Polytope codes for large-alphabet channels

Motivated by packet networks, we consider channels for which the blocklength is short, the input and output alphabets are large, and the transmitted symbols are subject to adversarial errors. Most work on channel coding for adversarial errors assumes that the number of errors is upper bounded by a known constant, and the code designs do not provide an improved performance guarantee should the actual number of errors be below this constant. We develop designs for which the source to be transmitted is recovered perfectly when there are no errors and partially, but correctly, when errors are introduced. Our main design is based on the polytope code design of Kosut, Tong, and Tse.