Reducing The Error Ratio (!)

Believe me, I do re-read these postings before handing them off to Lockergnome. Nevertheless, when I see the final version as posted, the number of typos and minor errors that appear still astound me. In the last column, I referred to the error rate in a signal transmission. Orvar Windisch called me on that and correctly pointed out that I really should have referred to the error in transmission ratio, not rate. The ratio indicates the number of bad bits in a string of good ones. The rate actually refers to the number of errors/second. These are related, but distinct parameters. Probably only a few professionals noticed my error. As Orvar points out, even communications professionals make this mistake in casual talk.

So why even bother to mention it? Because the article itself was about the propagation of errors. But when we talk about error in a document, we often use a casual definition of “error”. There was no error in transmitting from my typing fingers to my computer to the Internet to Lockergnome to your computer to your screen in the use of the word “rate”. However, I did make an error in choosing to type the wrong word. This is different from an error I made some time ago when I inadvertently posted the word “lightening” when I meant “lightning,” which is a whole different thing. The second type of error was really a comedy in that I had mis-spelled the word I wanted and the spell checker replaced what I had typed with the wrong option – and I didn’t notice. The first error was incorrect usage on my part.

Both these types of errors (using the wrong word accidentally or due to ignorance or incorrect usage) are different from the transmission errors that I discussed in the last two articles. A hidden assumption in the development so far is that a human has created a document that is defined as perfect (regardless of actual content). The job of the transmission system is to reproduce exactly that document at another location. In the process of converting the document to a form that can be transmitted (digital, analog, smoke signals, whatever), noise is introduced. During the actual transmission, more noise is introduced. In the conversion back to a document, even more noise in introduced. (We could carry this further by considering the ability of the receiving person to correctly read the document, but that is another story.) The only errors we have considered are mechanical ones that enter consideration after a perfect document is generated. For most applications, careful design coupled with error detection and correction methods can reduce the error ratio (!) so low that, for all practical purposes, it is zero.

In practice, we can copy tens of gigabytes of data from one HD to another and back again without a single bad bit in the final version. However, along the way, the data stream might have (most probably) contained errors that were corrected on the fly. In addition to the encoding algorithms for error correction, the system might decide to re-send portions of the message to correct errors. This happens in reading from hard drives. If a sector is getting weak, the system might have to read it several times to be satisfied it got a good chunk of data.

By sending a file back and forth between two hard drives, one could estimate the upper limit for the effective error ratio of the transfer function. Try it. Like I said, for practical purposes, it is zero. This is due to clever design. By comparison, the errors I make in generating the original document to begin with are due to design flaws in the specific model of human body I happen to be inhabiting.

[Side note concerning an example of correct English usage: Noah Webster was in the pantry making love to the kitchen maid when his wife came in and saw them. “Noah!” she exclaimed, “I am surprised…” With great aplomb, the famous word maven responded, “No, my dear, you are astonished. I am surprised.”]

In response to the interest my original tutorial generated, I have completely re – written and expanded it. Check out the tutorial availability through Lockergnome. The new version is over 100 pages long with chapters that alternate between discussion of the theoretical aspects and puzzles just for the fun of it. Puzzle lovers will be glad to know that I included an answers section that includes discussions as to why the answer is correct and how it was obtained. Most of the material has appeared in these columns, but some is new. Most of the discussions are expanded compared to what they were in the original column format.

[tags]decision theory,error ratio,orvar windisch,transmission noise,communcation error[/tags]

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