Title :
New multilevel codes over GF(q)
Author :
Wu, J. ; Costello, D.J., Jr.
Author_Institution :
Dept. of Electr. Eng., Notre Dame Univ., IN, USA
fDate :
5/1/1992 12:00:00 AM
Abstract :
Set partitioning is applied to multidimensional signal spaces over GF(q), i.e., GF/sup n1/(q) (n1or=d are presented. These codes use Reed-Solomon codes as component codes. Longer multilevel block codes are also constructed using q-ary block codes with block length longer than q+1 as component codes. Some quaternary multilevel block codes are presented with the same length and number of information symbols as, but larger distance than, the best previously known quaternary one-level block codes. It is proved that if all the component block codes are linear. the multilevel block code is also linear. Low-rate q-ary convolutional codes, word-error-correcting convolutional codes, and binary-to-q-ary convolutional codes can also be used to construct multilevel trellis codes over GF(q) or binary-to-q-ary trellis codes.<>
Keywords :
error correction codes; GF(q); Reed-Solomon codes; binary-to-q-ary convolutional codes; binary-to-q-ary trellis codes; block codes; block length; component codes; information symbols; minimum distance; multidimensional signal spaces; multilevel codes; q-ary block codes; q-ary convolutional codes; quaternary codes; set partitioning; trellis codes; word-error-correcting convolutional codes; Block codes; Convolution; Convolutional codes; Decoding; Information rates; Multidimensional systems; NASA; Phase modulation; Reed-Solomon codes;
Journal_Title :
Information Theory, IEEE Transactions on
