A proof is provided that a logarithmic redundancy factor is necessary for the reliable computation of the parity function by means of a network with noisy gates. This result was first stated by R.L. Dobrushin and S.I. Ortyukov (1977). However, the authors believe that the analysis given by Dobrushin and Ortyukov is not entirely correct. The authors establish the result by following the same steps and by replacing the questionable part of their analysis with entirely new arguments.
© 1991 Institute of Electrical and Electronics Engineers
Pippenger, N.; Stamoulis, G.D.; Tsitsiklis, J.N., "On a lower bound for the redundancy of reliable networks with noisy gates," Information Theory, IEEE Transactions on , vol.37, no.3, pp.639,643, May 1991. doi: 10.1109/18.79921