Given an information polynomial code I(x) = X^7 + x^6 + x^1 + 1, which

1.	Given an information polynomial code I(x) = X^7 + x^6 + x^1 + 1, which is its corresponding per-bit information frame?
Answer» Answer: ALSO called CRC (Cyclic Redundancy Check) Data is sent with a checksum. When arrives, checksum is recalculated. Should match the one that was sent. Bitstring represents polynomial. e.g. 110001 represents: 1 . x5 + 1 . x4 + 0 . x3 + 0 . x2 + 0 . x1 + 1 . x0 = x5 + x4 + x0 The order of a polynomial is the power of the highest non-zero COEFFICIENT. This is polynomial of order 5. Special CASE: We don't allow bitstring = all zeros. Easy to use framing or stuffing to make framed-and-stuffed TRANSMISSION never all-zero, while still allowing PAYLOAD within it to be all-zero.

Given an information polynomial code I(x) = X^7 + x^6 + x^1 + 1, which is its corresponding per-bit information frame?

Answer»

Answer:

ALSO called CRC (Cyclic Redundancy Check)

Data is sent with a checksum.

When arrives, checksum is recalculated. Should match the one that was sent.

Bitstring represents polynomial.

e.g. 110001 represents:

1 . x5 + 1 . x4 + 0 . x3 + 0 . x2 + 0 . x1 + 1 . x0

= x5 + x4 + x0

The order of a polynomial is the power of the highest non-zero COEFFICIENT. This is polynomial of order 5.

Special CASE: We don't allow bitstring = all zeros.

Easy to use framing or stuffing to make framed-and-stuffed TRANSMISSION never all-zero,

while still allowing PAYLOAD within it to be all-zero.