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This paper shows why Thomas Kailath received the medal of honor which is IEEE's highest commendation. It is said that his algorithms re-engineered digital communications and semiconductor processing. He has worked for four decades on algorithms that detect signals distorted by bouncing off objects in the environment, separate wireless signals by determining their direction using antenna arrays, and compensate for the distortion of optical systems used in semiconductor processing. Along the way, he established new ways of structuring complex problems to speed up their calculation. This work has improved the efficiency of much of the technology that makes modern life possible.