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What are the definitions of symbols and samples related to PCM? For example in binary encoding $\{0,1\}$ with 8 levels of quantization, is one symbol either of $ \ 0 \ or \ 1\ $? or is it the collection of $(x,y,z)$ where $x,y,z \ \epsilon \ \{0,1\}$.

Similary for ternary encoding $\{0,1,-1\}$,suppose with 9 levels of quantization, is a symbol either of $-1,1,or \ 0 \ $ or is it complete $(x,y)$ where $x,y \ \epsilon \ \{-1,0,1\} \ $ ?

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Quantization and encoding are largely independent. "Symbols" is another word for "pulses", and the line encoding can also play a role in how the information is transmitted.

Say you quantize one sample to $256 = 2^8$ levels, or 8 bits/sample. In order to transmit those 8 bits, you can, among other options:

  • use binary encoding, which requires transmitting eight symbols, each with amplitude in the set $\lbrace +, - \rbrace$, where $+$ and $-$ correspond to some predefined voltage levels.

  • Use ternary encoding with AMI (alternate mark inversion), which also requires eight symbols, but now with amplitudes in the set $\lbrace +, -, 0 \rbrace$.

  • Use quaternary (or 2B1Q) encoding, which requires four symbols.

Other examples may include Manchester encoding, CMI, block line codes.... but in all cases, one symbol correponds to one transmitted pulse.

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  • $\begingroup$ Wont ternary encoding require just 6 symbols? $log_{10}(256) \ = \ 5.04 $ so , number of 3 level symbols required is 6. Additonally just to clarify the "symbol" means one of the encoded amplitude, right? $\endgroup$ – helloworld1e. Sep 24 '19 at 17:53
  • $\begingroup$ Ternary with AMI encoding requires eight symbols. See en.wikipedia.org/wiki/Bipolar_encoding#Alternate_mark_inversion. Correct about the symbols. $\endgroup$ – MBaz Sep 24 '19 at 19:07

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