1. Dr. Richard Hamming’s Contributions to Computer Science and Telecommunications Dr. Charles C. Tappert Professor of Computer Science Seidenberg School of CSIS 2015 Research Day

2. Life Overview 1915 (February 11) – born in Chicago 1942 PhD – University of Illinois 1944 – Assistant Professor, University of Louisville 1945-1946 – Manhattan Project, Los Alamos, NM 1946-1976 – Bell Labs, Murray Hill, New Jersey 1976-1998 – Adjunct Professor of Computer Science, Naval Postgraduate School, Monterey, California 1998 (January 7) – died age 82 (almost 83) 2015 Research Day

3. Manhattan Project: 1945-1946 Worked in Hans Bethe's Theoretical Division Programmed on IBM calculating machines solving equations provided by the physicists Interesting story: In 1946 when Hamming left Los Alamos for Bell Labs in New Jersey, he bought Klaus Fuchs's old car. About the time he sold the car in 1950, Fuchs was found to be a spy conveying hydrogen bomb information to the Russians, and Hamming was interrogated by the FBI. 2015 Research Day

4. Hamming’s Key Contributions Hamming Distance Hamming Codes Hamming Window Hamming Numbers Hamming Bound or Sphere-Packing Bound 2015 Research Day

5. Hamming Distance Introduced by Richard Hamming in his fundamental paper Error detecting and error correcting codes in 1950 Used in telecommunication to count the number of flipped bits in a fixed-length binary word as an estimate of error Example: distance between 1011101 and 1001001 is 2 Usually used but not restricted to binary numbers 2015 Research Day

6. Hamming Codes A family of linear error-correcting codes used in telecommunication that generalize the Hamming(7,4)-code invented by Hamming in 1950 Hamming codes can detect up to two-bit errors or correct one-bit errors without detection of uncorrected errors They are perfect codes because they achieve the highest possible transmission rate for codes of their block length Example: Hamming(7,4) has 4 data bits and 3 parity bits for a total of 7 bits, yielding a data transmission rate of 4/7 = 0.57 2015 Research Day

7. Hamming Window In signal processing a window function is a mathematical function that is zero outside an interval Applications of window functions include spectral analysis, filter design, and beamforming Typical window functions are smooth "bell-shaped" curves because rectangular windows can cause problems 2015 Research Day

8. Hamming Numbers Regular numbers are numbers that evenly divide powers of 60. As an example, 60 2 = 3600 = 48 × 75, so both 48 and 75 are divisors of a power of 60. Equivalently, they are the numbers whose only prime divisors are 2, 3, and 5 In computer science, regular numbers are often called Hamming numbers, after Hamming proposed the problem of finding computer algorithms for generating these numbers in order 2015 Research Day

9. Hamming Bound or Sphere-Packing Bound A limit on the parameters of an arbitrary block code: Also the volume bound from an interpretation in terms of packing balls in the Hamming metric into the space of all possible words It gives an important limitation on the efficiency with which any error-correcting code can utilize the space in which its code words are embedded A code which attains the Hamming bound is said to be a perfect code 2015 Research Day

10. Some Hamming Quotes At Los Alamos I was brought in to run the computing machines which other people had got going, so those scientists and physicists could get back to business.... I saw Feynman up close. I saw Fermi and Teller. I saw Oppenheimer. I saw Hans Bethe: he was my boss. At Bell Labs I came into a very productive department. Shannon was there... I shared an office for a while with Shannon. At the same time he was doing information theory, I was doing coding theory. It is suspicious that the two of us did it at the same place and at the same time - it was in the atmosphere. 2015 Research Day