Construction and Decoding of Codes over the Dual-Parameter Barrier Error Model

Barrier-error channels have been suggested as a model for non-binary channels that are milder than symmetric-error channels. Such channels are motivated by practical applications in data storage and communications. The barrier-error model allows errors only to (downward) and from (upward) a specific symbol within the alphabet. We study a generalization of prior barrier-error models that considers different numbers of downward and upward errors. The results of this paper include a sufficient condition for error correction, code-size upper and lower bounds, a code construction decomposing to just two constituent symmetric-error codes (prior ones used many), and a decoding algorithm that decodes the two codes jointly. The decoder is shown empirically to achieve better block error rates when compared to previous algorithms.