Geometrical decoding algorithm and the correcting limit of high-dimensional hypercubic ring code: Correction ability at 20(-1) to 10(-2)

In this paper, a new decoding algorithm is proposed in which high-dimension al coding is done in a parity check code (high-dimensional ring code). The decoding method for the previously reported ring code has a complex correct ing algorithm and requires much calculation time. We have focused on the po int that a high-dimensional ring code can be divided into a number of two-d imensional ring codes, and by repeating the error correction of two-dimensi onal ring codes that requires small computation, we can perform error corre ction of high-dimensional ring codes. This decoding algorithm has a correct ion ability similar to the conventional decoding algorithms but with less c omputation. Moreover, when the error rate is high, random error and burst e rrors are mixed and an error correcting code is needed. However, since the decoding algorithm of the proposed code has a provision for dimensional div ision and the error generated on the transmitted block can be uniformly dis tributed on each two-dimensional plane, the error on the channel in the two -dimensional plane becomes random and error correction can be done efficien tly. Moreover, if analysis or simulation increases the number of dimensions , then the correction ability is increased and the limit of the correction ability is determined from the size m of the code. The performance of convo lutional codes and Reed Solomon codes is compared and it is shown that the ring code has high processing gain of error correction and that if the thre shold point of correction lies in the high-error-rate region, then the deco ding error rate is small and this code can be applied to high-error-rate co rrection. (C) 2001 Scripta Technica.