New Multi-Level Codes Over Gf(q)

By: Nasa, National Aeronautics and Space Adm

Set partitioning to multi-dimensional signal spaces over GF(q), particularly GF sup q-1(q) and GF sup q (q), and show how to construct both multi-level block codes and multi-level trellis codes over GF(q). Two classes of multi-level (n, k, d) block codes over GF(q) with block length n, number of information symbols k, and minimum distance d sub min greater than or = d, are presented. These two classes of codes use Reed-Solomon codes as component codes. They can be easily decoded as block length q-1 Reed-Solomon codes or block length q or q ] 1 extended Reed-Solomon codes using multi-stage decoding. Many of these codes have larger distances than comparable q-ary block codes, as component codes. Low rate q-ary convolutional codes, work error correcting convolutional codes, and binary-to-q-ary convolutional codes can also be used to construct multi-level trellis codes over GF(q) or binary-to-q-ary trellis codes, some of which have better performance than the above block codes. All of the new codes have simple decoding algorithms based on hard decision multi-stage decoding. Wu, Jiantian and Costello, Daniel J., Jr. Unspecified Center NSF NCR-89-03429; NAG5-557...

• Format: Paperback
• Language: English
• ISBN: 1729103944
• ISBN13: 9781729103944
• Release Date: January 1
• Publisher: Independently Published
• Length: 26 Pages
• Weight: 0.19 lbs.
• Dimensions: 0.1" x 8.5" x 11.0"