Statistics in Reliability
Shannon’s channel coding theorem showed, contrary to the popular belief at the time, that if and only if the average transmission rate is below C, iid messages can be transmitted with error probability decreasing to 0 by increasing the size of the message block. This theorem gives the operational meaning of C as the upper bound at which a channel can carry reliable communication. Shannon (1948) calculated the capacity of the additive Gaussian white noise channel with a power constraint. This capacity is being approached by sophisticated coding methods in applications such as space and satellite communications, audio/video transmission, and CDs and CD-ROMs. Models for wireless communication channels, such as those in cellular phones, must be time-varying and must accommodate multiple users (Biglieri, Proakis, and Shamai 1998; Lapidoth and Narayan 1998). Their decoding is essentially statistical inference with time-varying time series models. Joint source-channel coding gives better data throughput, but complicates decoding even further. With limited bandwidth to share, any decoding mileage is worthwhile. This demands efficient statistical inference procedures for special time-varying time series models, and fast algorithms in applications such as cellular phones. It is safe to say that wireless communication promises to be another good example of the happy union of theory and practice.