Data Rate Limits

- Data Rate Limits

- data rate 계산 공식

1. Nyquist: for noiseless channel

2. Shannon: for noisy channel

 

- Nyquist Rate

: 이론적인 최대 비트레이트를 정의함.

 BitRate = 2 * bandwidth * log2L  (L: 레벨 수)

ex) We need to send 265 kbps over a noiseless channel with a bandwidth of 20kHz. How many signal levels do we need?

: 265,000 = 2 * 20,000 * log2L  ->  log2L = 6.625  ->  L=26.625 = 98.7 levels

 

- Shannon Capacity

- 실제로 노이즈 없는 채널은 없다. Shannon capacity로 noisy channel의 이론적 최대 비트레이트를 정의한다.

- Capacity = bandwidth * log2(1+SNR)    (참고: SNRdB = 10log10SNR)

- extremely noisy channel의 Capacity C는 0이다.

ex) The signal-to-noise ratio is often given in decibels. Assume that SNRdB = 36 and the channel bandwidth is 2MHz. The theoretical channel capacity can be calculated as

: SNRdB = 10log10SNR -> SNR = 103.6 = 3981.  C=Blog2(1+SNR)=2*106*log23982=24 Mbps

ex) We have a channel with a 1-MHz bandwidth. The SNR for this channel is 63. What are the appropriate bit rate and signal level?

: C=106log2(1+63)=106log264=6 Mbps. 이는 upper limit이므로 noise를 고려해서 4Mbps를 선택하고 계산한다. -> 4Mbps = 2*1MHz*log2L -> L = 4