问题 单项选择题

利用海明码(HammingCode)纠正单位错,如果有6位信息位,则需要加入()位冗余位。

A.2

B.3

C.4

D.5

答案

参考答案:C

解析:

[分析]: 按照海明的理论,纠错码的编码就是把所有合法的码字尽量安排在n维超立方体的顶点上,使得任一对码字之间的距离尽可能大。如果任意两个码字之间的海明距离是d,则所有少于等于d-1位的错误都可以检查出来,所有少于d/2位的错误都可以纠正。一个自然的推论是,对某种长度的错误串,要纠正它就要用比仅仅检测它多一倍的冗余位。

如果对于m位的数据,增加k位冗余位,则组成n=m+k位的纠错码。对于2m个有效码字中的每一个,都有n个无效但可以纠错的码字。这些可纠错的码字与有效码字的距离是1,含单个错误位。对于一个有效的消息总共有n+1个可识别的码字。这n+1个码字相对于其他2m-1个有效消息的距离都大于1。这意味着总共有2m(n+1)个有效的或是可纠错的码字。显然这个数应小于等于码字的所有可能的个数,即2n。于是,有

2m(n-1)<2n

因为n=m+k,所以得出

m+k+1<2k

对于给定的数据位m,上式给出了k的下界,即要纠正单个错误,A必须取最小值。据此可以计算如下:

m=6,6+k+1<2k,可取k=4,得到6+4+1=11<24=16

选择题
阅读理解

阅读理解。

     After graduation I returned home to my small town in Indiana. I didn't have a job yet. Mr. Hobbs, a

friend of my father's, owned a small shirt factory in town. Within the past five years it had grown from

twenty to eighty workers. Mr. Hobbs was worried that his plant was getting too big and inefficient, so he

asked me to come in on a short-term basis as a consultant.

    I went to the plant and spent about a week looking around and making notes. I was really a mazed at

what I saw.

    Most curious of all, there was no quality control at all. No one inspected the final product of the factory. As a result some of the shirts that were put in boxes for shipment were missing one or two buttons, the

collar, and even a sleeve sometimes!

    The working conditions were poor. The tables where the workers sat were very high and

uncomfortable. Except for a half hour at lunchtime, there were no breaks in the day to relieve the boring

work. There was no music. The walls of the workrooms were a dull gray color. I was amazed that the

workers hadn't gone on strike.

    Furthermore, the work flow was irregular. There was one especially absent-minded young man in the

assembly (组装) line who sewed on buttons. After a while I recognized him as "Big Jim", who used to sit

behind me in math class in high school. He was very slow and all the shifts were held up at his position.

Workers beyond him in line on his shift had to wait with nothing to do; therefore, a great deal of time and

efficiency were lost as Big Jim daydreamed while he worked. All week I wondered why he wasn't fired.

    After I made observations for a week, Mr. Hobbs asked me for an oral report of my findings.

1. The shirts from Mr. Hobbs' factory can be described as ____.

A. of low quality    

B. of high quality  

C. fashionable  

D. unfashionable

2. Why did Mr. Hobbs ask the writer to the factory?

A. The factory was too big.

B. The factory was not producing fast enough.

C. The factory was not big enough.

D. The writer was a college graduate.

3. Which is not likely to happen in the factory?

A. The workers will have more rest in the day.    

B. Someone will examine the final product.

C. New machines will be bought.             

D. The factory will be repainted.

4. Big Jim may get fired mainly because ____.

A. he was slow                                  

B. he wasted much time

C. he was absent-minded                  

D. the work flow was irregular