A note on some efficient estimates of the noise variance for first-order Reed-Muller codes (Corresp.)

The maximum-likelihood estimate based on order statistics for both a single-sample and an
M
-sample estimate are derived for the first-order Reed-Muller code sent over a zero-mean white Gaussian noise channel. The estimation method is subject to an equipment-complexity constraint. The constraint imposed requires that the estimates be obtained from successive comparisons of the correlations in a serial system, without the use of arithmetic operations. The maximum-likelihood estimates obtained here are compared to that of Posner [1], Posner et aL [2], and also the unrestricted maximum-likelihood estimate.