Shannon and Gallagher's research is extremely important to wireless communications, without them we would still be talking using wires. A CRC checksum can only

Shannon and Gallagher's research is extremely important to wireless communications, without them we would still be talking using wires. A CRC checksum can only tell you when some bits flipped while in transmission -- these codes can tell you which bits they were and correct them so that you don't need to resend the packet (or drop it on the floor).