Studies on Codes for Error Detection

The basic idea of error coding is to introduce redundancy that can be utilized to detect and, for some applications, correct errors that have occurred during a transmission over a channel. Here "transmission" is used in a wide sense, including any process which may corrupt the data, e.g. transmission, storage, etc. Usually it is a much more complex task to correct errors than merely detect them. Moreover, using the full power of the code for error detection, many more errors can be detected. On the other hand, in most applications, just detecting the errors is not sufficient. In traditional link to link coding, we may request a retransmission (this is the essence of the ARQ (automatic retransmission request) system). In a network, where the same message is received via different routes, error detection is used to erase received messages that are in error. Error detecting codes have been studied and used for many years. An updated presentation of the known results is my book: T. Kløve, Codes for Error D etection, World Scientific, Singapore, 2007. The bulk of the book considers codes for symmetric channels, but also codes over asymmetric channels are considered. A number of basic questions are open, and the goal of this project is to answer these questio ns or at least obtain partial results. For a given channel, a basic question is: what is the "best" of these code for use on the channels? Another question is: is a given code "good enough" for use on the channel? To approach such questions, we have to d efine more precisely that we mean by "best" and "good enough". In many situations, we may want codes with some particular property. Then the first question may be: do there exist codes with this property for the given parameters? And if so, what are the b est such codes or the good enough such codes? The goal of the project is to answer fully or partially these questions (stated much more precisely in the project) for the symmetric and asymmetric channels.