In this paper we study function-correcting codes, a new class of codes designed to protect the function evaluation of a message against errors. We show that FCCs are equivalent to irregular-distance codes, i.e., codes that obey some given distance requirement between each pair of codewords. Using these connections, we study irregular-distance codes and derive general upper and lower bounds on their optimal redundancy. Since these bounds heavily depend on the specific function, we provide simplified, suboptimal bounds that are easier to evaluate. We further employ our general results to specific functions of interest and compare our results to standard error-correcting codes, which protect the whole message.

翻译：本文研究函数纠错码——一种旨在保护消息函数评估免受错误影响的新型编码。我们证明函数纠错码等价于非正则距离码，即每对码字之间满足特定距离要求的编码。利用这种关联，我们研究了非正则距离码，并推导出关于其最优冗余度的通用上界与下界。由于这些界严重依赖于具体函数，我们进一步提出了易于评估的简化次优界。最后，我们将通用结论应用于特定目标函数，并将结果与保护完整消息的标准纠错码进行比较。