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.