A novel least significant bit first processing parallel CRC circuit

In HDLC serial communication protocol, CRC calculation can first process the most or least significant bit of data. Nowadays most CRC calculation is based on the most significant bit (MSB) first processing. An algorithm of the least significant bit (LSB) first processing parallel CRC is proposed in this paper. Based on the general expression of the least significant bit first processing serial CRC, using state equation method of linear system, we derive a recursive formula by the mathematical deduction. The recursive formula is applicable to any number of bits processed in parallel and any series of generator polynomial. According to the formula, we present the parallel circuit of CRC calculation and implement it with VHDL on FPGA. The results verify the accuracy and effectiveness of this method.