# Bert Simonovich's Design Notes

Innovative Signal Integrity & Backplane Solutions

## To Know The Bit Error Rate Is To Know The Bit Error Ratio

Recently I came across a blog post titled, “Can Oscilloscopes Really Calculate BERs?”, written by Ransom Stephens.

I liked this article. I liked it because, as usual, Ransom likes to challenge your way of thinking and makes you go back to basics in order to understand. For example, when he debates whether BER is “bit error ratio” or “bit error rate”, it stopped me in my tracks to question if I was using the correct terminology, and why. For the record, when I started my career working on T1 line repeaters, I was taught it was “rate”. But, technically, Ransom’s assertion that it really is “ratio” is also correct.

Before you discount this and say, “In mathematics, there can be only one answer”, stay with me here, and let me try to explain where I’m coming from. According to Merriam-Webster dictionary, the definition of ratio is, “the indicated quotient of two mathematical expressions”, or “the relationship in quantity, amount, or size between two or more things: proportion”. If you take the number of bit errors and divide them by the total number of bits, then you have, by definition, a ratio, as Ransom claims. For example, if you have 1 error in 1 TBits of data, then you have a “bit error ratio” of 1E-12.

When you look up the word rate, in the same dictionary, the definition is, “reckoned value: valuation” or “a fixed ratio between two things”. In terms of BER, when it is defined as rate, the fixed ratio between two things is the number of errors over some period of time. Since a bit has a time component associated with it, you can convert the total number of bits into time by multiplying it by the bit time. For example, at 10 GB/s, the bit time is 100 ps. So 1TB of data takes 100 seconds to transmit all of the bits. If there was 1 bit error during that time, you would have a “bit error rate” of 1 error per 100 seconds.

In mission critical applications, we usually aspire to have error-free performance for the life of the product. As bit rates continue to climb, that’s an awful lot of bits. Theoretically, if you want your product to have a bit error rate of 1 error in 25 yrs, then, at 10GB/s, you would need to transmit 7.884E+18 bits;[25yrs*(60*60*24*365)sec/yr*10GB/s] to have a bit error ratio of 1.268E-19!

Bit error ratio, or bit error rate? It kind of reminds me of part of the song, “Let’s Call the Whole Thing Off”, by George and Ira Gershwin; “You like to-may-toes, and I like to-mah-toes”. At the end of the day, it’s still tomatoes. In the right context, I think both terms are equally valid. You need to be ambidextrous, so to speak, in your analysis and how you quote the number.

Written by Bert Simonovich

May 23, 2012 at 10:23 am

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