Coding for channels with localized errors: The non-binary cases (Q752664)

The author considers the following coding problem: Messages are sent over a ``channel'' such that the encoder knows in advance the locations where an error might occur. The decoder does not know these locations in advance. The problem is to find the maximum number of messages M(n,t,q) which can be encoded into words of wordlength n over an alphabet having q symbols (using the knowledge over the possible error locations) such that the decoder can decode correctly (i.e. find the message back). The author finds upper and lower bounds for M(n,t,q) which are asymptotically equal i.e. he finds the exact value of \(\lim_{n\to \infty}(1/n) \log M(n,{\mathcal T}n,q).\) In the binary case \((q=2)\) this result was already obtained by Bassalygo, Gelfand and Pinsker and presented at the 4th Swedish-Soviet International Workshop on Information Theory.