  A popular method of improving the throughput of blockchain systems is by
running smaller side blockchains that push the hashes of their blocks onto a
trusted blockchain. Side blockchains are vulnerable to stalling attacks where a
side blockchain node pushes the hash of a block to the trusted blockchain but
makes the block unavailable to other side blockchain nodes. Recently, Sheng et
al. proposed a data availability oracle based on LDPC codes and a data
dispersal protocol as a solution to the above problem. While showing
improvements, the codes and dispersal protocol were designed disjointly which
may not be optimal in terms of the communication cost associated with the
oracle. In this paper, we provide a tailored dispersal protocol and specialized
LDPC code construction based on the Progressive Edge Growth (PEG) algorithm,
called the dispersal-efficient PEG (DE-PEG) algorithm, aimed to reduce the
communication cost associated with the new dispersal protocol. Our new code
construction reduces the communication cost and, additionally, is less
restrictive in terms of system design.
