His seminal research contributions include the celebrated Baum-Welch algorithm that is used to find unknown parameters of a hidden Markov model, and which has found widespread application in many fields including speech processing, cryptanalysis, and bioinformatics; the Berlekamp-Welch algorithm used to efficiently decode Reed-Solomon codes; the McEliece-Rodemich-Rumsey-Welch best asymptotic upper bound on the rate of a binary code; the Welch lower bound on the maximum cross-correlation of signals; and the family of Gordon-Mills-Welch sequences having ideal autocorrelation and large linear span.
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The initial vision of cellular communications was to deliver ubiquitous voice communications to anyone anywhere. In a simplified view, 1G delivered voice services for business customers, and only 2G for consumers. Next, this also initiated the appetite for cellular data, for which 3G was designed. However, Blackberry delivered business smartphones, and 4G made smartphones a consumer device. The promise of 5G is to start the Tactile Internet, to control real and virtual objects in real-time via cellular. However, the hype around 5G is, again, focusing on business customers, in particular in the context of campus networks. Consequently, 6G must provide an infrastructure to enable remote-controlled mobile robotic solutions for everyone—the Personal Tactile Internet. Which role can information and communication theory play in this context, and what are the big challenges ahead?