Data availability (DA) attack is a well-known problem in certain blockchains where users 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. These codes perform well across various metrics such as DA detection probability and communication cost. However, these codes are difficult to apply to blockchains with large blocks due to large decoding complexity and coding fraud proof size (2D-RS codes), and intractable code guarantees for large code lengths (LDPC codes). In this paper, we focus on large block size applications and address the above challenges by proposing the novel Graph Coded Merkle Tree (GCMT): a Merkle tree encoded using polar encoding graphs. We provide a specialized polar encoding graph design algorithm called Sampling Efficient Freezing and an algorithm to prune the polar encoding graph. We demonstrate that the GCMT built using the above techniques results in a better DA detection probability and communication cost compared to LDPC codes, has a lower coding fraud proof size compared to LDPC and 2D-RS codes, provides tractable code guarantees at large code lengths (similar to 2D-RS codes), and has comparable decoding complexity to 2D-RS and LDPC codes.
