Ring code – code symmetry and uncorrectable errors
Tadayoshi Noda, Masayasu Hata · Electronics and Communications in Japan (Part III Fundamental Electronic Science) · 1990
Abstract This paper proposes a ring code as a new burst error‐correcting code, where the check sequence forms a ring on a square code array. The code is a quasi‐cyclic quasi‐optimal code with a symmetrical structure. Because of its cyclic decoding process, it has a feature that the error‐correcting code for a long burst can easily be constructed. This paper discusses also the properties of the code, as well as the correspondence between the code symmetry and the uncorrectable property. The relation is described clearly from the viewpoints of geometrical structure and the group theory. The computation for the uncorrectable probability is established. Finally, the two‐dimensional ring code is considered, but the theory can be extended to the three‐dimensional and the higher‐dimensional ring code. Due to the symmetry of higher order, the hidden errors are reduced and the error‐correcting power is improved. The exact evaluation of the performance of the code, however, is left to another paper.