Citation
Abstract
Solomon and van Tilborg [2] have developed convolutional encoding algorithms for quadratic residue (QR) codes of lengths 48 and beyond. For these codes and reasonable constraint lengths, there are sequential decodings for both hard and soft decisions. There are also Viterbi type decodings that may be simple, as in a convolutional encoding/decoding of the extended Golay Code. In addition, the previously found constraint length K = 9 for the (48, 24; 12) QR code was lowered to K = 8 by Solomon [1]. In our search for the smallest possible constraint lengths K for (80, 40; 16) self-dual quadratic residue and nonquadratic residue codes, we have found the constraint lengths K = 14 and K = 13, respectively. We have discovered a K = 21 convolutional encoding for the (104, 52; 20) QR code; there may be a smaller K for a (104, 52; 20) self-dual code that is not a quadratic residue code. The smaller the K, the less complex the sequential or Viterbi decoder. I. (80, 40; 16) QR Code The vector (c ) is a codeword of the (79;40;15) QR code generated by check polynomial g(x) = i x40+x39+x37+x35+x32+x29+x28+x24+x22+x18+x17+x16+x15+x13+x12+x11+x6+x4+x3+1, where c = 1 for i = 0;1;14;15;24;30;34;35;37;39;41; i 43;47;53;57;58;61;66;68;69;70;71;74 c = 0 otherwise i Let 1Independent consultant to the Communications Systems Research Section. 2Student at the California Institute of Technology, Pasadena, California.
Details
- Volume
- 42-118
- Published
- August 15, 1994
- Pages
- 1–4
- File Size
- 245.9 KB