Error-Correcting-Codes in Computer Arithmetic
Abstract
Arithmetic codes are useful for error-control in digital computation as well as in data transmission. These codes are especially suitable for checking or correcting errors in arithmetic processors due to carry propagation. Two known classes of arithmetic codes are the small-distance high-rate perfect single-error correcting codes and the large-distance low-rate Mandelbaum-Barrows codes. These codes are analogous to the Hamming codes and the maximum-length sequence codes in parity-check block codes respectively. Most other arithmetic codes known have been obtained by computer-search. The discovery for a systematic way of constructing arithmetic codes with intermediate-rate and intermediate-distance has been the subject of research for many years. Finding simpler decoding algorithms is another major unsolved problem in arithmetic codes. Decoding for arithmetic codes by matching the orbits or permuting the residues associated with the codes is straightforward but largely impractical. A particularly interesting question is the possibility of decoding arithmetic codes by majority-logic. In the paper, the author has constructed a class of intermediate-rate intermediate-distance binary cyclic arithmetic codes.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1972
- Accession Number
- AD0748201
Entities
People
- Chao-kai Liu
Organizations
- University of Illinois Urbana–Champaign