Interactive Error Correcting Codes Over Binary Erasure Channels Resilient to >1/2 Adversarial Corruption
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An error correcting code (𝖤𝖢𝖢) allows a sender to send a message to a receiver such that even if a constant fraction of the communicated bits are corrupted, the receiver can still learn the message correctly. Due to their importance and fundamental nature, 𝖤𝖢𝖢s have been extensively studied, one of the main goals being to maximize the fraction of errors that the 𝖤𝖢𝖢 is resilient to. For adversarial erasure errors (over a binary channel) the maximal error resilience of an 𝖤𝖢𝖢 is 1/2 of the communicated bits. In this work, we break this 1/2 barrier by introducing the notion of an interactive error correcting code (𝗂𝖤𝖢𝖢) and constructing an 𝗂𝖤𝖢𝖢 that is resilient to adversarial erasure of 3/5 of the total communicated bits. We emphasize that the adversary can corrupt both the sending party and the receiving party, and that both parties' rounds contribute to the adversary's budget. We also prove an impossibility (upper) bound of 2/3 on the maximal resilience of any binary 𝗂𝖤𝖢𝖢 to adversarial erasures. In the bit flip setting, we prove an impossibility bound of 2/7.
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