We have to start by talking about redundancy. I don’t think error detection and correction can be handled this way, so no matter what I do, I’m either going to have to leave out some important background, or this article is just going to be too damn long. But this subject is different from some of the previous articles in which I’ve made the same disclaimer… spread-spectrum communication and system identification are things that can be discussed very narrowly, and with enough empirical usefulness to get around the whirlwind of theory behind them. As I stated in the last few articles, I am not an expert, so if you see something here that is incorrect, please bring it to my attention so I can fix it. I like the subject, but there is just no nice way to present it, without getting sucked into a quagmire of algebra or in some aspect of communications theory that I don’t know enough about. I have had a really really tough time writing this article. This time we are wading into the field of error detection and correction, in particular CRCs and Hamming codes. Last time, we talked about Gold codes, a specially-constructed set of pseudorandom bit sequences (PRBS) with low mutual cross-correlation, which are used in many spread-spectrum communications systems, including the Global Positioning System.
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