effect of linear feedback shift register seed

The taps are XOR'd sequentially with the output bit and then fed back into the leftmost bit. The rightmost bit of the LFSR is called the output bit. The bit positions that affect the next state are called the taps. The state shown, 0xACE1 ( hexadecimal) will be followed by 0x5670. The feedback tap numbers in white correspond to a primitive polynomial in the table so the register cycles through the maximum number of 65535 states excluding the all-zeroes state. The mathematics of a cyclic redundancy check, used to provide a quick check against transmission errors, are closely related to those of an LFSR.Ī 16-bit Fibonacci LFSR. Both hardware and software implementations of LFSRs are common. However, an LFSR with a well-chosen feedback function can produce a sequence of bits which appears random and which has a very long cycle.Īpplications of LFSRs include generating pseudo-random numbers, pseudo-noise sequences, fast digital counters, and whitening sequences. Likewise, because the register has a finite number of possible states, it must eventually enter a repeating cycle. The initial value of the LFSR is called the seed, and because the operation of the register is deterministic, the stream of values produced by the register is completely determined by its current (or previous) state. Thus, an LFSR is most often a shift register whose input bit is driven by the exclusive-or (XOR) of some bits of the overall shift register value.

The most commonly used linear function of single bits is XOR.

The maximal sequence consists of every possible state except the '0000' state.Ī linear feedback shift register (LFSR) is a shift register whose input bit is a linear function of its previous state. The XOR gate provides feedback to the register that shifts bits from left to right.

A 4-bit Fibonacci LFSR with its state diagram.

Effect of linear feedback shift register seed