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The question is broadly about bit error rate, but to be concrete, I am asking it in context of 16-QAM.

Consider we have a rectangular 16-QAM modulation and also assume that we have grey coding. As I understand, grey coding is helpful because even if there is noise, we are off by just 1 bit.

Now, consider the symbols shown in red rectangle in the image below: '0000', '0001' and '0100'. If we incorrectly detect '0000' as '0001' or '0100', bit error is same as in both cases we are off by just 1 bit. However, if we incorrectly fall in '0001', error is tolerable as we are off by the least significant bit. On the other hand, if we fall in '0100', error should be worse as we are off by a higher significant bit.

To sum it up: do we take significance of bit into account while calculating bit error rate? If not, why is that?

enter image description here

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    \$\begingroup\$ Most modern coding schemes do take bit significance into account. For instance one of the later GSM speech codecs uses heavier forward error correction on the 'important' bits in the frame, and less protection on lesser bits. This tends to equalise the importance of all bits that are transmitted. Most physical channel coding, like OFDM, or CDMA, also has this bit importance equalisation as an aim, or at least a useful side effect. \$\endgroup\$
    – Neil_UK
    Commented Dec 7, 2016 at 14:12

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No, because that would imply knowing something about the semantics of the content. Bits are bits; either they're right or they're not, and if they're wrong then it makes no sense to use them.

This is where error detection and error recovery comes in. Checksum or MAC (message authentication code) systems will detect an error in any bit. Sometimes this results in requesting a retransmission.

An alternative approach is to use forward error correction, such as Reed-Solomon, which transmits extra bits which allow the reciever to recover from a certain number of single-bit errors. Again, it doesn't matter which bit position the error is in.

(Also, we should not presume that the LSB of the transmission coding maps to the LSB of anything in the recieved data stream! What if it's the most significant nibble of a quantity representing a 128-bit number?)

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  • \$\begingroup\$ Also, of course, the encoder has no way of knowing if the data chunks (bytes, words, etc) are Little-Endian or Big-Endian. \$\endgroup\$
    – WhatRoughBeast
    Commented Dec 7, 2016 at 17:38
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Bit error rate is precisely what it says: the total number of errored bits per unit time.

Whether the bit happened to be the least significant bit in the coding scheme is of no importance at all in the vast majority of links.

Consider video; if a frame has an erroneous bit, then in some applications I would need to completely discard the frame in some applications if the link had no way of requesting a resend.

Even if the link has a method of requesting the errored frame (such as in ethernet, PCI express and others) errors will effectively reduce the overall throughput of the link.

So - no; the position of the errored bit in the stream is of no consequence.

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