  We consider a queue-channel model that captures the waiting time-dependent
degradation of information bits as they wait to be transmitted. Such a scenario
arises naturally in quantum communications, where quantum bits tend to decohere
rapidly. Trailing the capacity results obtained recently for certain
queue-channels, this paper aims to construct practical channel codes for the
erasure queue-channel (EQC) -- a channel characterized by highly correlated
erasures, governed by the underlying queuing dynamics. Our main contributions
in this paper are twofold: (i) We propose a generic `wrapper' based on
interleaving across renewal blocks of the queue to convert any
capacity-achieving block code for a memoryless erasure channel to a
capacity-achieving code for the EQC. Next, due to the complexity involved in
implementing interleaved systems, (ii) we study the performance of LDPC and
Polar codes without any interleaving. We show that standard Ar{\i}kan's Polar
transform polarizes the EQC for certain restricted class of erasure probability
functions. We also highlight some possible approaches and the corresponding
challenges involved in proving polarization of a general EQC.
