 randomness, and other stochastic properties." have amplitudes 12.5 dB above the rms level is 1 in 105 or about 14 dB for 1 in 106 10,11 Hence, if we wish to ensure an error rate of 10-5 in a particular system using binary polar modulation, the rms noise should be at least 12.5 dB below the signal level (Ref. 8, p. 114). This simple analysis is only valid for the type of modulation used (i.e., binary polar baseband modulation), assuming that no other factors are degrading the operation of the system and that a cosine-shaped receiving filter is used. If we were to interject distortion such as EDD into the system, we could translate the degradation into an equiv- alent signal-to-noise ratio improvement necessary to restore the desired error rate. For example, if the delay distortion were the equivalent of one pulse width, the signal-to- noise ratio improvement required for the same error rate would be about 5 dB, or the required signal-to-noise ratio would now be 17.5 dB. Unlike random noise, which is measured by its rms value when we measure level, impulse noise is measured by the number of "hits" or "spikes" per interval of time above a certain threshold. In other words, it is a measurement of the recurrence rate of noise peaks over a specified level. The word "rate" should not mislead the reader. The recurrence is not uniform per unit time, as the word "rate" may indicate, but we can consider a sampling and convert it to an average. Remember that random noise has a Gaussian distribution and will produce noise peaks at 12.5 dB above the rms value 0.001% of the time on a data bit stream for an equivalent error rate of 1 X 10-5. The 12.5 dB above rms random noise floor should establish the impulse noise threshold for measurement purposes. We should assume that a well-designed data-transmission system traversing the telephone network, the signal-to-noise ratio of the data signal will be well in excess of 12.5 dB. Thus impulse noise may well be the major contributor to the degradation of the error rate. The abbreviat