计算机网络第四版中文答案(补充)
答:信噪比为20 dB 即 S/N =100.由于 log2101≈6.658,由香农定理,该信道的信道容量为3log2(1+100)=19.98kbps。
又根据乃奎斯特定理,发送二进制信号的3kHz 信道的最大数据传输速率为
2*3 log22=6kbps。
所以可以取得的最大数据传输速率为6kbps。
5. 答:为发送T1 信号,我们需要
所以,在50kHz 线路上使用T1 载波需要93dB 的信噪比。
6. 答:无源星没有电子器件,来自一条光纤的光照亮若干其他光纤。有源中继器把光信号转换成电信号以作进一步的处理。
7. 答:
因此,在0.1 的频段中可以有30THz。
8. 答:数据速率为480×640×24×60bps,即442Mbps。
需要442Mbps 的带宽,对应的波长范围是 。
9. 答:奈奎斯特定理是一个数学性质,不涉及技术处理。该定理说,如果你有一个函数,它的傅立叶频谱不包含高于f 的正弦和余弦,那么以2 f 的频率采样该函数,那么你就可以获取该函数所包含的全部信息。因此奈奎斯特定理适用于所有介质。
10. 答:3 个波段的频率范围大约相等,根据公式
小的波段⊿ 也小,才能保持⊿f 大约相等。
顺便指出,3 个带宽大致相同的事实是所使用的硅的种类的一个碰巧的特性反映。
11. 答:
12. 答:1GHz 微波的波长是30cm。如果一个波比另一个波多行进15cm,那么它们到达时将180异相。显然,答案与链路长度是50km 的事实无关。
13. 答:
If the beam is off by 1 mm at the end, it misses the detector. This amounts to a triangle with base 100 m and height 0.001 m. The angle is one whose tangent is thus 0.00001. This angle is about 0.00057 degrees.
14. With 66/6 or 11 satellites per necklace, every 90 minutes 11 satellites pass overhead. This means there is a transit every 491 seconds. Thus, there will be a handoff about every 8 minutes and 11 seconds.
15. The satellite moves from being directly overhead toward the southern horizon, with a maximum excursion from the vertical of 2. It takes 24 hours to go from directly overhead to maximum excursion and then back.
16. The number of area codes was 8×2×10, which is 160. The number of prefixes was 8×8 ×10, or 640. Thus, the number of end offices was limited to 102,400. This limit is not a problem.
17. With a 10-digit telephone number, there could be 1010 numbers, although many of the area codes are illegal, such as 000. However, a much tighter limit is given by the number of end offices. There are 22,000 end offices, each with a maximum of 10,000 lines. This gives a maximum of 220 million telephones. There is simply no place to connect more of them. This could never be achieved in practice because some end offices are not full. An end office in a small town in Wyoming may not have 10,000 customers near it, so those lines are wasted.
18. 答:每部电话每小时做0.5 次通话,每次通话6 分钟。因此一部电话每小时占用一条电路3 分钟,60/3=20,即20 部电话可共享一条线路。由于只有10%的呼叫是长途,所以200 部电话占用一条完全时间的长途线路。局间干线复用了1000000/4000=250 条线路,每条线路支持200 部电话,因此,一个端局可以支持的电话部数为200*250=50000。
19. 答:双绞线的每一条导线的截面积是 ,每根双绞线的两条导线在10km 长的情况下体积是 ,即约为15708cm。由于铜的密度等于9.0g/cm3,每个本地回路的质量为 9×15708 =141372 g,约为141kg。这样,电话公司拥有的本地回路的总质量等于141×1000×104=1.41×109kg,由于每千克铜的价格是3 美元,所以总的价值等于3×1.4×10 9=4.2×109美元。
20. Like a single railroad track, it is half duplex. Oil can flow in either direction, but not both ways at once.
21. 通常在物理层对于在线路上发送的比特不采取任何差错纠正措施。在每个调制解调器中都包括一个CPU 使得有可能在第一层中包含错误纠正码,从而大大减少第二层所看到的错误率。由调制解调器做的错误处理可以对第二层完全透明。现在许多调制解调器都有内建的错误处理功能。
22. 每个波特有4 个合法值,因此比特率是波特率的两倍。对应于1200 波特,数据速率是2400bps。
23. 相位总是0,但使用两个振幅,因此这是直接的幅度调制。
24. If all the points are equidistant from the origin, they all have the same amplitude, so amplitude modulation is not being used. Frequency modulation is never used in constellation diagrams, so the encoding is pure phase shift keying.
25. Two, one for upstream and one for downstream. The modulation scheme itself just uses amplitude and phase. The frequency is not modulated.
26. There are 256 channels in all, minus 6 for POTS and 2 for control, leaving 248 for data. If 3/4 of these are for downstream, that gives 186 channels for downstream. ADSL modulation is at 4000 baud, so with QAM-64 (6 bits/baud) we have 24,000 bps in each of the 186 channels. The total bandwidth is then 4.464 Mbps downstream.
27. A 5-KB Web page has 40,000 bits. The download time over a 36 Mbps channel is 1.1 msec. If the queueing delay is also 1.1 msec, the total time is 2.2 msec. Over ADSL there is no queueing delay, so the download time at 1 Mbps is 40 msec. At 56 kbps it is 714 msec.
28. There are ten 4000 Hz signals. We need nine guard bands to avoid any interference. The minimum bandwidth required is 4000×10 400×9 =43,600 Hz.
29. 答:125 的采样时间对应于每秒8000 次采样。一个典型的电话通道为4kHz。根据奈奎斯特定理,为获取一个4kHz 的通道中的全部信息需要每秒8000 次的采样频率。
(Actually the nominal bandwidth is somewhat less, but the cutoff is not sharp.)
30. 每一帧中,端点用户使用193 位中的168(7*24)位,开销占25(=193-168)位,因此开销比例等于25/193=13%。
31. 答:比较使用如下方案的无噪声4kHz 信道的最大数据传输率:
(a) 每次采样2 比特的模拟编码 ——16kbps
(b) T1 PCM 系统——56kbps
In both cases 8000 samples/sec are possible. With dibit encoding, two bits are sent per sample. With T1, 7 bits are sent per period. The respective data rates are 16 kbps and 56 kbps.
32. 答:10 个帧。
在数字通道上某些随机比特是0101010101 模式的概率是1/1024。察看10 个帧,若每一帧中的第一位形成比特串0101010101,则判断同步成功,而误判的概率为1/1024,小于0.001。
33. 答:有。编码器接受任意的模拟信号,并从它产生数字信号。而解调器仅仅接受调制了的正弦(或余弦)波,产生数字信号。
34. 答:a.CCITT 2.048Mbps 标准用32 个8 位数据样本组成一个125 的基本帧,30 个信道用于传信息,2 个信道用于传控制信号。在每一个4kHz 信道上发送的数据率就是
8*8000=64kbps。
b.差分脉码调制(DPCM)是一种压缩传输信息量的方法,它发送的不是每一次抽样的二进制编码值,而是两次抽样的差值的二进制编码。现在相对差值是4 位,所以对应每个4kHz 信道实际发送的比特速率为4*8000=32bps。
c.增量调制的基本思想是:当抽样时间间隔s t 很短时,模拟数据在两次抽样之间的变化很小,可以选择一个合适的量化值? 作为阶距。把两次抽样的差别近似为不是增加一个?就是减少一个? 。这样只需用1bit 二进制信息就可以表示一次抽样结果,而不会引入很大误差。因此,此时对应每个4kHz 信道实际发送的数据速率为1*8000=8kHz。
35. 答:在波的1/4 周期内信号必须从0 上升到A。为了能够跟踪信号,在T/4 的时间内(假定波的周期是T)必须采样8 次,即每一个全波采样32 次,采样的时间间隔是1/x,因此波的全周期必须足够的长,使得能包含32 次采样,即T > 32/x,或f max =x/32。
36. 答:10-9的漂移意味着109 秒中的1 秒,或1 秒中的10-9 秒。对于OC-1 速率,即51.840Mbps,取近似值50Mbps,大约一位持续20ns。这就说明每隔20 秒,时钟就要偏离1位。这就说明,时钟必须每隔10 秒或更频繁地进行同步,才能保持不会偏离太大。
37. 答:基本的SONET 帧是美125 产生810 字节。由于SONET 是同步的,因此不论是否有数据,帧都被发送出去。每秒8000 帧与数字电话系统中使用的PCM 信道的采样频率完全一样。
810字节的SONET 帧通常用90列乘以9行的矩形来描述,每秒传送51.84Mbps,即8×810×8000=51840000bps。这就是基本的SONET 信道,它被称作同步传输信号STS-1,所有的SONET 干线都是由多条STS-1构成。
每一帧的前3 列被留作系统管理信息使用,前3 行包含段开销,后6 行包含线路开销。
剩下的87 列包含87×9×8×8000=50112000bps。被称作同步载荷信封的数据可以在任何位置开始。线路开销的第一行包含指向第一字节的指针。同步载荷信封(SPE)的第一列是通路开销。
通路开销不是严格的SONET 结构,它在嵌入在载荷信封中。通路开销端到端的流过网络,因此把它与端到端的运载用户信息的SPE 相关联是有意义的。然而,它确实从可提供给端点用户的50.112Mbps 中又减去1×9×8×8000=576000bps,即0.576Mbps,使之变成49.536Mbps 。OC-3相当于3个OC-1复用在一起,因此其用户数据传输速率是49.546×3=148.608 Mbps。
38. VT1.5 can accommodate 8000 frames/sec ×3 columns×9 rows×8 bits =1.728 Mbps. It can be used to accommodate DS-1. VT2 can accommodate 8000 frames/sec ×4 columns×9 rows ×8 bits = 2.304 Mbps. It can be used to accommodate European CEPT-1 service. VT6 can accommodate 8000 frames/sec×12 columns×9 rows×8 bits = 6.912 Mbps. It can be used to accommodate DS-2 service.
39. Message switching sends data units that can be arbitrarily long. Packet switching has a maximum packet size. Any message longer than that is split up into multiple packets.
40. 答:当一条线路(例如OC-3)没有被多路复用,而仅从一个源输入数据时,字母c(表示conactenation,即串联)被加到名字标识的后面,因此,OC-3 表示由3 条单独的OC-1 线路复用成155.52Mbps,而OC-3c 表示来自单个源的155.52Mbps 的数据流。OC-3c 流中所包含的3 个OC-1 流按列交织编排,首先是流1 的第1 列,流2 的第1 列,流3 的第1 列,随后是流1 的第2 列,流2 的第2 列,⋯⋯以此类推,最后形成270 列宽9 行高的帧。
OC-3c 流中的用户实际数据传输速率比OC-3 流的速率略高(149.760Mbps 和148.608Mbps),因为通路开销仅在SPE 中出现一次,而不是当使用3 条单独OC-1 流时出现的3 次。换句话说,OC-3c 中270 列中的260 列可用于用户数据,而在OC-3 中仅能使用258列。更高层次的串联帧(如OC-12c)也存在。
OC-12c 帧有12*90=1080 列和9 行。其中段开销和线路开销占12*3=36 列,这样同步载荷信封就有1080-36=1044 列。SPE 中仅1 列用于通路开销,结果就是1043 列用于用户数据。
由于每列9 个字节,因此一个OC-12c 帧中用户数据比特数是8 ×9×1043=75096。每秒8000 帧,得到用户数据速率75096×8000 =600768000bps,即600.768Mbps。
所以,在一条OC-12c 连接中可提供的用户带宽是600.768Mbps。
41. 答:The three networks have the following properties:
星型:最好为2,最差为2,平均为2;
环型:最好为1,最差为n/2,平均为n/4
如果考虑n 为奇偶数,
则n 为奇数时,最坏为(n-1)/2,平均为(n+1)/4
n 为偶数时,最坏为 n/2,平均为n2/4(n1)
全连接:最好为1,最差为1,平均为1。
42. 对于电路交换, t= s时电路建立起来;t=s+ x /d 时报文的最后一位发送完毕;t= s+x/b+kd时报文到达目的地。而对于分组交换,最后一位在t=x/b时发送完毕。
为到达最终目的地,最后一个分组必须被中间的路由器重发k1次,每次重发花时间p/ b,所以总的延迟为
为了使分组交换比电路交换快,必须:
所以:
43. 答:所需要的分组总数是x /p ,因此总的数据加上头信息交通量为(p+h)x/p位。
源端发送这些位需要时间为(p+h)x/pb
中间的路由器重传最后一个分组所花的总时间为(k-1)(p+h)/ b
因此我们得到的总的延迟为
对该函数求p 的导数,得到
令
得到
因为p>0,所以
故
时能使总的延迟最小。
44. Each cell has six neighbors. If the central cell uses frequency group A, its six neighbors can use B, C, B, C, B, and C respectively. In other words, only 3 unique cells are needed. Consequently, each cell can have 280 frequencies.
45. First, initial deployment simply placed cells in regions where there was high density of human or vehicle population. Once they were there, the operator often did not want to go to the trouble of moving them. Second, antennas are typically placed on tall buildings or mountains. Depending on the exact location of such structures, the area covered by a cell may be irregular due to obstacles near the transmitter. Third, some communities or property owners do not allow building a tower at a location where the center of a cell falls. In such cases, directional antennas are placed at a location not at the cell center.
46. If we assume that each microcell is a circle 100 m in diameter, then each cell has an area of 2500. If we take the area of San Francisco, 1.2 108 m2 and divide it by the area of 1 microcell, we get 15,279 microcells. Of course, it is impossible to tile the plane with circles (and San Francisco is decidedly three-dimensional), but with 20,000 microcells we could probably do the job.
47. Frequencies cannot be reused in adjacent cells, so when a user moves from one cell to another, a new frequency must be allocated for the call. If a user moves into a cell, all of whose frequencies are currently in use, the user’s call must be terminated.
48. It is not caused directly by the need for backward compatibility. The 30 kHz channel was indeed a requirement, but the designers of D-AMPS did not have to stuff three users into it. They could have put two users in each channel, increasing the payload before error correction from 260 ×50=13 kbps to 260×75 =19.5 kbps. Thus, the quality loss was an intentional trade-off to put more users per cell and thus get away with bigger cells.
49. D-AMPS uses 832 channels (in each direction) with three users sharing a single channel. This allows D-AMPS to support up to 2496 users simultaneously per cell. GSM uses 124 channels with eight users sharing a single channel. This allows GSM to support up to 992 users simultaneously. Both systems use about the same amount of spectrum (25 MHz in each direction).
D-AMPS uses 30 KHz×892 = 26.76 MHz. GSM uses 200 KHz ×124 =24.80 MHz. The difference can be mainly attributed to the better speech quality provided by GSM (13 Kbps per user) over D-AMPS (8 Kbps per user).
50. The result is obtained by negating each of A, B, and C and then adding the three chip sequences. Alternatively the three can be added and then negated.
The result is (+3 +1 +1 1 3 1 1 +1).
51. By definition
If T sends a 0 bit instead of 1 bit, its chip sequence is negated, with the i-th element becoming Ti . Thus,
52. When two elements match, their product is +1. When they do not match, their product is 1. To make the sum 0, there must be as many matches as mismatches. Thus, two chip sequences are orthogonal if exactly half of the corresponding elements match and exactly half do not match.
53. Just compute the four normalized inner products:
(1 +1 3 +1 1 3 +1 +1) d (1 1 1 +1 +1 1 +1 +1)/8 = 1
(1 +1 3 +1 1 3 +1 +1) d (1 1 +1 1 +1 +1 +1 1)/8 = 1
(1 +1 3 +1 1 3 +1 +1) d (1 +1 1 +1 +1 +1 1 1)/8 = 0
(1 +1 3 +1 1 3 +1 +1) d (1 +1 1 1 1 1 +1 1)/8 = 1
The result is that A and D sent 1 bits, B sent a 0 bit, and C was silent.
54. 答:可以,每部电话都能够有自己到达端局的线路,但每路光纤都可以连接许多部电话。忽略语音压缩,一部数字PCM电话需要64kbps 的带宽。如果以64kbps 为单元来分割10Gbps,我们得到每路光缆串行156250 家。现今的有线电视系统每根电缆串行数百家。
55. 答:它既像TDM,也像FDM。100 个频道中的每一个都分配有自己的频带(FDM),在每个频道上又都有两个逻辑流通过TDM 交织播放(节目和广告交替使用频道)。
This example is the same as the AM radio example given in the text, but neither is a fantastic example of TDM because the alternation is irregular.
56. A 2-Mbps downstream bandwidth guarantee to each house implies at most 50 houses per coaxial cable. Thus, the cable company will need to split up the existing cable into 100 coaxial cables and connect each of them directly to a fiber node.
57. The upstream bandwidth is 37 MHz. Using QPSK with 2 bits/Hz, we get 74 Mbps upstream. Downstream we have 200 MHz. Using QAM-64, this is 1200 Mbps. Using QAM-256, this is 1600 Mbps.
58. Even if the downstream channel works at 27 Mbps, the user interface is nearly always 10-Mbps Ethernet. There is no way to get bits to the computer any faster than 10-Mbps under these circumstances. If the connection between the PC and cable modem is fast Ethernet, then the full 27 Mbps may be available. Usually, cable operators specify 10 Mbps Ethernet because they do not want one user sucking up the entire bandwidth.
第 3 章 数据链路层
1. 答:由于每一帧有0.8 的概率正确到达,整个信息正确到达的概率为 p=0.810=0.107。
为使信息完整的到达接收方,发送一次成功的概率是p ,二次成功的概率是(1-p)p,三次成功的概率为(1-p)2 p,i 次成功的概率为(1-p)i-1 p,因此平均的发送次数等于:
2. The solution is
(a) 00000100 01000111 11100011 11100000 01111110
(b) 01111110 01000111 11100011 11100000 11100000 11100000 01111110
01111110
(c) 01111110 01000111 110100011 111000000 011111010 01111110
3. After stuffing, we get A B ESC ESC C ESC ESC ESC FLAG ESC FLAG D.
4. If you could always count on an endless stream of frames, one flag byte might be enough. But what if a frame ends (with a flag byte) and there are no new frames for 15 minutes. How will the receiver know that the next byte is actually the start of a new frame and not just noise on the line? The protocol is much simpler with starting and ending flag bytes.
5. The output is 011110111110011111010.
6. 答:可能。假定原来的正文包含位序列01111110 作为数据。位填充之后,这个序列将变成01111010。如果由于传输错误第二个0 丢失了,收到的位串又变成01111110,被接收方看成是帧尾。然后接收方在该串的前面寻找检验和,并对它进行验证。如果检验和是16 位,那么被错误的看成是检验和的16 位的内容碰巧经验证后仍然正确的概率是1/216。如果这种概率的条件成立了,就会导致不正确的帧被接收。显然,检验和段越长,传输错误不被发现的概率会越低,但该概率永远不等于零。
7. 答:如果传播延迟很长,例如在探测火星或金星的情况下,需要采用前向纠错的方法。还有在某些军事环境中,接收方不想暴露自己的地理位置,所以不宜发送反馈信号。如果错误率足够的低,纠错码的冗余位串不是很长,又能够纠正所有的错误,前向纠错协议也可能是比较合理和简单的。 |