外文翻譯--數(shù)字通信交織

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 則 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 交織 交織可以在不附加任何開銷的 情況下，使數(shù)字通信系統(tǒng)獲得時(shí)間分量。由于數(shù)字語(yǔ)言編碼（把模擬語(yǔ)言信號(hào)轉(zhuǎn)變?yōu)榭稍跓o線鏈路中傳輸?shù)母咝?shù)字信號(hào)。語(yǔ)音編碼器將在第 7章介紹。）的迅速發(fā)展，在所有的第二代數(shù)字蜂窩系統(tǒng)中，交織成為極其有用的一項(xiàng)技術(shù)。 由于語(yǔ)音編碼器要將語(yǔ)音頻帶的信息轉(zhuǎn)變?yōu)榻y(tǒng)一，高效的數(shù)字信息格式，因而被編碼的數(shù)據(jù)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，有些源比特特別重要，所以有必要加以保護(hù)，不讓其產(chǎn)生誤碼。許多語(yǔ)音編碼器都會(huì)在其編碼序列中產(chǎn)生幾個(gè)很重要的源比特，而交織器的作用就是將這些源比特分散到不同的時(shí)間段 中，以便出現(xiàn)深衰落或突發(fā)干擾時(shí)，來自源比特中某一塊的最重要的碼位不會(huì)被同時(shí)擾亂。而且源比特被分開后，還可以利用差錯(cuò)控制編碼（又稱為信道編碼）來自減弱信道干擾對(duì)源比特的影響。信道編碼是為了保護(hù)信號(hào)免受隨機(jī)的和突發(fā)的干擾的影響，而交織器是在信道編碼之前打亂了源比特的時(shí)間順序。 交織器有兩種結(jié)構(gòu)類型：分組結(jié)構(gòu)和卷積結(jié)構(gòu)。分組結(jié)構(gòu)是把待編碼的 m n個(gè)數(shù)據(jù)位放入一個(gè) m行 n列的矩陣中，即每次是對(duì) m*n個(gè)數(shù)據(jù)位進(jìn)行交織。通常，每行由 n個(gè)數(shù)據(jù)位組成一個(gè)字，而交織器的深度，即行數(shù)為 m，其結(jié)構(gòu)示于圖 6。 17。由圖可見，數(shù)據(jù)位被按列填入，而在發(fā)送時(shí)卻是按行讀出的，這樣就產(chǎn)生了對(duì)原始數(shù)據(jù)位以 m 個(gè)比特為周期進(jìn)行分隔的效果。在接受機(jī)一端的解交織操作則是與此相反進(jìn)行的。 采用卷積結(jié)構(gòu)的交織器，在多數(shù)情況下可以代替分組結(jié)構(gòu)的交織器。而且卷積結(jié)構(gòu)在用于卷積編碼時(shí)，可以取得很理想的效果。 因?yàn)榻邮軝C(jī)在收到了 m*n 位并進(jìn)行解交織以后才能解碼，所以所有的交織器都帶有一個(gè)固有的延時(shí)。在現(xiàn)實(shí)中，當(dāng)語(yǔ)音延時(shí)小于 40ms時(shí)人們還是可以忍受的，所以所有的無線數(shù)據(jù)交織器的延時(shí)都不超過 40ms。另外，交織器的字長(zhǎng)和深度 與所用的語(yǔ)音編碼器，編碼速率和最大允許時(shí)延有較大的關(guān)系。 信道編碼原理 信道編碼原理通過在被傳輸數(shù)據(jù)中引入冗余來避免數(shù)字?jǐn)?shù)據(jù)在傳送過程中出現(xiàn)誤碼。用于檢測(cè)錯(cuò)誤的信道編碼被稱作檢錯(cuò)編碼，而既可檢錯(cuò)又可糾錯(cuò)的信道編碼被稱為糾錯(cuò)編碼。 1948 年，香農(nóng)論證了通過對(duì)信息的恰當(dāng)編碼，由信道噪聲引入的錯(cuò)誤可以被控制在任何誤差范圍之內(nèi)，而且這并不需要降低信息傳輸速率。應(yīng)用于 AWGN 信道的香農(nóng)信道容量公式如下： C=B /1(log2 p 0NB)=B 2log (1+S/N) 其中， c為信道容量， B傳輸帶寬， P接受信號(hào)的功率，0N為單邊帶噪聲功率譜密度 (w/Hz)功率為： P=bbRE其中， Eb比特信號(hào)的平均能量， Rb號(hào)傳輸速率。公式可用傳輸帶寬歸一化，即： C/B= 2log (1+bbRE/0NB) 其中 C/B表示寬效率。 檢 錯(cuò)和糾錯(cuò)技術(shù)的基本目的，是通過在無線鏈路的數(shù)據(jù)傳輸中引入冗余來改進(jìn)信道的質(zhì)量。冗余的引入將增加信號(hào)的傳輸速率，也就會(huì)增加帶寬。這會(huì)降低在高 SNR 情況下的頻譜效率，但它卻可以大大降低在低 SNR情況下的誤碼率。 眾所周知，假如每個(gè)比特的 SNR 超過了香農(nóng)下限，即 SNbR -1.6dB，則我們可以通過擴(kuò)展正交信號(hào)集，即讓信號(hào)波形數(shù) M ，來使誤碼率減小到任意程度 Vit79。香農(nóng)指出在上 述條件下，只要 SNR 足夠大，就可以用很寬的帶寬實(shí)現(xiàn)無差錯(cuò)的通信。另一方面，差錯(cuò)控制編碼的帶寬是隨編碼長(zhǎng)度的增加而增加的。因而，糾錯(cuò)編碼用于帶寬受限或功率受限的環(huán)境是有一定優(yōu)勢(shì)的。信道編碼器的輸入信息源是數(shù)字信息源。檢錯(cuò)碼和糾錯(cuò)碼有兩種基本類型，分組碼和卷積碼。 分組碼 分組碼一種前向糾錯(cuò) (FEC)編碼。它是一種不需要重復(fù)發(fā)送就可以檢出并糾正有限個(gè)錯(cuò)誤的編碼。當(dāng)其他改進(jìn)方法（如增加傳輸功率或使用更復(fù)雜的解調(diào)器等）不易實(shí)現(xiàn)時(shí)，可以用分組碼改進(jìn)通信系統(tǒng)的性能。 在分組碼中，校驗(yàn)為被加到信息位之后，以形成新的碼字（ 或碼組）。在分組編碼是，k個(gè)信息位被編為 n個(gè)比特，而 n-k個(gè)校驗(yàn)為的作用就是檢錯(cuò)和糾錯(cuò) Lin83。分組碼將以（ n，k）表示，其編碼效率被定義為cR=k/n。這也是原始信息速率與信道信息速率的比值。 分組碼的糾錯(cuò)能力是碼距的函數(shù)。不同的編碼方案提供了不同的差錯(cuò)控制能力Cou93,Hay94,Lin83,Sk193,Vit79. 例 6.5 在無線語(yǔ)音通信中，交織和分組碼通常被結(jié)合起來使用。對(duì)于 m 行 n 列的交織器，其碼字長(zhǎng)為 n 比特。假設(shè)每個(gè)碼字中有 k 個(gè)源比特（信息位），（ n-k）個(gè)校驗(yàn)位，那么把交織和分組編碼相結(jié)合就可以使一個(gè)長(zhǎng)度為的 l=mb 的信道突發(fā)誤碼分解為 m 個(gè)長(zhǎng)度為 b 的誤碼。 因而一個(gè)能夠處理 b（ n-k） /2個(gè)誤