Decoding Algorithm of High-dimensional Ring Code
Shinichi Kuroda, Ichi Takumi, Masayasu Hata · International Symposium on Information Theory and its Applications · 1994
In this paper, we proposed a decoding algorithm of the high-dimensional Ring Code, based on two-dimensional Ring Codes. Because the Ring Code consists of torus knot and spreads errors, this code can decode errors without distinguishing burst or random. Also, we give an approximate formula of BER improvement after correction, and show that by choosing size m satisfying m2 x p < 1, BER after correction approaches to zero, as the dimension n of Ring Code approaches infinity. By computer simulation, we show this code can decode errors in severe channel error rate of l0-1 - 10-2, and further effective application condition of the Ring Code. It is generally sufficient to use 3-D Ring Code, however more than three dimension is suitable where BER is more severe situations. In the results, Ring Code can decode errors of channel error rate 8 x 10-3 with transmission rate 1/2 , 2 x l0-2 with rate 1/3, for an uncorrectable block rate of l0-4.