BCH 2-Bit and 3-Bit Error Correction with Fast Multi-Bit Error Detection

Abstract

In this paper an new approach combining 2-bit and 3-bit BCH error correction with fast and simple error detection for errors of higher order is presented. Under the assumption that a 2-bit error or 3-bit error occurred, the corresponding correction bits are determined using the syndrome components $s_1, s_3$ for 2-bit errors and $s_1, s_3, s_5$ for 3-bit errors. These correction bits are used to calculate higher syndrome components up to $s_{2T-1}$, which are compared to the actual corresponding syndrome components. If the syndrome components match, a 2-bit error or 3-bit error was detected. In the case of a syndrome mismatch, an error other than a 2-bit error or 3-bit error occurred and was detected. The proposed method provides a simple way to differentiate between 2-bit errors (3-bit errors) and errors of higher order.