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\} \ $ ?


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.

  • $\begingroup$ 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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.