Homework 2
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1
“Fast” Ethernet operates 10x faster (100Mbps) than regular ethernet. Explain why the following changes were made.
(a) Encoding changed to 4B/5B.
(b) CAT-5 cable has more twists
（a）
常规 Ethernet 使用曼彻斯特编码，频谱效率低，因为一半的带宽用于传输时钟信号
4B/5B编码将4位数据编码成5位信号，这5位信号中至少有一位是1，保证了时钟信号的提取，提高了频谱效率，在相同的带宽下传输更多的数据，能够更好地满足高速传输的需求
（b）
常规Ethernet 通常使用CAT-3电缆，扭曲较少，易受外部干扰，影响信号质量
CAT-5电缆扭曲更多，更密集的扭曲有助于降低外部干扰对信号的影响，提高信号质量，从而支持更高的传输速率
100Mbps的数据速率比10Mbps高很多，对信号完整性要求更高，更多的扭曲可以确保在更高的数据速率下，信号仍然能够保持完整和可靠
2
If a binary signal is sent over a 3-kHz channel whose signal-to-noise radio is 20dB, what is the maximum achievable data rate?
\(20 = 10 log_{10}(S/N )\)
\(\Rightarrow S/N=100\)
$C = W log_2(1+S/N),W=3kHz $
\(\Rightarrow C = 19.97463 kbps\)
3
What are the advantages of fiber optics over copper as a transmission medium? Is there any downside of using fiber optics over copper?
优点
- 更高的带宽： 光纤可以传输更多的数据，因为光信号的频率比电信号高得多。这使得光纤更适合高带宽应用，如互联网、视频流和云计算。
- 更长的传输距离： 光纤可以传输信号更远的距离而不会衰减太多，这使得它更适合长距离通信。
- 更低的损耗： 光纤的损耗比铜线低得多，这意味着信号可以传输更远的距离而不会受到干扰。
- 更强的抗干扰性： 光纤不受电磁干扰的影响，这使得它更适合在电磁干扰强烈的环境中使用。
- 更高的安全性： 光纤信号不容易被窃听或篡改，这使得它更适合用于敏感数据的传输。
缺点：
- 更高的成本： 光纤设备和安装成本通常比铜线设备和安装成本更高。
- 更复杂的安装： 光纤的安装比铜线更复杂，需要更专业的技术和工具。
- 更脆弱： 光纤比铜线更脆弱，更容易断裂。
- 更难维修： 光纤的维修比铜线更难，需要更专业的技术和设备。
4
Is the Nyquist theorem true for high-quality single-mode optical fiber or only for copper wire?
Nyquist theorem 是一个数学性质，和具体技术无关。
其实质是指，如果一个函数的傅里叶频谱不包含频率在 f 之上的正弦和余弦分量，以频率 2f 对该函数采样，就可以获得全部信息
因此，Nyquist theorem 适用于任何传输媒体。
5
What is the minimum bandwidth needed to achieve a data rate of B bits/sec if the signal is transmitted using NRZ and Manchester encoding? Explain your answer
With NRZ, the signal may cycle between the positive and negative levels up to every 2 bits (in the case of alternating 1s and 0s).
This means that we need a bandwidth of at least B/2 Hz when the bit rate is B bits/sec.
In MLT-3, the signal(+,0,-) completes a cycle at most every 3 bits, thus requiring at least B/3 Hz to achieve B bits/sec data rate.
Manchester encoding mix the clocks signal with the data signal by XORing them together so that no extra line is needed.
So it requires twice as much bandwidth as NRZ because of the clock.(2B)
6
Is an oil pipeline a simplex system, a half-duplex system, a full-duplex system, or none of the above? What about a river or a walkie-talkie-style communication?
Is an oil pipeline a simplex system, a half-duplex system, a full-duplex system, or none of the above? What about a river or a walkie-talkie-style communication?
7
A modem constellation diagram similar to Fig. 2-17(a) has data points at the following coordinates: (1,1), (1,-1), (-1,1), (-1,-1). How many bps can a modem with these parameters achieve at 1200 symbols/sec?
8
What is the difference, if any, between the demodulator part of a modem and the coder part of codec? (After all, both convert analog signals to digital ones.)
9
What is the available user bandwidth in an OC-12c connection?
10
Suppose that A, B, and C are simultaneously transmitting 0 bits, using a CDMA system with the chip sequences of Fig.(a). What is the resulting chip sequence