# Degradation and Restoration of Digital Signals

The signals used to transmit bits always suffer from degradation, because any physical process degrades. However, the degraded signal can be “cleaned up,” because we know that each bit is either 0 or 1. Thus, the previous signal might be degraded to give figure below;

Despite the general erosion of the signal, we can still figure out which are the 0s and which are the Is, and restore it what we have as properly corrected.

This restoration isn’t possible with analog signals, because with analog there arent’t just two possibilities. Compare a photocopy of a photocopy… with a copy of copy of a copy of a computer file. The computer files are (very probably) perfect copies of the original file.

The actual implementation of digital transmission is somewhat more complex than this, but the general technique is the same: two signals that are easily distinguishable even when they are degraded.

Error Detection
Suppose we have a really bad bit of static, so a I turns into a 0 or vice versa. Then what? We can detect errors by transmitting some additional, redundant information. Usually, we transmit a “parity” bit : this is an extra bit that is 1 if the original binary data has an odd number of 1s. therefore, the transmitted bytes always have an even number of 1s. this is called “even” parity. (There’s also “odd” parity.)

How does this help? If the receiver gets a byte with an odd number of 1s, there must have been and error, so we ask for a re-transmission. Thus, we can detect errors in transmission.

Error Correction
With some additional mathematical tricks, we can not only detect that a bit is wrong, but which bit is wrong, which means we can correct the value. Thus, we don’t even have to ask for re-transmission, we can just fix the problem and go on.

What if more than one bit is wrong? What if a whole burst of errors comes along? There are mathematical tricks involving larger chunks of bits to check whether the transmission was correct. If not, re-transmission is often possible.

The main point here is that digital transmission and storage of information offers the possibility of perfect (undegraded) copies, because we are only trying to distinguish is from 0s, and because of mathematical error checking and error correcting.