Fully parallel encoding method and fully parallel decoding method of memory system

Abstract

A memory system, a fully parallel encoding method, and a fully parallel decoding method are disclosed. The encoding method utilizes a plurality of minimal polynomials that constitute a generator polynomial to derive a plurality of roots from the minimal polynomials. A first encoding matrix derived according to the roots of the minimal polynomials is subsequently decomposed to derive a second encoding matrix, in which partial elements of the second encoding matrix are common in those of a parity check matrix of the decoder, such that the encoder and the decoder can efficiently share the same hardware. In addition, the decoding method defines a new error locator polynomial and utilizes a cubic matrix operation to respectively combine the equations, which reduces the hardware required by the fully parallel architecture.