Universal Lossless Compression of Erased Symbols

A source X goes through an erasure channel whose output is Z. The goal is to compress losslessly X when the compressor knows X and Z and the decompressor knows Z. We propose a universal algorithm based on context-tree weighting (CTW), parameterized by a memory-length parameter. We show that if the erasure channel is stationary and memoryless, and X is stationary and ergodic, then the proposed algorithm achieves a compression rate of H(X ₀|X _- l ^-1, Z ^l) bits per erasure.