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As a result of huge advancements in VLSI technology, more and more complex circuits are being implemented making not only the whole digital system more prone to faults, but also the fault detector itself susceptible to faults resulting in the requirement of concurrent fault detection architecture of the encoders and decoders. In this paper, we present a multiple-bit parity-based fault detection architecture for parallel CRC computation. After analyzing the parallel implementation of CRC, we present a formulation to generate a multiple-bit parity prediction structure to incorporate the fault detection architecture. Using the formulations of digit level CRC architecture, the checksum is divided into few blocks and predicted multiple-bit parity of the blocks are compared with the actual parity bits. Finally, with the help of software simulation and ASIC implementation, we show that the proposed scheme is highly efficient in terms of fault detection capability whereas it involves small area and time overhead. As an example, we have shown that the worst case area overhead is $25.7$ percent for CRC $-32$ with four parity bits, and corresponding time overhead is $15.6$ percent. [ABSTRACT FROM PUBLISHER]