A BDD-Based Method for LFSR Parallelization with Application to Fast CRC Encoding
Elena Dubrova and Shohreh Sharif Mansouri
Galois Fields of order 2k, GF (2k), provide a unified theoretical framework for constructing parallel devices generating k output bits per clock cycle. In this paper, we use GF(2k) for constructing Linear Feedback Shift Registers (LFSRs) for the parallel encoding of Cyclic Redundancy Check (CRC) codes. CRC codes are widely used in data communication and storage for detecting burst errors. Traditional methods for the parallel encoding of CRC are based on computing the kth power of the connection matrix of the LFSR. We propose an alternative method based on computing the kth power of the transition relation of the LFSR. We use Binary Decision Diagrams (BDDs) for representing the transition relation in a partitioned form. This allows us to bound the size of BDDs by O(n2), where n is the size of the LFSR. The presented algorithm is asymptotically faster than previous algorithms for LFSR parallelization.
Keywords: CRC, LFSR, BDD, transition relation