2004  American Math Society's "Arnold Ross Lecturer"

1999: National Academy of Sciences, Computer and Information Sciences Section
        (and affiliate member, Applied Mathematics Section)
        Plus: NAS/NAE Boards and Committees

1977: National Academy of Engineering, Computer Science Section

1996: American Academy of Arts and Sciences, Mathematics Section

2001: Fellow, American Association for the Advancement of Science

IEEE Information Theory Society

1998: Golden Jubilee Award
1993: Shannon Award
1969: Best Research Paper Award

IEEE

1991: R. W. Hamming Medal
1990: Koji Kobayashi Computers and Communications Award
1984: Centennial Medal
1971: Fellow

1975-1976: ACM Lecturer for Special Interest Group on Symbolic and Algebraic Manipulation

1971: Eta Kappa Nu "Outstanding Young Electrical Engineer" Award

1961: William Lowell Putnam Intercollegiate Mathematics Competition, top 5