If I recall correctly, broadband protocols, such as Ethernet, do not use parity bits. Those are used by telephone modems.
However, in the TCP/IP protocol there is other overhead, such as the packet headers. For TCP it is usually 20 bytes per packet. Add to that the IP header which is also usually 20 bytes.
Then there is the transmission protocol, such as Ethernet, which also adds its own headers (12 at the front, 4 at the end.) The 4 at the end is a CRC value, which is where the error checking takes place.
The usual broadband maximum transmission unit (MTU) for TCP/IP is 1500 bytes, which consists of the TCP header, 20 bytes, the IP header, 20 bytes and the payload, 1460 bytes. Ethernet adds 16 bytes for a total of 1516 bytes travelling the wire.
That means, under ideal conditions, the maximum speed that data that can be transferred is 96.3 percent of the bandwidth.
Using base 2 for the math, a 1mbps connection (1048576 bits per second) can (again, under ideal conditions) transfer a maximum of 123.26 KB/s.
1048576 / 8 * .963 / 1024
A 5mbps connection would have a maximum transfer rate of 616.32 KB/s.
Of course, there are other factors that will slow down the transfer, such as latency, resending bad packets, etc.