  Light nodes in blockchain systems are known to be vulnerable to data
availability (DA) attacks where they accept an invalid block with unavailable
portions. Previous works have used LDPC and 2-D Reed Solomon (2D-RS) codes with
Merkle Trees to mitigate DA attacks. While these codes have demonstrated
improved performance across a variety of metrics such as DA detection
probability, they are difficult to apply to blockchains with large blocks due
to generally intractable code guarantees for large codelengths (LDPC), large
decoding complexity (2D-RS), or large coding fraud proof sizes (2D-RS). We
address these issues by proposing the novel Polar Coded Merkle Tree (PCMT)
which is a Merkle Tree built from the encoding graphs of polar codes and a
specialized polar code construction called Sampling-Efficient Freezing (SEF).
We demonstrate that the PCMT with SEF polar codes performs well in detecting DA
attacks for large block sizes.
