# What are the definitions of symbols and samples related to PCM?

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\} \$$ ?

## 1 Answer

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.

• 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? – helloworld1e. Sep 24 '19 at 17:53
• Ternary with AMI encoding requires eight symbols. See en.wikipedia.org/wiki/Bipolar_encoding#Alternate_mark_inversion. Correct about the symbols. – MBaz Sep 24 '19 at 19:07