I know that radio waves travel at the speed of light in vacuum so the minimal latency to communicate between Earth and Moon would be about 1.25 second each way. This latency figure will then increase because of the signal processing involved but how much will it increase? Are there some resources that show the relationship between latency and bit-rate when communicating between Earth and Moon?
Once the communications get to earth the latency increase is minimal in comparison. In telecommunications and networking we generally use milliseconds (ms or thousanths of a second) to measure communications delay. 1.25 seconds is 1250ms. There's 2 major components to latency:
- Digital Signal Processing of the satellite feed, both sending and receiving: this is hard to calculate, it depends on the type of signal and the equipment, but generally about 20ms would be the maximum I would expect
- The speed of communications through the physical medium: Fiber optics is the most widespread data communications medium these days, the speed of light through fiber optics is about 200M meters/second, so it all depends on how far the communications has to go. The maximum I would expect to see would be sending data halfway around the world: half of the earth's circumference is 20M meters, so .1 of a second or 100ms
There is also latency from network devices to be considered, the more hops through equipment the more this will be, factoring 1-2ms per hop. If you are NASA or another major space agency you probably can minimize this, so factor in about 5ms for this.
So adding it all up you have a minimum of around 20ms to a maximum expected Earth latency of 125ms, which is exactly 1/10th of the space latency. Chances are it's less than that due to less distance between the receiver and the endpoint for the data.
EDIT: For reference, the definition of latency in data communications is how long it takes a single piece of information to get from one point to another, for instance a packet. Bandwidth is not a factor in latency, but it is a factor in how long it takes to get a body of information from one point to another.
You can still have arbitrarily high bandwidth even with high latency (e.g., a FedEx transporter full of hard disks driving around the country has awful latency, but incredible bandwidth).
If you use TCP/IP as communications protocol, you are limited by the fact that you cannot transfer more than one tcp receive windows per round trip time. Using the TCP Windows Scale option, the window could be up to 1 GB in size, so the maximal sustainable bandwidth would be 1 GB per 2.5 seconds, or 0.4 Gigabyte per second. Some caveats: This would require to reserve 1 GB as buffer space per TCP connection, and if retransmits become necessary, this may throw you back in the range of GB as well.