輕節點在區塊鏈中透過僅存儲部分區塊鏈帳本來提高系統的可擴展性。然而，在某些區塊鏈中，輕節點容易受到數據可用性攻擊，惡意節點藉由隱藏區塊中的一小部分不合法交易數據，其中隱藏的數據對應到低密度檢查碼中的一組停止集，使誠實的全節點無法成功解碼回原始區塊，最後輕節點將接受新產生的不合法區塊。本論文引進了兩種改進的LDPC解碼策略，以提高全節點的解碼成功機率。我們通過猜測LDPC碼中被隱藏之變數節點的數值來執行進一步的解碼，並使用停止集列舉演算法來找出小於某個臨界值的所有停止集，，其中我們提出一組初始約束集合的設定方法來提高演算法的搜索效率，。我們的模擬結果顯示出當改善全節點解碼的成功機率時，能大幅降低輕節點接受不合法區塊的機率。

Light nodes in blockchain systems enhance scalability by storing only a portion of the blockchain ledger. However, in certain blockchains, light nodes are susceptible to data availability attacks. Malicious nodes can hide a small portion of illegal transaction data within the blocks, corresponding to a stopping set in low density parity check codes. This makes it impossible for honest full nodes to successfully decode the original block, causing light nodes to eventually accept newly generated illegal blocks. In this paper, we introduce two advanced decoding strategies to increase the decoding success probability of full nodes. By guessing the values of hidden variable nodes in the LDPC code, we execute further decoding. Additionally, we employ a stopping set enumeration algorithm to find all stopping sets smaller than a certain threshold. We propose an initial constraint set to improve the search efficiency of the algorithm. Our simulation results show that improving the decoding success probability of full nodes significantly reduces the probability of light nodes accepting illegal blocks.

[1] M. Yu, S. Sahraei, S. Li, S. Avestimehr, S. Kannan, and P. Viswanath, “Coded Merkle Tree: Solving data availability attacks in blockchains,” arXiv:1910.01247v2 [cs.CR], Dec. 2019.

[2] D. Mitra, L. Tauz, and L. Dolecek, “Overcoming data availability attacks in blockchain systems: Short code-length LDPC code design for coded Merkle tree,” IEEE Trans. Commun., vol. 70, no. 9, pp. 5742–5755, Sep. 2022.

[3] E. Rosnes and Ø. Ytrehus, “An efficient algorithm to find all small-size stopping sets of low-density parity-check matrices,” IEEE Trans. Inf. Theory, vol. 55, no. 9, pp. 4167–4178, Sep. 2009.

[4] H. Pishro-Nik and F. Fekri, “On decoding of low-density parity-check codes over the binary erasure channel,” IEEE Trans. Inf. Theory, vol. 50, no. 3, pp. 439–454, Mar. 2004.

[5] Sareh Majidi Ivari, M. Reza Soleymani, and Yousef R. Shayan, “Low decoding complexity of LDPC Codes over the binary erasure channel,” in Proc. 26th Iranian Conference on Electrical Engineering (ICEE2018), pp. 52-56, 2018.

[6] M. J. Casey and P. Wong, “Global supply chains are about to get better, thanks to blockchain,” Harvard Bus. Rev., vol. 13, pp. 1–6, Mar. 2017.

[7] X. Wang et al., “Survey on blockchain for Internet of Things,” Comput. Commun., vol. 136, pp. 10–29, Feb. 2019.

[8] M. Mettler, “Blockchain technology in healthcare: The revolution starts 1374 here,” in Proc. IEEE 18th Int. Conf. e-Health Netw., Appl. Services 1375 (Healthcom), Sep. 2016, pp. 1–3.

[9] X.-Y. Hu, E. Eleftheriou, and D. M. Arnold, “Regular and irregular progressive edge-growth Tanner graphs,” IEEE Trans. Inf. Theory, vol. 51, no. 1, pp. 386–398, Jan. 2005.

[10] R. G. Gallager, “Low-density parity-check codes,” IRE Trans. Inform. Theory, vol. IT-8, pp. 21–28, Jan. 1962.

[11] T. Richardson and R. Urbanke, Modern Coding Theory. Cambridge, U.K.: Cambridge Univ. Press, 2008.

[12] T. R. Halford and K. M. Chugg, “An algorithm for counting short cycles in bipartite graphs,” IEEE Trans. Inform. Theory, vol. 52, no. 1, 2006.