Linear-time binary codes correcting localized erasures

We consider a communication model over a binary channel in which the transmitter knows which bits of the n-bit transmission are prone to loss in the channel. We call this model channel with localized erasures in analogy with localized errors studied earlier in the literature. We present two constructions of binary codes with t(1+ε) check bits, where t=αn is the maximal possible number of erasures. One construction is on-line and has encoding complexity of order n/ε ⁴ and decoding complexity of order n/ε². The other construction is recursive. The encoding/decoding algorithms assume a delay of n bits i.e. rely on the entire codeword. The encoding/decoding complexity behaves roughly as n/ε² and n/ε, respectively