On deletion codes

Abstract

In a deletion channel, some symbols might be "dropped off" during transmission. The receiver knows that some symbols were omitted, but does not know either their values or their indices. We introduce a linear-time code correcting a fixed number of deletions, with a message-overhead linear in the number of deletions and less than log squared in the original message length. We also present some extensions of known bounds for deletion codes. In a UEP (unequal error protection) coding setting, each message part is assigned a priority value, determining its required resiliency to errors. Depending on this priority, and the numbers of errors actually taking place, this message part should be recoverable. Extending previous work that dealt with UEP in the context of erasures, we introduce codes and bounds for UEP in the context of deletions, which are relevant to lossy packet-networks.