A sequential code such as an arithmetic code is a code that determines a prefix of the codeword from a prefix of the source sequence. The reciprocal of the time period in which the transmitter can send a single code symbol is called the transmission velocity. Since, at every moment, the restored length cannot be longer than the source length, the decoding rate is one at most. In this manuscript, we derive a transmission velocity at which the decoding rate is one almost surely with sequential codes.

We introduce a source that emits symbols at infinitesimal time slots. The source may emit no symbol at a slot. The outputs from the source are encoded on the real-time basis. We derive the minimum loss probability and reveal a connection to the continuous model. Moreover, we define the utilization factor of the channel and show that it coincides with the loss probability for any code. We consider the situation in which the number of division of time unit goes infinity keeping the entropy rate constant. In this artificial case, the process does not approach to a Poisson process. We show that the ordinary entropy coding is not optimal but sub-optimal.

We consider on coding for continuous-time Markov chains from the viewpoint of real-time transmission. The theoretical relation between the transmission rate of the channel and the loss probability is described. It is shown that the channel use efficiency coincides with the loss probability.

Restoration of writing order from a single-stroked handwriting image can be seen as the problem of finding the smoothest path in its graph representation. In this paper, a 3-phase approach to restore a writing order is proposed within the framework of the Edge Continuity Relation (ECR). In the initial, local phase, in order to obtain possible ECRs at an even-degree node, a neural network is used for the node of degree 4 and a theoretical approach is presented for the node of degree higher than 4 by introducing certain reasonable assumptions. In the second phase, we identify double-traced lines by employing maximum weighted matching. This makes it possible to transform the problem of obtaining possible ECRs at odd-degree node to that at even-degree node. In the final, global phase, we find all the candidates of single-stroked paths by depth first search and select the best one by evaluating SLALOM smoothness. Experiments on static images converted from online data in the Unipen database show that our method achieves a restoration rate of 96.0 percent.

We consider a new class of information sources called word-valued sources in order to investigate coding algorithms based upon string parsing. A word-valued source is defined as a pair of an independent and identically distributed (i.i.d.) source with a countable alphabet and a function that maps each symbol into a finite sequence over a finite alphabet. A word-valued source is a nonstationary process and has countable states. If the function of a word-valued source is prefix-free, the entropy rate is characterized with a simple expression and the AEP (asymptotic equipartition property) holds.