Efficient encoding of significance maps in wavelet based image compression

XST Design Flow OverviewThe following figure shows the flow of files through the XST software.XST Input and Output FilesXST supports extensive VHDL and Verilog subsets from the following standards:∙VHDL: IEEE 1076-1987, IEEE 1076-1993, including IEEE standard and Synopsys®∙Verilog: IEEE 1364-1995, IEEE 1364-2001In addition to a VHDL or Verilog design description, XST can also accept the following files as input:∙XCFXilinx constraints file in which you can specify synthesis, timing, and specificimplementation constraints that can be propagated to the NGC file.∙Core filesThese files can be in either NGC or EDIF format. XST does not modify cores. It uses them to inform area and timing optimization surrounding the cores.Note Cores are supported for FPGAs only, not CPLDs.In addition to NGC files, XST also generates the following files as output:∙Synthesis ReportThis report contains the results from the synthesis run, including area andtiming estimation. For details, see Viewing a Synthesis Report.∙RTL schematicThis is a schematic representation of the pre-optimized design shown at theRegister Transfer Level (RTL). This representation is in terms of genericsymbols, such as adders, multipliers, counters, AND gates, and OR gates, andis generated after the HDL synthesis phase of the synthesis process. Viewingthis schematic may help you discover design issues early in the design process.For details, see Viewing an RTL Schematic - XST.∙Technology schematicThis is a schematic representation of an NGC file shown in terms of logic elements optimized to the target architecture or "technology," for example, in terms of LUTs, carry logic, I/O buffers, and other technology-specific components. It is generated after the optimization and technology targeting phase of the synthesis process. Viewing this schematic allows you to see a technology-level representation of your HDL optimizedfor a specific Xilinx architecture, which may help you discover design issues early in the design process. For details, see Viewing a Technology Schematic - XST.Note When the design is run in Incremental Synthesis mode, XST generates multiple NGC and NGR files, which each represent a single user design partition.XST Detailed Design FlowThe following figure shows each of the steps that take place during XST synthesis. The following sections describe each step in detail.HDL ParsingDuring HDL parsing, XST checks whether your HDL code is correct and reports any syntax errors.HDL SynthesisDuring HDL synthesis, XST analyzes the HDL code and attempts to infer specific design building blocks or macros (such as MUXes, RAMs, adders, and subtracters) for which it can create efficient technology implementations. To reduce the amount of inferred macros, XST performs a resource sharing check. This usually leads to a reduction of the area as well as an increase in the clock frequency.Finite state machine (FSM) recognition is also part of the HDL synthesis step. XST recognizes FSMs independent of the modeling style used. To create the most efficient implementation, XST uses the target optimization goal, whether area or speed, to determine which of several FSM encoding algorithms to use.You can control the HDL synthesis step using constraints. You can enter constraints using any of the following methods:∙HDL source fileEnter VHDL or Verilog attributes.∙XCFEnter global parameters and module-level constraints in the Xilinx constraints(XCF) file. See the "Design Constraints" chapter of the XST User Guide for moreinformation on the use of constraints in the XCF file.∙Project Navigator Process PropertiesSet global parameters, such as the optimization goal or effort level. You can modify the synthesis properties in the following tabs of the Synthesize Process Properties dialog box:o Synthesis Optionso HDL Optionso Xilinx Specific OptionsDefault property values are used for the Synthesize process, unless you modify them.Note For more information on entering constraints, see Constraints Entry Methods.TranslateThe Translate process merges all of the input netlists and design constraints and outputs a Xilinx native generic database (NGD) file, which describes the logical design reduced to Xilinx primitives. See the following table for details.MapThe Map process maps the logic defined by an NGD file into FPGA elements, such as CLBs and IOBs. The output design is a native circuit description (NCD) file that physically represents the design mapped to the components in the Xilinx FPGA. See the following table for details.Place and RouteThe Place and Route process takes a mapped NCD file, places and routes the design, and produces an NCD file that is used as input for bitstream generation. See the following table for details.Programming File GenerationThe Generate Programming File process produces a bitstream for Xilinx device configuration. After the design is completely routed, you must configure the device so it can execute the desired function. See the following table for details.。

What is a genetic algorithm?●Methods of representation●Methods of selection●Methods of change●Other problem-solving techniquesConcisely stated, a genetic algorithm (or GA for short) is a programming technique that mimics biological evolution as a problem-solving strategy. Given a specific problem to solve, the input to the GA is a set of potential solutions to that problem, encoded in some fashion, and a metric called a fitness function that allows each candidate to be quantitatively evaluated. These candidates may be solutions already known to work, with the aim of the GA being to improve them, but more often they are generated at random.The GA then evaluates each candidate according to the fitness function. In a pool of randomly generated candidates, of course, most will not work at all, and these will be deleted. However, purely by chance, a few may hold promise - they may show activity, even if only weak and imperfect activity, toward solving the problem.These promising candidates are kept and allowed to reproduce. Multiple copies are made of them, but the copies are not perfect; random changes are introduced during the copying process. These digital offspring then go on to the next generation, forming a new pool of candidate solutions, and are subjected to a second round of fitness evaluation. Those candidate solutions which were worsened, or made no better, by the changes to their code are again deleted; but again, purely by chance, the random variations introduced into the population may have improved some individuals, making them into better, more complete or more efficient solutions to the problem at hand. Again these winning individuals are selected and copied over into the next generation with random changes, and the process repeats. The expectation is that the average fitness of the population will increase each round, and so by repeating this process for hundreds or thousands of rounds, very good solutions to the problem can be discovered.As astonishing and counterintuitive as it may seem to some, genetic algorithms have proven to be an enormously powerful and successful problem-solving strategy, dramatically demonstratingthe power of evolutionary principles. Genetic algorithms have been used in a wide variety of fields to evolve solutions to problems as difficult as or more difficult than those faced by human designers. Moreover, the solutions they come up with are often more efficient, more elegant, or more complex than anything comparable a human engineer would produce. In some cases, genetic algorithms have come up with solutions that baffle the programmers who wrote the algorithms in the first place!Methods of representationBefore a genetic algorithm can be put to work on any problem, a method is needed to encode potential solutions to that problem in a form that a computer can process. One common approach is to encode solutions as binary strings: sequences of 1's and 0's, where the digit at each position represents the value of some aspect of the solution. Another, similar approach is to encode solutions as arrays of integers or decimal numbers, with each position again representing some particular aspect of the solution. This approach allows for greater precision and complexity than the comparatively restricted method of using binary numbers only and often "is intuitively closer to the problem space" (Fleming and Purshouse 2002, p. 1228).This technique was used, for example, in the work of Steffen Schulze-Kremer, who wrote a genetic algorithm to predict the three-dimensional structure of a protein based on the sequence of amino acids that go into it (Mitchell 1996, p. 62). Schulze-Kremer's GA used real-valued numbers to represent the so-called "torsion angles" between the peptide bonds that connect amino acids. (A protein is made up of a sequence of basic building blocks called amino acids, which are joined together like the links in a chain. Once all the amino acids are linked, the protein folds up into a complex three-dimensional shape based on which amino acids attract each other and which ones repel each other. The shape of a protein determines its function.) Genetic algorithms for training neural networks often use this method of encoding also.A third approach is to represent individuals in a GA as strings of letters, where each letter again stands for a specific aspect of the solution. One example of this technique is Hiroaki Kitano's "grammatical encoding" approach, where a GA was put to the task of evolving a simple set of rules called a context-freegrammar that was in turn used to generate neural networks for a variety of problems (Mitchell 1996, p. 74).The virtue of all three of these methods is that they make it easy to define operators that cause the random changes in the selected candidates: flip a 0 to a 1 or vice versa, add or subtract from the value of a number by a randomly chosen amount, or change one letter to another. (See the section on Methods of change for more detail about the genetic operators.) Another strategy, developed principally by John Koza of Stanford University and called genetic programming, represents programs as branching data structures called trees (Koza et al. 2003, p. 35). In this approach, random changes can be brought about by changing the operator or altering the value at a given node in the tree, or replacing one subtree with another.Figure 1:Three simple program trees of the kind normally used in genetic programming. The mathematical expression that each one represents is given underneath.It is important to note that evolutionary algorithms do not need to represent candidate solutions as data strings of fixed length. Some do represent them in this way, but others do not; for example, Kitano's grammatical encoding discussed above can be efficiently scaled to create large and complex neural networks, and Koza's genetic programming trees can grow arbitrarily large as necessary to solve whatever problem they are applied to.Methods of selectionThere are many different techniques which a genetic algorithm can use to select the individuals to be copied over into the next generation, but listed below are some of the most common methods.Some of these methods are mutually exclusive, but others can be and often are used in combination.Elitist selection: The most fit members of each generation are guaranteed to be selected. (Most GAs do not use pure elitism, but instead use a modified form where the single best, or a few of the best, individuals from each generation are copied into the next generation just in case nothing better turns up.)Fitness-proportionate selection: More fit individuals are more likely, but not certain, to be selected.Roulette-wheel selection: A form of fitness-proportionate selection in which the chance of an individual's being selected is proportional to the amount by which its fitness is greater or less than its competitors' fitness. (Conceptually, this can be represented as a game of roulette - each individual gets a slice of the wheel, but more fit ones get larger slices than less fit ones. The wheel is then spun, and whichever individual "owns" the section on which it lands each time is chosen.)Scaling selection: As the average fitness of the population increases, the strength of the selective pressure also increases and the fitness function becomes more discriminating. This method can be helpful in making the best selection later on when all individuals have relatively high fitness and only small differences in fitness distinguish one from another.Tournament selection: Subgroups of individuals are chosen from the larger population, and members of each subgroup compete against each other. Only one individual from each subgroup is chosen to reproduce.Rank selection: Each individual in the population is assigned a numerical rank based on fitness, and selection is based on this ranking rather than absolute differences in fitness. The advantage of this method is that it can prevent very fit individuals from gaining dominance early at the expense of less fit ones, which would reduce the population's genetic diversity and might hinder attempts to find an acceptable solution.Generational selection: The offspring of the individuals selected from each generation become the entire next generation. No individuals are retained between generations.Steady-state selection: The offspring of the individuals selected from each generation go back into the pre-existing gene pool, replacing some of the less fit members of the previous generation. Some individuals are retained between generations.Hierarchical selection: Individuals go through multiple rounds of selection each generation. Lower-level evaluations are faster and less discriminating, while those that survive to higher levels are evaluated more rigorously. The advantage of this method is that it reduces overall computation time by using faster, less selective evaluation to weed out the majority of individuals that show little or no promise, and only subjecting those who survive this initial test to more rigorous and more computationally expensive fitness evaluation.Methods of changeOnce selection has chosen fit individuals, they must be randomly altered in hopes of improving their fitness for the next generation. There are two basic strategies to accomplish this. The first and simplest is called mutation. Just as mutation in living things changes one gene to another, so mutation in a genetic algorithm causes small alterations at single points in an individual's code.The second method is called crossover, and entails choosing two individuals to swap segments of their code, producing artificial "offspring" that are combinations of their parents. This process is intended to simulate the analogous process of recombination that occurs to chromosomes during sexual reproduction. Common forms of crossover include single-point crossover, in which a point of exchange is set at a random location in the two individuals' genomes, and one individual contributes all its code from before that point and the other contributes all its code from after that point to produce an offspring, and uniform crossover, in which the value at any given location in the offspring's genome is either the value of one parent's genome at that location or the value of the other parent's genome at that location, chosen with 50/50 probability.Figure 2:Crossover and mutation. The above diagrams illustrate the effect of each of these genetic operators on individuals in a population of 8-bit strings. The upper diagram shows two individuals undergoing single-point crossover; the point of exchange is set between the fifth and sixth positions in the genome, producing a new individual that is a hybrid of its progenitors. The second diagram shows an individual undergoing mutation at position 4, changing the 0 at that position in its genome to a 1.Other problem-solving techniquesWith the rise of artificial life computing and the development of heuristic methods, other computerizedproblem-solving techniques have emerged that are in some ways similar to genetic algorithms. This section explains some of these techniques, in what ways they resemble GAs and in what ways they differ.Neural networksA neural network, or neural net for short, is a problem-solving method basedon a computer model of how neurons are connected in the brain. A neuralnetwork consists of layers of processing units called nodes joined bydirectional links: one input layer, one output layer, and zero or more hiddenlayers in between. An initial pattern of input is presented to the input layer ofthe neural network, and nodes that are stimulated then transmit a signal to thenodes of the next layer to which they are connected. If the sum of all theinputs entering one of these virtual neurons is higher than that neuron'sso-called activation threshold, that neuron itself activates, and passes on itsown signal to neurons in the next layer. The pattern of activation thereforespreads forward until it reaches the output layer and is there returned as asolution to the presented input. Just as in the nervous system of biologicalorganisms, neural networks learn and fine-tune their performance over timevia repeated rounds of adjusting their thresholds until the actual outputmatches the desired output for any given input. This process can be supervisedby a human experimenter or may run automatically using a learning algorithm(Mitchell 1996, p. 52). Genetic algorithms have been used both to build and totrain neural networks.Figure 3:A simple feedforward neural network, with one input layer consisting of four neurons, one hidden layer consisting of three neurons, and one output layer consisting of four neurons. The number on each neuron represents its activation threshold: it will only fire if it receives at least that many inputs. The diagram shows the neural network being presented with an input string and shows how activation spreads forward through thenetwork to produce an output.Hill-climbingSimilar to genetic algorithms, though more systematic and less random, ahill-climbing algorithm begins with one initial solution to the problem at hand, usually chosen at random. The string is then mutated, and if the mutationresults in higher fitness for the new solution than for the previous one, thenew solution is kept; otherwise, the current solution is retained. The algorithmis then repeated until no mutation can be found that causes an increase in thecurrent solution's fitness, and this solution is returned as the result (Koza et al.2003, p. 59). (To understand where the name of this technique comes from,imagine that the space of all possible solutions to a given problem isrepresented as a three-dimensional contour landscape. A given set ofcoordinates on that landscape represents one particular solution. Thosesolutions that are better are higher in altitude, forming hills and peaks; thosethat are worse are lower in altitude, forming valleys. A "hill-climber" is thenan algorithm that starts out at a given point on the landscape and movesinexorably uphill.) Hill-climbing is what is known as a greedy algorithm,meaning it always makes the best choice available at each step in the hopethat the overall best result can be achieved this way. By contrast, methodssuch as genetic algorithms and simulated annealing, discussed below, are notgreedy; these methods sometimes make suboptimal choices in the hopes thatthey will lead to better solutions later on.Simulated annealingAnother optimization technique similar to evolutionary algorithms is known as simulated annealing. The idea borrows its name from the industrial process of annealing in which a material is heated to above a critical point to soften it, then gradually cooled in order to erase defects in its crystalline structure, producing a more stable and regular lattice arrangement of atoms (Haupt and Haupt 1998, p. 16). In simulated annealing, as in genetic algorithms, there is a fitness function that defines a fitness landscape; however, rather than a population of candidates as in GAs, there is only one candidate solution.Simulated annealing also adds the concept of "temperature", a global numerical quantity which gradually decreases over time. At each step of the algorithm, the solution mutates (which is equivalent to moving to an adjacent point of the fitness landscape). The fitness of the new solution is then compared to the fitness of the previous solution; if it is higher, the new solution is kept. Otherwise, the algorithm makes a decision whether to keep or discard it based on temperature. If the temperature is high, as it is initially, even changes that cause significant decreases in fitness may be kept and used as the basis for the next round of the algorithm, but as temperature decreases, the algorithm becomes more and more inclined to only accept fitness-increasing changes. Finally, the temperature reaches zero and the system "freezes"; whatever configuration it is in at that point becomes the solution. Simulated annealing is often used for engineering design applications such as determining the physical layout of components on a computer chip (Kirkpatrick, Gelatt and V ecchi 1983).。

Test Bank—Chapter One (Data Representation)Multiple Choice Questions1. Which of the following Boolean operations produces the output 1 for the fewest number of input patterns?A. ANDB. ORC. XORANSWER: A2. Which of the following best describes the NOR operation?A. An XOR followed by a NOTB. An OR followed by a NOTC. A NOT followed by a NOT C. An AND followed by a NOTANSWER: B3. Which of the following bit patterns cannot be expressed in hexadecimal notation?A. 11111111B. 1001C. 110011D. 100000000001ANSWER: C4. Which of the following is the binary representation of 4 5/8?A. 100.11B. 10.011C. 110.101D. 100.101ANSWER: D5. Which of the following bit patterns represents the value 5 in two’s complement notation?A. 00011010B. 11111011C. 00000101D. 11111011ANSWER: C6. Which of the following bit patterns represents the value -5 in two’s complement notation?A. 00011010B. 11111011C. 00000101D. 11111011ANSWER: D7. In which of the following addition prob lems (using two’s complement notation) does an overflow error occur?A. 0011B. 0100C. 1100+ 1010 + 0100 + 1100ANSWER: B8. Which of the following representations in two’s complement notation represents the largest value?A. 00000010B. 11111111C. 00000001D. 11111110ANSWER: A9. Which of the following bit patterns (represented in hexadecimal notation) represents a negative number in two’s complement notation?A. 7FB. 55C. A6D. 08ANSWER: C10. What value is represented by the bit pattern 01011100 when interpreted using floating-point format in which the most significant bit is the sign bit, the next three bits represent the exponent field in excess notation, and the last four bits represent the mantissa?A. -1 1/2B. 1 1/2C. -3/8D. 3/8ANSWER: B11. Which of the following values cannot be stored accurately using a floating-point format in which the most significant bit is the sign bit, the next three bits represent the exponent field in excess notation, and the last four bits represent the mantissa?A. 2 1/2B. 3/16C. 7D. 6 1/4ANSWER: D121. Which of the following bit-patterns represents the smallest value using the floating-point format in which the most significant bit is the sign bit, the next three bits represent the exponent field in excess notation, and the last four bits represent the mantissa?A. 01001000B. 01011000C. 00101000D. 01111000ANSWER: C13. Which of the following data storage systems provides the most efficient random access to individual data items?A. Main memoryB. Magnetic diskC. Optical CDs and DVDsANSWER: A14. Which of the following storage systems is best suited for storing and retrieving long strings of data that are processed in their sequential order?A. Main memoryB. Magnetic diskC. Optical CDs and DVDsANSWER: C15. Which of the following mass storage system does not require physical motion?A. Magnetic tapeB. Magnetic diskC. DVDsD. Flash drives ANSWER: D16. Assuming that each of the following bit patterns originally had even parity, which one contains an error?A. 10110100B. 11000011C. 00011000D. 10001001 ANSWER: D17. How many errors per pattern could be corrected when using an error-correcting code in which any two code patterns differ by a Hamming distance of 8?A. 3B. 4C. 5D. 6ANSWER: A18. Which of the following is a possible LZW compression of the message “xyz xyz xyz”?A. 1234B. 1234545C. 232D. 12ANSWER: B19. How many different symbols can be encoded using Unicode?A. 256B. 4,096C. 65,536D. 1,046,476ANSWER: C20. Which of the following systems is least efficient when encoding numeric values?A. Two’s complement notationB. Excess notationC. ASCIID. Floating-point notationANSWER: C21. Which of the following is a means of encoding music?A. ASCIIB. MIDIC. JPEGD. GIFANSWER: BVocabulary (Matching) QuestionsThe following is a list of terms from the chapter along with descriptive phrases that can be used to produce questions (depending on the topics covered in your course) in which the students are ask to match phrases and terms. An example would be a question of the form, “In the blank next to each phrase, write the term fr om the following list that is best described by the phrase.”Term Descriptive Phrasebit Binary digitBoolean operation AND, OR, XOR, NOTaddress A numeric value used to identify a memory cellhexadecimal notation An efficient way of representing bit patternssector A segment of a track in a mass storage systemzoned-bit recording A means of increasing the storage capacity of a magnetic disk system buffer A storage area used to hold data on a temporary basis, often as a stepin transferring the data from one device to anotherISO An international organization for establishing standardsANSI A major standardization organization within the United StatesASCII A system developed by the American Standards Institute for encodingtext.flip-flop A digital circuit capable of holding a single digittwo’s complement notation A means of encoding whole numbersfloating-point notation A means of encoding numeric values that may involve fractions truncation An error that may occur when using floating-point notationpixel A small part of an imageGIF A means of compressing an image file by restricting the number ofcolors availableJPEG A means of compressing images by blurring the boundaries betweendifferent colors while maintaining all brightness information Unicode A means of encoding text in which each symbol is represented by 16bitsLZW An example of adaptive dictionary encodingMIDI A means of encoding music in terms of notes and instruments ratherthan actual audioKey field A part of a logical record in a file used to identify the record.VLSI A means of constructing complex circuitry in a very small space.。

频谱效率频谱效率（Spectral efficiency、Spectrum efficiency）是指在数位通信系统中的限制下，可以传送的资料总量。

在有限的波下，物理层通信协议可以达到的使用效率有一定的限度。

链路频谱效率数字通信系统的链路频谱效率（Link spectral efficiency）的单位是.) 1/4～～1/5 ～+ ～～最大通常8 最大通常1/5+ 最大通常8 最大通常～ 11 8 ～1/5 ～+ ～ 11 8 ～光纤用数位38 6 1电视TVSpectral efficiencySpectral efficiency, spectrum efficiency or bandwidth efficiency refers to the that can be transmitted over a given in a specific communication system. It is a measure of how efficiently a limited frequency spectrum is utilized by the protocol, and sometimes by the (the protocol).Link spectral efficiencyThe link spectral efficiency of a digital communication system is measured in It is the (useful information rate excluding ) or divided by the in hertz of a or a . Alternatively, the spectral efficiency may be measured in in bit/symbol, which is equivalent to bits per (bpcu), implying that the net bit rate is divided by the (modulation rate) or line code pulse rate.Link spectral efficiency is typically used to analyse the efficiency of a method or , sometimes in combination with a (FEC) code and other physical layer overhead. In the latter case, a "bit" refers to a user data bit; FEC overhead is always excluded.The modulation efficiency in bit/s is the (including any error-correcting code) divided by the bandwidth.Example 1: A transmission technique using one of bandwidth to transmit 1,000 bits per second has a modulation efficiency of 1 (bit/s)/Hz.Example 2: A modem for the telephone network can transfer 56,000 bit/s downstream and 48,000 bit/s upstream over an analog telephone network. Due to filtering in the telephone exchange, the frequency range is limited to between 300 hertz and 3,400 hertz, corresponding to a bandwidth of 3,400 300 = 3,100 hertz. The spectral efficiency or modulation efficiency is 56,000/3,100 = (bit/s)/Hz downstream, and 48,000/3,100 = (bit/s)/Hz upstream.An upper bound for the attainable modulation efficiency is given by the or as follows: For a signaling alphabet with M alternative symbols, each symbol represents N= log2M bits. N is the modulation efficiency measured in bit/symbol or bpcu. In the case of ( or ) with a baseband bandwidth (or upper cut-off frequency) B, the can not exceed 2B symbols/s in view to avoid . Thus, the spectral efficiency can not exceed 2N(bit/s)/Hz in the baseband transmission case. In the passband transmission case, a signal with passband bandwidth W can be converted to an equivalent baseband signal (using or a ), with upper cut-off frequency W/2. If double-sideband modulation schemes such as QAM, ASK, PSK or OFDM are used, this results in a maximum symbol rate of W symbols/s, and in that the modulation efficiency can not exceed N (bit/s)/Hz. If digital is used, the passband signal with bandwidth W corresponds to a baseband message signal with baseband bandwidth W, resulting in a maximum symbol rate of 2W and an attainable modulation efficiency of 2N (bit/s)/Hz.Example 3:An 16QAM modem has an alphabet size of M = 16 alternative symbols, with N = 4 bit/symbol or bpcu. Since QAM is a form of double sideband passband transmission, the spectral efficiency cannot exceed N = 4 (bit/s)/Hz. Example 4:The (8-level vestigial sideband) modulation scheme used in the gives N=3 bit/symbol or bpcu. Since it can be described as nearly single-side band, the modulation efficiency is close to 2N = 6 (bit/s)/Hz. In practice, ATSC transfers a gross bit rate of 32 Mbit/s over a 6 MHz wide channel, resulting in a modulation efficiency of 32/6 = (bit/s)/Hz.Example 5:The downlink of a modem uses a pulse-amplitude modulation with 128 signal levels, resulting in N = 7 bit/symbol. Since the transmitted signal before passband filtering can be considered as baseband transmission, the spectral efficiency cannot exceed 2N = 14 (bit/s)/Hz over the full baseband channel (0 to 4 kHz). As seen above, a higher spectral efficiency is achieved if we consider the smaller passband bandwidth.If a code is used, the spectral efficiency is reduced from the uncoded modulation efficiency figure.Example 6:If a forward error correction (FEC) code with 1/2 is added, meaning that the encoder input bit rate is one half the encoder output rate, the spectral efficiency is 50% of the modulation efficiency. In exchange for this reduction in spectral efficiency, FEC usually reduces the , and typically enables operation at a lower (SNR).An upper bound for the spectral efficiency possible without in a channel with a certain SNR, if ideal error coding and modulation is assumed, is given by the .Example 7:If the SNR is 1 times expressed as a ratio, corresponding to 0 , the link spectral efficiency can not exceed 1 (bit/s)/Hz for error-free detection (assuming an ideal error-correcting code) according to Shannon-Hartley regardless of the modulation and coding.Note that the (the amount of application layer useful information) is normally lower than the used in the above calculations, because of packet retransmissions, higher protocol layer overhead, flow control, congestion avoidance, etc. On the other hand, a data compression scheme, such as the or compression used in telephone modems, may however give higher goodput if the transferred data is not already efficiently compressed.The link spectral efficiency of a wireless telephony link may also be expressed as the maximum number of simultaneous calls over 1 MHz frequency spectrum in erlangs per megahertz, or /MHz. This measure is also affected by the source coding (data compression) scheme. It may be applied to analog as well as digital transmission.In wireless networks, the link spectral efficiency can be somewhat misleading, as larger values are not necessarily more efficient in their overall use of radio spectrum. In a wireless network, high link spectral efficiency may result in high sensitivity to co-channel interference (crosstalk), which affects the capacity. For example, in a network with frequency reuse, and reduce the spectral efficiency in (bit/s)/Hz but substantially lower the required signal-to-noise ratio in comparison to non-spread spectrum techniques.This can allow for much denser geographical frequency reuse that compensates for the lower link spectral efficiency, resulting in approximately the same capacity (the same number of simultaneous phone calls) over the same bandwidth, using the same number of base station transmitters. As discussed below, a more relevant measure for wireless networks would be system spectral efficiency in bit/s/Hz per unit area. However, in closed communication links such as telephone lines and cable TV networks, and in noise-limited wireless communication system where co-channel interference is not a factor, the largest link spectral efficiency that can be supported by the available SNR is generally used.System spectral efficiency or area spectral efficiencyIn digital , the system spectral efficiency or area spectral efficiency is typically measured in (bit/s)/Hz per unit area, (bit/s)/Hz per , or(bit/s)/Hz per site. It is a measure of the quantity of users or services that can be simultaneously supported by a limited radio frequency bandwidth in a defined geographic area. It may for example be defined as the maximum or , summed over all users in the system, divided by the channel bandwidth. This measure is affected not only by the single user transmission technique, but also by schemes and techniques utilized. It can be substantially improved by dynamic . If it is defined as a measure of the maximum goodput, retransmissions due to co-channel interference and collisions are excluded. Higher-layer protocol overhead (above the sublayer) is normally neglected. Example 8:In a cellular system based on (FDMA) with a (FCA) cellplan using a of 4, each base station has access to 1/4 of the total available frequency spectrum. Thus, the maximum possible system spectral efficiency in (bit/s)/Hz per site is 1/4 of the link spectral efficiency. Each base station may be divided into 3 cells by means of 3 sector antennas, also known as a 4/12 reuse pattern. Then each cell has access to 1/12 of the available spectrum, and the system spectral efficiency in (bit/s)/Hz per cell or (bit/s)/Hz per sector is 1/12 of the link spectral efficiency.The system spectral efficiency of a may also be expressed as the maximum number of simultaneous phone calls per area unit over 1 MHz frequency spectrum in /MHz per cell, E/MHz per sector, E/MHz per site, or (E/MHz)/m2. This measure is also affected by the source coding (data compression) scheme. It may be used in analog cellular networks as well.Low link spectral efficiency in (bit/s)/Hz does not necessarily mean that an encoding scheme is inefficient from a system spectral efficiency point of view. As an example, consider , which is not a particularly spectral efficient encoding scheme when considering a single channel or single user. However, the fact that one can "layer" multiple channels on the same frequency band means that the system spectrum utilization for a multi-channel CDMA system can be very good.Example 9:In the 3G cellular system, every phone call is compressed to a maximum of 8,500 bit/s (the useful bitrate), and spread out over a 5 MHz wide frequency channel. This corresponds to a link throughput of only8,500/5,000,000 = (bit/s)/Hz. Let us assume that 100 simultaneous (non-silent) simultaneous calls are possible in the same cell. makes it possible to have as low a frequency reuse factor as 1, if each base station is divided into 3 cells by means of 3 directional sector antennas. This corresponds to a system spectrum efficiency of over 1 × 100 × = (bit/s)/Hz per cell or sector. The spectral efficiency can be improved by techniques such as efficient fixed or dynamic , , and .A combined and system spectral efficiency measure is the .Comparison tableExamples of numerical spectral efficiency values of some common communication systems can be found in the table below.Spectral efficiency of common communication systems.Service Standard Lau R per B per Link Typical Systemnch ed yea rcarrier(Mbit/s)carrier(MHz)spectralefficiencyR/B((bit/s)/Hz)1/K spectralefficiencyApprox.((R/B)/K)((bit/s)/Hzpersite)cellular 198117cellular 1983[]17cellular 1991× 8timeslots=19(13in1999)cellular1991× 3timeslots=19(13in1999)in1997) 1× voice200Max. permobilepermobile1(fullyloaded) +2003Max.: ;Typ.: ;Max.: ;Typ.: ;13HS + Max.: ;Typ.: ;Max.: ;Typ.: ;13cellular FDD 2001Max.:permobile;5Max.: permobile;1cellular1x PD 2002Max.:permobile;Max.: permobile;1(fullyloaded)cellular1×EV-DO 2002Max.:permobile;Max.: permobile;1averageloadedsectorFixed 20049620 , ,7, ...)14cellular 2007Max.: 21permobile;5Max.: permobile;12005Max.:percarrier;Max.: percarrier;12009Max.:permobile;20Max.: permobile;1Max.:;2003Max.: 54;20Max.: ;13200Max.: ;20Max.: ;137199 84 timeslots =199 5 to to 15towith 1995to to 1 to 1997Max.: ;Typ.: ;8Max.: ;Typ.: ;15with 1996Max.: ;Typ.: ;8Max.: ;Typ.: ;1Max.:;Typ.:;2007to 118 to 15towith 2007to 118 to 1 tomode386N/A N/A downlink12N/A N/A 1999N/A14。