On Error Detection in Asymmetric Channels

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
≥x
_i
. A general setting is assumed, where the noise vectors are (potentially) restricted in: 1) the amplitude, y
_i
-x
_i
≤a, 2) the Hamming weight, Σ
_i=1
ⁿ
1
_{y
i≠xi
}
≤ h, and 3) the total weight, Σ
_i=1
ⁿ
(y
_i
-x
_i
)≤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 (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.