外文翻译--数字通信交织

INTERLEAVING Interleaving is used to obtain time diversity in a digital communications system without adding any second generation digital cellular system, due to the rapid proliferation of digital speech coders which transform analog voices into efficient digital messages that are transmitted over wireless links (speech coders are presented in Chapter 7). Because speech coders attempt to represent a wide range of voices in a uniform and efficient digital format, the encoded data bits (called source bits)carry a great deal of information, and as explained in Chapter 7 and 10, some source bits are more important than others and must be protected from error .It is typical for many speech coders to produce several “important” bits in succession, and it is the function of the interleaver to spread these bits out in time so that if there is a fade or noise burst , the important bits form a block of source data are not corrupted at the same time . By spreading the source bits over time, it becomes possible to make use of error control coding(called channel coding)which protects the source data from corruption by the channel. Since error control codes are designed to protect against channel errors that may occur randomly or in a bursty manner , interleavers scramble the time order of source bits before they are channel code. An interleaver can be one of two forms-a block structure or a convolutional structure. A block interleaver formats the encoded data into a rectangular array of m rows and n columns, and interleaves nm bits at a time. Usually, each row contains a word of source data having n bits. An interleaver of degree m (or depth m) consists of m rows. The structure of block interleaver is shown in Figure 6.17. As seen, source bits are placed into the interleaver by sequentially increasing the row number for each successive bit, and filling the columns. The interleaved source data is then read out row-wise and transmitted over the channel. This has the effect of separating the original source bits by m bit periods. At the receiver, the de-interleaver stores the received data by sequentially increasing the row number of each successive bit, and then clocks out the data row-wise, one word (row) at a time. Convolutional interleavers can be used in place of block interleavers in much the same fashion. Convolutional interleavers are ideally suited for use with convolutional codes. There is an inherent delay associated with an interleaver since the received message block cannot be fully decoded until all of the nm bits arrive at the receiver and de-interleaved. In practice, human speech is tolerable to listen to until delays of greater than 40 ms occur. t is for this reason that al of the wireless data interleavers have delays which do not exceed 40ms.The interleaver word size and depth are closely related to the type of speech coder used, the source coding rate and the maximum tolerable delay. FUNDAMENTAL OF CHANNEL CODING Channel coding protects digital data form errors by 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 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=B /1(log2 p 0NB)=B 2log (1+S/N) Where C is the channel capacity (bits per second), B is the transmission band-width (Hz), P is the received signal power (watts), and N0 is the single-sided noise power density (watts/Hz). The receiver is given as P=bbREWhere bEis the average bit energy, and bRis the transmission bit rate. Equation can be normalized by the transmission bandwidth and is given by Where C/B denotes bandwidth efficiency. 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 the 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 know that the use of orthogonal signaling allows the probability 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 SNbR=-1.6dBVit79.In the limit, Shannons result indicates that extremely wideband signals could be used to achieve error free communications, as long as sufficient SNR exists. Error control coding waveforms, on the other hand, have bandwidth expansion factors that grow only linearly with the code block length. Error correction coding thus offers advantages in bandwidth limited applications, and also provides 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 : block codes and convolutional codes. BLOCK CODES Block codes are forward error correction (FEC) codes that enable a limited number of errors to be detected and corrected without retransmission. Block codes can be used to improve the performance of a communications system when other means of improvement (such as increasing transmitter power or using a more sophisticated demodulator) are impractical. In block codes, parity bits are added to blocks of messages bits to make code words or code blocks. In a block encoder, k information bits are encoded into n code bits. A total of n-k redundant bits are added to the k information bits for the purpose of detecting and correcting errors. The block codes is referred to as an (n, k) code , and the rate of the code is defined as cR=k/n and is equal to the rate of information divided by the raw channel rate. The ability of a block code to correct errors is a function of the code distance. Many families of codes exist that provide varying degrees of error protection Cou93,Hay94,Lin83,Sk93,andVit79. Example 6.5 Interleavers and block codes are typically combined for wireless speech transmission. Consider an interleaver with m rows and n bit words. Assume each word of the interleaver is actually made up of k source bits and (n,k) bits from a block code. The resulting interleaver/coder combination will break up a burst of channel error of length l=mb into m burst of length b. Thus an (n,k) code that can handle burst errors of length b(n-k)/2 can be combined with an interleaver of degree m to create an interleaved (mn,mk) block code that can handle bursts of length mb. As long as mb or fewer bits are corrupted during the transmission of the coded speech signal from the interleaver, the received data will be error free. Besides the code rate, other important parameters are the distance and the weight of a code. These are defined below. Distance of Code The distance of a codeword is the number of elements in which two codewords iCand iCdiffer d(iC,jC)=ljNi liCC ,1 ,(模 q) Where d is the distance of the codeword and q is the number of possible values of iCand iC. If the code used binary, the distance is known as the Hamming distance. The minimum distance mind is the smallest distance for the given set and is given as |),(|m in ji CCdM ind Weight of a Code , The weight of a codeword is given by the number of nonzero elements in the codeword. For a binary code, the weight is basically the number of 1s in the codeword and is given as )( iC Nl liC1 ,PROPERTIES OF BLOCK CODES Linearity Suppose iCand iCare two code words in an (n, k) block code. Let 1 and 2 be any two elements selected form the alphabet. Then the code is said to be linear if and only if 1 21 CC 2 is also a code word. A linear code must contain the all-zero code word. Consequently, a constant-weight code is nonlinear. Systematic A systematic code is one in which the parity bits 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 combination of the k information bits. Cyelie-Cyelie codes are a subset of the class of linear codes which satidfy the following cyclic shift property: If C= C=021 ,., ccc nn is a code word of a cyclic code, then C=021 ,., ccc nn , obtained by a cyclic shift of the elements of C, is also a code word. That is, all cyclic shift of C are code words. As a consequence of the cyclic property, the codes possess a considerable amount of structure which can be exploited in the encoding and decoding operations. Encoding and decoding techniques makes use of the mathematical constructs knows as finite fields. Finite fields are algebraic systems which contain a finite set of elements. Addition, subtraction, multiplication, and division of finite field elements is accomplished without leaving the set (i.e., the sum/product of two field elements is a field element). Addition and multiplication must satisfy the commutative, associative, and distributive laws. A formal definition of a finite field is given below: Let F be a finite set of elements on which two binary operations-addition and multiplication are defined. The set F together with the two binary operations is a field if the following conditions are satisfied: F is a commutative group under addition. The identity element with respect to addition is called the zero element and is denoted by 0. The set of nonzero elements in F is a commutative group under multiplication. The identity element with respect to multiplication is called the unit element and is denoted by 1. Multiplication is distributive over addition； that is, for any three elements a, b and c in F. The additive inverse of a field element a, denoted by a, is the field element which produces the sum 0 when added to a a+(-a)=0. The multiplicative inverse of a, denoted by 1a , is the field element which produces the product 1 when multiplied by a . Four basic properties of field can be derived from the definition of a field. They are as follows: Property I: aa 00 Property II: For nonzero field elements a and b , 0ba Property III: 0ba 且 ,0a 则 b=0 Property IV: )()()( bababa For any prime number p, there exists a finite field which contain p elements. This prime field is denoted as GF(p) because finite field are also called Galois field GF (p) to a field of mp elements which is called an extension field of GF (p) and is denoted by GF ( mp ) , where m is a positive integer. Codes with symbols from the binary field GF(2) or its extension field GF( m2 ) are most commonly used in digital data transmission and storage systems, since information in these systems is always encoded in binary form in practice. In binary arithmetic, modulo-2 addition and multiplication are used. This arithmetic is actually equivalent to ordinary arithmetic except that 2 is considered equal to 0 (1+1=2=0). Note that since 1+1=0,1=-1,and hence for the arithmetic used to generate error control codes, addition is equivalent to subtraction. Reed-Solomon codes makes use of nonbinary field GF( m2 ) . These fields have more than 2 elements and are extensions of the binary field GF (2)=0,1. The additional elements in the extension field GF( m2 ) can not be 0 or 1 since all of the elements are unique, so a new symbol a is used to represent the other elements in the field. Each nonzero element can be represented by a power of a. The multiplication operation”.” For the extension field must be defined so that the remaining elements of the field can be represented as sequence of powers of a. The multiplication operation can be used to produce the infinite set of elements F shown below To obtain the finite set of elements of GF( ) from F, a condition must be imposed on F so that it may contain only elements and is a close set under multiplication (i.e., multiplication of two field elements is performed without leaving the set). The condition which closes the set of field elements under multiplication is known as the irreducible polynomial, and it typically takes the following form Rhe89: ,.,.,0,.,.,1,0 2102 jj aaaaaaaF 交织 交织可以在不附加任何开销的 情况下，使数字通信系统获得时间分量。由于数字语言编码（把模拟语言信号转变为可在无线链路中传输的高效数字信号。语音编码器将在第 7章介绍。）的迅速发展，在所有的第二代数字蜂窝系统中，交织成为极其有用的一项技术。 由于语音编码器要将语音频带的信息转变为统一，高效的数字信息格式，因而被编码的数据位（或叫做源比特）中大量信息。并且正如第 7章到第 10 章所表述的，有些源比特特别重要，所以有必要加以保护，不让其产生误码。许多语音编码器都会在其编码序列中产生几个很重要的源比特，而交织器的作用就是将这些源比特分散到不同的时间段 中，以便出现深衰落或突发干扰时，来自源比特中某一块的最重要的码位不会被同时扰乱。而且源比特被分开后，还可以利用差错控制编码（又称为信道编码）来自减弱信道干扰对源比特的影响。信道编码是为了保护信号免受随机的和突发的干扰的影响，而交织器是在信道编码之前打乱了源比特的时间顺序。 交织器有两种结构类型：分组结构和卷积结构。分组结构是把待编码的 m n个数据位放入一个 m行 n列的矩阵中，即每次是对 m*n个数据位进行交织。通常，每行由 n个数据位组成一个字，而交织器的深度，即行数为 m，其结构示于图 6。 17。由图可见，数据位被按列填入，而在发送时却是按行读出的，这样就产生了对原始数据位以 m 个比特为周期进行分隔的效果。在接受机一端的解交织操作则是与此相反进行的。 采用卷积结构的交织器，在多数情况下可以代替分组结构的交织器。而且卷积结构在用于卷积编码时，可以取得很理想的效果。 因为接受机在收到了 m*n 位并进行解交织以后才能解码，所以所有的交织器都带有一个固有的延时。在现实中，当语音延时小于 40ms时人们还是可以忍受的，所以所有的无线数据交织器的延时都不超过 40ms。另外，交织器的字长和深度 与所用的语音编码器，编码速率和最大允许时延有较大的关系。 信道编码原理 信道编码原理通过在被传输数据中引入冗余来避免数字数据在传送过程中出现误码。用于检测错误的信道编码被称作检错编码，而既可检错又可纠错的信道编码被称为纠错编码。 1948 年，香农论证了通过对信息的恰当编码，由信道噪声引入的错误可以被控制在任何误差范围之内，而且这并不需要降低信息传输速率。应用于 AWGN 信道的香农信道容量公式如下： C=B /1(log2 p 0NB)=B 2log (1+S/N) 其中， c为信道容量， B传输带宽， P接受信号的功率，0N为单边带噪声功率谱密度 (w/Hz)功率为： P=bbRE其中， Eb比特信号的平均能量， Rb号传输速率。公式可用传输带宽归一化，即： C/B= 2log (1+bbRE/0NB) 其中 C/B表示宽效率。 检 错和纠错技术的基本目的，是通过在无线链路的数据传输中引入冗余来改进信道的质量。冗余的引入将增加信号的传输速率，也就会增加带宽。这会降低在高 SNR 情况下的频谱效率，但它却可以大大降低在低 SNR情况下的误码率。 众所周知，假如每个比特的 SNR 超过了香农下限，即 SNbR -1.6dB，则我们可以通过扩展正交信号集，即让信号波形数 M ，来使误码率减小到任意程度 Vit79。香农指出在上 述条件下，只要 SNR 足够大，就可以用很宽的带宽实现无差错的通信。另一方面，差错控制编码的带宽是随编码长度的增加而增加的。因而，纠错编码用于带宽受限或功率受限的环境是有一定优势的。信道编码器的输入信息源是数字信息源。检错码和纠错码有两种基本类型，分组码和卷积码。 分组码 分组码一种前向纠错 (FEC)编码。它是一种不需要重复发送就可以检出并纠正有限个错误的编码。当其他改进方法（如增加传输功率或使用更复杂的解调器等）不易实现时，可以用分组码改进通信系统的性能。 在分组码中，校验为被加到信息位之后，以形成新的码字（ 或码组）。在分组编码是，k个信息位被编为 n个比特，而 n-k个校验为的作用就是检错和纠错 Lin83。分组码将以（ n，k）表示，其编码效率被定义为cR=k/n。这也是原始信息速率与信道信息速率的比值。 分组码的纠错能力是码距的函数。不同的编码方案提供了不同的差错控制能力Cou93,Hay94,Lin83,Sk193,Vit79. 例 6.5 在无线语音通信中，交织和分组码通常被结合起来使用。对于 m 行 n 列的交织器，其码字长为 n 比特。假设每个码字中有 k 个源比特（信息位），（ n-k）个校验位，那么把交织和分组编码相结合就可以使一个长度为的 l=mb 的信道突发误码分解为 m 个长度为 b 的误码。 因而一个能够处理 b（ n-k） /2个误