McEliece, R. J. | Engineering Papers

NASA NTRS1995

Trellis Decoding Complexity of Linear Block Codes

We consider the problem of finding a trellis for a linear block code that minimizes one or more measures of trellis complexity. The domain of optimization may be different permutations of the same code, or different codes with the same parameters. Constraints on trellises, including relationships between the minimal trellis of a code and that of the dual code, are used to derive bounds on complexity. We define a partial ordering on trellises: if a trellis is optimum with respect to this partial ordering, it has the desirable property that it simultaneously minimizes all of the complexity measures examined. We examine properties of such optimal trellises and give examples of optimal permutations of codes, most notably the (48,24,12) quadratic residue code.

trellis decoding↗

NASA NTRS1994

Reed-Solomon Codes and the Exploration of the Solar System

The exploration of the solar system by unmanned spacecraft is one of the triumph of the 20th century. The dramatic photographs of Mercury, Venus, Mars, Jupiter, Saturn, Uranus, and Neptune transmitted by spacecraft with romantic names like Mariner, Voyager, Viking, etc. over distances of hundreds of millions, even billions, of miles, have made these planets, which were previously known to us only as fuzzy telescopic images in textbooks, as real to us in the 1990's as, say, the Himalayas, the Sahara Desert, or Antarctica.

Reed-Solomon coding↗