On Error Detection in Asymmetric Channels

Abstract

We study the error detection problem in $q$-ary asymmetric channels wherein every input symbol $x_i$ is mapped to an output symbol $y_i$ satisfying $y_i\ge x_i$. A general setting is assumed where the noise vectors are (potentially) restricted in: 1) the amplitude, $y_i-x_i\le a$, 2) the Hamming weight, ${\sum }_{i=1}^n{1}_{\{y_i\ne x_i\}}\le h$, and 3) the total weight, ${\sum }_{i=1}^n(y_i-x_i)\le t$. Optimal codes detecting these types of errors are described for certain sets of parameters $a,h,t$, both in the standard and in the cyclic ($\mathrm{mod}q$) version of the problem. It is also demonstrated that these codes are optimal in the large alphabet limit for every $a,h,t$ and every block-length $n$.

4 pages, 2 figures

References in corpus (1)

• On q-ary codes correcting all unidirectional errors of a limited magnitude