- Input split up into blocks of length
*k*, each block denoted**u** - Outputs codewords of length
*n*, each codeword entry called a*symbol*, each codeword denoted**v** - Block length and codeword length combo called a (
*n,k*) block code - Code rate =
*R=k/n*= number of information bits per transmitted symbol - Each message is coded independantly
- Block coder can be made as a combinational logic circuit, has no memory

*k*bit blocks,**u**and**v**represent sequences of blocks instead of a single block- Each block depends on
*m*previous message blocks - Has memory
- Must be implemented with a sequential logic circuit

How bits are represented being sent through the channel

- Binary Phase Shift Keying
- The phase of the sin wave is shifted between 0 and π to represent a 0 and 1

- M-ary Phase Shift Keying
- has M different phased sin waves representing combinations of bits
- for 4psk (also called QPSK), each phase represents 2 bits
- for 8psk, each phase represents 3 bits
- etc... 2
^{# bits}=*M*psk

- Doesn't depend on any previous messages (
*memoryless*) - M-ary input modulator
- Physical channel
- Q-ary output modulator
- Uses
*transition probabilities*, probability of*j*output given*i*input

- If one encoded symbol is transmitted every T seconds,
- Baud Rate = symbol transmission rate = 1/T
- Data rate = information transmission rate = R/T bits per second (bps) = (
*k/n*)/T - Bandwidth = Difference between upper and lower frequencies representing the range of frequencies the channel is capable of
- Bandwidth should be at least T/2 hertz

**u**= encoder input**v**= encoder output**r**= decoder input**u**= decoder output^{^}- Chooses output with maximum probability of being correct
- Equivalent to maximizing the log-likelyhood function
- log
*P*(**r**|**v**) = log*P*(*r*|_{0}*v*) + log_{0}*P*(*r*|_{1}*v*) + log_{1}*P*(*r*|_{2}*v*) ..._{2} - MLD for a DMC chooses
**v**which maximizes the above, which is then decoded to get^{^}**u**^{^}

- log

- The number of bits or symbols that differ between the encoder output
**v**and received decoder input**r** - denoted
*d*(**r**,**v**) - For a modulation where M=2 and Q=2 (modulator and demodulator both produce only a 0 or 1) (binary symmetric channel, BSC),
MLD chooses
**v**with smallest hamming distance^{^} - Also called minimum distance decoder

- Errors are only corrected at the receiver end since transmission is one way only

- Error probability: probability there is still an error after decoding
- Word Error Rate (WER): probability a decoded block/word has an error
- Block Error Rate (BLER): same as WER
- Bit Error Rate (BER): probability a bit in the decoded output is an error
- Signal to Noise Ratio (SNR): Energy-per-information-bit vs. noise power spectral density at receiver input, in decibels