Linear hashes are known to possess error-correcting capabilities. However, in most applications, non-linear hashes with pseudorandom outputs are utilized instead. It has also been established that classical non-systematic random codes, both linear and non-linear, are capacity achieving in the asymptotic regime. Thus, it is reasonable to expect that non-linear hashes might also exhibit good error-correcting capabilities. In this paper, we show this to be the case. Our proof is based on techniques from multiple access channels. As a consequence, we show that Systematic Random Non-Linear Codes (S-RNLC) are capacity achieving in the asymptotic regime. We validate our results by comparing the performance of the Secure Hash Algorithm (SHA) with that of Systematic Random Linear Codes (SRLC) and S-RNLC, demonstrating that SHA performs equally.

翻译：线性散列已知具有纠错能力。然而，在大多数应用中，使用的是具有伪随机输出的非线性散列。已有研究证明，经典的非系统随机码（包括线性和非线性）在渐近条件下能够达到信道容量。因此，有理由认为非线性散列也可能展现出良好的纠错能力。本文证实了这一点。我们的证明基于多址接入信道技术。作为结果，我们证明了系统随机非线性码（S-RNLC）在渐近条件下能够达到信道容量。通过比较安全散列算法（SHA）与系统随机线性码（SRLC）及S-RNLC的性能，我们验证了结果，表明SHA表现相当。