The Analysis And Computation For The Channel Capacity Of A Two-dimensional Run-length Constrained Code

With the development of the techniques of optical storage and digital recording, many advanced optical storage and digital recording channels have been proposed, which have been forwarding the research of the signal processing and coding. Moreover, the optical storage in multi-dimensional has been one important carrier to increase the record density of information and read/write speed. For meeting the needs of multi-dimensional storage channels, the corresponding coding for the two-dimensional run-length limited has been proposed particularly and some elementary achievements have been obtained with it.Multi-channel (d,k) code has appeared in multi-channel magnetic storage as the origin of two-dimensional run-length limited codes, which has been presented by Marcellin and other researchers. In this model, each record channel should satisfy the limitation of the minimal run-length limited d, and united multi-channels must meet the limitation of the maximal run-length limited k.With the development of page storage and holographic optical storage, two-dimensional run-length limited codes, known as 2-D RLL(d,k) code, has been attracted many researchers' interest. In the two-dimensional model, one-dimensional run-length limited constraints (d,k) must be satisfied in both horizontal and vertical directions in data page, which is helpful to control the interference of codes of data page on two dimensions. Compared with the traditional (d,k) codes, the capacity of two-dimensional constrained (d,k) code has some special characteristics. For example, the capacity of two-dimensional constrained (d,k) code is zero if and only if k=d+1 for each positive integer d. However, there are few theoretical results about two-dimensional constrained (d,k) code until now due to the lack of methods for computing channel capacity and the techniques for constructing code.The length of sequential and identical segment in channel sequences is named as run-length. The limitation of run-length is classical in the optical storage channel which could not be too short or too long. Based on this fundamental, in this thesis we first introduce the model of digital communication, the elementary theory of coding, and the primary idea of the channel coding, then describe the framework of the topic, and the concept of the constrained system, the constrained channel and the constrained coding, and the transfer matrix which is a basic tool used tocompute the capacity of constrained coding. Afterward we present the computing technique of the capacity of 1-D and 2-D constrained channels. We then establish theoretical results about the channel capacity of 2-D constrained codes. Finally, we develop new techniques for analyzing and computing the lower and upper bounds of capacities.