Search

In this paper, we consider encoding strategies for the Z-channel with noiseless feedback. We analyze the combinatorial setting where the maximum number of errors inflicted by an adversary is proportional to the number of transmissions, which goes to infinity. Without feedback, it is known that the rate of optimal asymmetric-error-correcting codes for the error fraction $\tau \ge 1/4$ vanishes as the blocklength grows. In this paper, we give an efficient feedback encoding scheme with $n$ transmissions that achieves a positive rate for any fraction of errors $\tau < 1$ and $n\to \infty $. Additionally, we state an upper bound on the rate of asymptotically long feedback asymmetric error-correcting codes. [ABSTRACT FROM AUTHOR]

In digital systems such as fiber optical communications, the ratio between probability of errors of type 1 → 0 and 0 → 1 can be large. Practically, one can assume that only one type of error can occur. These errors are called asymmetric. Unidirectional errors differ from asymmetric type of errors; here both 1 → 0 and 0 → 1 type of errors are possible, but in any submitted codeword all the errors are of the same type. This can be generalized for the q -ary case. We consider q -ary unidirectional channels with feedback where the errors have magnitude one and give bounds for the capacity error function. It turns out that the bounds depend on the parity of the alphabet size q. Furthermore, we show that for feedback, the capacity error function for the binary asymmetric channel is different from the symmetric channel. This is in contrast to the behavior of the function without feedback. [ABSTRACT FROM AUTHOR]