CRC Checking for High Speed LFSR with Modified State-Space Transformation Model

Linear Feedback Shift Register (LFSR) is a shift register with its input bit as a linear operation of its previous state. Most commonly, this function is a Boolean exclusive OR(XOR) .LFSRs are as such used in cyclic error correcting codes like BCH and CRC encoders. Parallelization of LFSR increases the system throughput rate, thus makes it useful for high-speed communication. State-space transformation technique reduces the circuit complexity of parallel architectures and the encoder consists of matrix multiplications, with searching of transformation matrices. The new technique is the construction of a modified transformation matrix and the corresponding searching algorithms for the desirable transformation matrix which has both speed and area advantages. The register with a well chosen feedback produces sequence of bits which exhibits psuedo-random behavior thus making it applicable for very fast generation of pseudo-random sequence such as in cryptography, digital broadcasting, fast counters, test-pattern generation, radio jamming systems etc. Keywords - BCH, CRC, LFSR, State-Space Transformation.