1、Fundamentals of Channel CodingNew words and phrases1 selectively adv.善于挑选地，仔细挑选2 formula n.公式(pl.formulas,formulae)3 sacrifice v.牺牲4 redundant adj.冗余的，多余的5 demonstrate vt.证明，论证6 orthogonal adj.正交的，直角的7 arbitrarily adv.任意地8 raw adj.未加工的(raw data原始数据)9 denote vt.指示，表示10 retransmission n.转发，转播，中继11 sop
2、histicated adj.复杂的12 impractical adj.不切实际的,不能实行的JP13 parity n.奇偶校验14 encoder n.编码器15 codeword n.码字 16 modulo prep.以为模(modulo2 adder模2加法器)Fundamentals of Channel Coding17 alphabet n.字符表，字母表18 linearity n.线性 19 systematic adj.系统的，体系的(systematic code系统码)20 cyclic n.循环的,周期的(cyclic code循环码cyclic shift循环移
3、位)21 subset n.子集22 convolutional adj.卷积的(convolutional code卷积码)23 algebraic adj.代数的;代数学的(algebraic function代数函数)24 stage n.级 25 outline n.提纲；要点；概要 26 fundamentally adv.基础地，根本地 27 polynomial n.多项式(generator polynomial 生成多项式)28 adder n.加法器29 vector n.矢量，向量(vector array向量数组(矩阵)30 identical adj.一致的，相同的
4、31 reveal vt.揭示，显示，展现32 trellis n.格子，格子结构 trellis diagram网格图)33 emanate vi.散发，发出，发源(emanate from发出,发源)Fundamentals of Channel Coding1 error detection code 检错码2 error correction code 纠错码,差错检验码 3 AWGN(Additive White Gaussian Noise)加性高斯白噪声4 channel capacity 信道容量5 transmission bandwidth 传输带宽6 signal pow
5、er 信号功率7 singlesided noise power density 单边噪声功率密度8 bandwidth efficiency 带宽效率9 SNR(S/N,signaltonoise ratio)信噪比,信号噪声比 10 BER(Bit Error Ratio)误码率,误比特率11 in the limit 在极限情况下12 block code 分组码,块码Fundamentals of Channel Coding13 FEC(Forward Error Correction)前向纠错14 code rate 编码率15 code distance(distance of
6、a code)码距 16 code weight(weight of a code)码权,码重 17 Hamming distance 汉明距离，汉明间距18 coding gain 编码增益19 shift register 移位寄存器20 constraint length 制约长度21 generator 生成矩阵22 logic table 逻辑表23 state diagram 状态图24 tree diagram 树形图Fundamentals of Channel Coding Channel coding protects digital data from errors by
7、 selectively introducing redundancies in the transmitted data.Channel codes that are used to detect errors are called error detection codes,while codes that can detect and correct errors are called error correction codes.In 1948,Shannon demonstrated that by proper encoding of the information,errors
8、induced by a noisy channel can be reduced to any desired level without sacrificing the rate of information transfer.Shannons channel capacity formula is applicable to the AWGN channel and is given by C=Blog2(1+P/N0B)=Blog2(1+S/N)(4.1)where C is the channel capacity(bits per second),B is the transmis
9、sion bandwidth(Hz),P is the received signal power(W),and N0 is the singlesided noise power density(W/Hz).The received power at a receiver is given as P=Eb/Rb(4.2)where Eb is the average bit energy,and Rb is the transmission bit rate.Equation(4.1)can be normalized by the transmission bandwidth and is
10、 given byC/B=log2(1+Eb/N0*Rb/B)(4.3）where C/B denotes bandwidth efficiency.Fundamentals of Channel Coding The basic purpose of error detection and error correction techniques is to introduce redundancies in the data to improve wireless link performance.The introduction of redundant bits increases th
11、e raw data rate used in the link,hence increases the bandwidth requirement for a fixed source data rate.This reduces the bandwidth efficiency of the link in high SNR conditions,but provides excellent BER performance at low SNR values.It is well known that the use of orthogonal signaling allows the p
12、robability of error to become arbitrarily small by expanding the signal set,i.e.,by making the number of waveforms M,provided that the SNR per bit exceeds the Shannon limit of SNR b-16 dB.In the limit,Shannons result indicates that extremely wideband signals could be used to achieve error free commu
13、nications,as long as sufficientSNR exists.Error control coding waveforms,on the other hand,have bandwidth expansion factors that grow onlylinearly with the code block length.Fundamentals of Channel CodingError correction coding thus offers advantages in bandwidth limited applications,and also provid
14、es link protection in power limited applications.A channel coder operates on digital message(or source)data by encoding the source information into a code sequence for transmission through the channel.There are two basic types of error correction and detection codes:blockcodes and convolutional code
15、s.Exercises.Please translate the following words and phrases into Chinese.1.channel coding2.transmission bandwidth3.Single sided noise power density4.orthogonal signaling 5.FEC6.logic table7.systematic code8.AWGN 信道编码信道编码传输带宽传输带宽单边带噪声功率密度单边带噪声功率密度正交信号正交信号前向纠（前向纠（forwarderrorcorrection)逻辑表逻辑表系统码系统码加性
16、高斯白噪声加性高斯白噪声(additive white Gaussian noise)Exercises9.BER10.trellis diagram 11.constraint length12.vector array 13.algebraic function 14.state diagram15.cyclic shift16.generator matrix误码率误码率,误比特率误比特率(Bit Error Ratio)网格图网格图 制约长度制约长度向量数组向量数组(矩阵矩阵)代数函数代数函数状态图状态图循环移位循环移位生成矩阵生成矩阵Exercises.Please translat
17、e the following words and phrases into English.1.检错码 2.信道容量 3.分组码 4.卷积码 5.移位寄存器 6.汉明距离 7.码重 8.树形图9.编码增益error detection codeschannel capacityblock codesconvolutional codesshift registerHamming distancecode weight(weight of a code)tree diagramcoding gainExercises10.平均比特能量11.码距12.纠错码13.带宽效率14.模2加法器15.原
18、始数据16.编码率17.生成多项式18.循环码 average bit energycode distance(distance of a code)error correction codesbandwidth efficiencymodulo 2 adderraw datacode rategenerator polynomialcyclic codesExercises.Fill in the blanks with the missing word(s).1.Channel coding protects digital data errors by selectively intro
19、ducing redundancies in the transmitted data.2.By proper encoding of the information,errors induced a noisy channel can be reduced any desired level without sacrificing the rate of information transfer.3.Error control coding waveforms,the other hand,have bandwidth expansion factors that grow only lin
20、early the code block length.4.In a block encoder,k information bits are encoded ncode bits.frombytoonwithintoExercises5.The block code is referred to an(n,k)code,and the rate of the code is defined Rc=k/nand is equal the rate of information divided by the raw channel rate.6.Convolutional codes are f
21、undamentally different block codes in that information sequences are not grouped distinct blocks and encoded.7.The tree diagram shows the structure of the encoder the form of a tree with the branches （represent，represented，representing）the various states and the outputs of the coder.8.This reduces t
22、he bandwidth efficiency of the link high SNR conditions,but provides excellent BER performance low SNR values.9.A systematic code is one which the parity bits are appended the end of the information bits.10.A channel coder operates digital message(or source)data by encoding the source information a
23、code sequence for transmission the channel.astoasfromintoinrepresentinginatintoonintothroughExercises.Answer the following questions according to the text.1.Please write down the Shannons channel capacity formula.2.What is the basic purpose of error detection and error correction techniques?3.How to
24、 define the distance of a codeword?4.Please describe the cyclic shift property in English.C=Blog2(1+P/N0B)=Blog2(1+S/N)The basic purpose of error detection and error correction techniques is to introduce redundancies in the data to improve wireless link performance.The distance of a codeword is the
25、number of elements in which two codewords Ci and Cjdiffer d(Ci,Cj)=(Nl=1)(Ci,Cj,)(modulo q)where d is the distance of the codeword and q is the number of possible values of Cj and Cj.If C=cn-1,cn-2,，c0is a codeword of a cyclic code,then C=cn-2,cn-3,c0,obtained by a cyclic shift of the elements of C,
26、is also a codeword.That is,all cyclic shifts of C are code words.Exercises5.What is a systematic code?6.What is the fundamental difference between convolutional codes and block codes?7.Please give at least three ways to represent convolutional codes.A systematic code is one in which the parity bits
27、are appended to the end of the information bits.For an(n,k)code,the first k bits are identical to the information bits,and the remaining(n-k)bits of each code word are linear combinations of the kinformation bits.Convolutional codes are different from block codes in that informationsequences are not
28、 grouped into distinct blocks and encoded.Instead a continuous sequence of information bits is mapped into a continuous of encoder output bits.Following,is an outline of the various ways of representing convolutional codes:generator matrix,Generator Polynomials,logic table,StateDiagram,Tree Diagram,Trellis Diagram.
