FEC encoding: BCH-LDCP

Abstract

At this fully digital age and with the massive transmission of information by electronic media, the error detection and correction is something inherent to the electronic transmission of information. This transmission is performed by several channels: copper cable, optical fiber, electromagnetic waves.... There exist interferences, noise, that affect to these channels and can introduce errors during the transmission. For this reason it is necessary to know how to detect when these errors occur and to be able to correct them whenever it is required. In the theory of information, the Shannon-Hartley theorem is an application of the theorem of codification for noisy channels. The theorem determines the Shannon-capacity of the channel, a superior bound that establishes the maximum quantity of digital data that can be transmitted without error (i.e. information) by that channel with a specific bandwidth and which is affected by the presence of noise. The last few years have witnessed a significant decrease in the gap between the Shannon channel capacity limit and what is practically achievable. Progress has resulted from novel extensions of previously known coding techniques involving interleaved concatenated codes. A considerable body of simulation results is now available, supported by an important but limited theoretical basis. This thesis presents a deep analysis about the types of coding used in the ultimate versions of the DVB standards, such as terrestrial (T2), satellite (S2) and cable (C2). This codes are Bose and Chaudhuri Hocquenghem (BCH) and Low-Density ParityCheck (LDPC) and they successfully approach the Shannon limit. It is presented, first of all, an introduction to the world of error-correcting codes so as to get a global idea. There is also a final comparison between LDPC and Turbo-Codes, another important type of coding although not used in the standards mentioned before. At the end, it is presented a brief summary of the main ideas and a list of conclusions