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We know that Coding Theory depends on the fact that the probability p of a bit flip must be less than 0.5. From Fundamentals of Error-Correcting Codes (pg.39), it states

In most practical situations p is very small.

Using the technology we have in 2020 such as Fiber-optic cable, other types of cables, or wireless medium, what is the practical probability a bit encountering a flip during transmission?

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  • \$\begingroup\$ Bits don't flip; it's noise added to the signal that cons the receiver into believing it received a 1 when it was a zero (or vice versa). A different receiver placed several miles away in a different direction may not witness any error therefore, you cannot say that a bit has flipped during transmission else it would affect both receivers i.e. it's a local phenomenon. So, the probability is down to how much noise is present and how good the receiver is at distinguishing an error free bit over the symbol duration period. \$\endgroup\$ – Andy aka Aug 8 at 23:22
  • \$\begingroup\$ It depends on the system. For example a music CD can tolerate some manufacturing imperfections due to ECC, but it will also tolerate degrading media such as scratches. \$\endgroup\$ – Justme Aug 9 at 7:21
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For fiber optic communications the design point is frequently taken as an error rate of 1 in 10**12 bits.

For wired links such as ethernet the raw bit rate is approximately 1 in 10**14.

Error rates and testability

WHAT IS BER (BIT ERROR RATIO)

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  • \$\begingroup\$ As a point of comparison, some 100 Gb Ethernet protocols have a maximum BER of $10^{-5}$, and user error correction codes to achieve a lower system BER. \$\endgroup\$ – The Photon Aug 9 at 0:15
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Bit Errors depend on

  • sampling jitter (phase noise)

  • squareness of the dataeye

  • deterministic and random amplitude noise

  • appropriate thresholding

  • whether Noise is measured in BitRate bandwidth, or in HalfBitRate bandwidth

From my bit_synchronizer work of decades ago, for NRZ data, once out past 16dB SNR, the BER is dropping over a decade per dB ----- unless there is significant timing jitter.

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  • \$\begingroup\$ I agree but the slope above 16dB depends on the compression ratio of bits/baud and other factors and whether the noise is Gaussian or not. On @Kevin's example WHAT IS... it appears to be 0.5 dB per decade above 20 dB SNR. i.stack.imgur.com/leuq9.png With FEC or ECC it becomes steeper and almost brick wall e,g,--75 to -70dBm for 11Mbps practically error free on WiFi while -80 dBm is almost unusable. with a 1 mm change in direction of the laptop. from Ricean fading can make this difference. but +1 anyways. \$\endgroup\$ – Tony Stewart Sunnyskyguy EE75 Aug 8 at 23:30

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