponding distributed line graph.

On the capacities of balanced codes with run-length constraints

A balanced code is a set of words over [a, b} such that the number of as and the number of bs in a word are equal, and many applications using balanced codes have been proposed so far. Recently, not only the original balanced code, but also balanced codes with some other constraints have been studied mainly for an application of data storage media. However, contrary to other typical sets of words satisfying some constraints, the capacities of such balanced codes have not been well studied up to this moment. In this paper, we focus on balanced codes satisfying various run-length constraints and analyze their capacities. More precisely, we exhibit lower bounds on the capacities, or present the explicit capacities for certain cases.

On rate tradeoffs for erasable write-once memory codes

To formulate rewriting operations on flash memory, we extend Write-Once Memory (WOM) and introduce Erasable WOM (EWOM) which allows block erasures, and then we define codes to rewrite on them. To measure performances of EWOM codes, we introduce the rate tradeoff pair, which is derived from the sum rate. We give an outer bound of the region of the possible tradeoff pairs for a certain class of EWOMs. We also propose fixed-rate EWOM codes calledWOM2E codes that utilize existing WOM codes. It reveals that WOM2E scheme is optimal in terms of rate tradeoff pair when the block size of EWOM is “infinity.”

On the capacity of Write-Constrained Memories

Rivest and Shamir introduced Write-Once Memory (WOM), a model of storage devices whose storage elements have restrictions on state transitions, and they presented some coding methods to reuse WOM. An interesting question about WOM is how efficiently we can reuse it with the best coding method, and as an answer to the question, Fu and Han Vinck determined the capacity of Fiat and Shamirs generalized WOM. In this paper, we extend their results, introducing Write-Constrained Memory (WCM) that considers state transition cost, and determining the capacity of WCM under a certain type of cost constraints.