Error Detection and Correction for Symmetric and Asymmetric Channels

Abstract

When a message is sent over a channel errors can occur due to noise during the transmission. So it is very important to know the error correction and detection capability of the code, which is used to encode the message. There are di®erent types of channels in terms of the memory. In this work we consider channels without memory. Depending on the symbol probability, the channels are symmetric or non-symmetric. The properties of the both types of channels are discussed. For symmetric channels we present codes which are good and proper for error detection. Necessary conditions for codes to be good for error detection are derived and it is shown that large codes are proper for error detection. For the non-symmetric channels some optimal binary and ternary codes which can correct up to t errors and detect all unidirectional errors are con- structed. The method includes a generalized lower bound for the length of a code over arbitrary alphabet size. First we make this generalization and then we give a method which is used for the construction. A generalization of the Bose-Lin codes, a class of codes detecting asymmetric errors is made and the minimum weight of an undetected error is determined.