Syndrome key equation solution is one of the important processes in the decoding of Reed-Solomon codes. This paper proposes a low power key equation solver (KES) architecture where the power consumption is reduced by decreasing the required number of multiplications without degrading the decoding throughput and latency. The proposed method employs smaller number of multipliers than a conventional low power KES architecture. The critical path in the proposed KES circuit is minimized so that the operation at a high clock frequency is possible. A low power folded KES architecture is also proposed to further reduce the hardware complexity by executing folded operations in a pipelined manner with a slight increase in decoding latency.

Reed-Solomon (RS) code is one of the well-known and widely used error correction codes. Among the components of a hardware RS decoder, the key equation solver (KES) unit occupies a relatively large portion of the hardware. It is important to develop an efficient KES architecture to implement efficient RS decoders. In this paper, a novel polynomial division technique used in the Euclidean algorithm (EA) of the KES is presented which achieves the short critical path delay of one Galois multiplier and one Galois adder. Then a KES architecture with the EA is proposed which is efficient in the sense of the product of area and time.