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Contents Line coding Reasons For Using Line Coding Properties of a Line Code Line coding schemes Error Correction
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Line Coding Line coding is always needed; which is a technique to convert binary data to digital signal. In the transmission of digital information over wire or optical fiber systems, line coding (also known as modulation/data translation coding) is the method by which 1’s & 0’s are represented as transmitted waveforms.
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Reasons For Using LineCoding Spectrum shaping and relocation without modulation or filtering. This is important in telephone line applications, e.g, where the transfer characteristic has heavy attenuation below 300 Hz. Error detection capabilities. Bandwidth usage; the possibility of transmitting at a higher rate than other schemes over the same bandwidth.
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Cotnd.. DC component can be eliminated; this allows AC (capacitor or transformer) coupling between stages (as in telephone lines )
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Properties of a Line Code:Self–Synchronization : There is enough timing information built into the code so that bit synchronizers can extract the timing or clock signal. A long series of binary 1’s or 0’s should not cause a problem in time recovery
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Contd.. Low Probability of Bit Error : Receivers can be designed that will recover the binary data with a low probability of bit error when the input data is corrupted by noise or ISI. A Spectrum that is Suitable for the Channel: In addition, the signal bandwidth needs to be sufficiently small compared to the channel bandwidth, so that ISI will not be a problem.
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Contd.. Transmission Bandwidth: This should be as small as possible Error Detection Capability: It should be possible to implement this feature easily by the addition of channel encoders and decoders, or the feature should be incorporated into the line code
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Unipolar encoding Unipolar encoding uses only one voltage level ( use only one polarity +ve or -ve).
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Unipolar Encoding’sProblems:Two problems: A dc component Lack of synchronization : If data contain long sequence of 0’s or 1’s, there is no transition in the signal during this duration that can alert the receiver to synchronization problem. The receiver receives a continuous voltage and determines how many bits are sent by relaying on its clock (bit-duration), which may not be synchronized with the sender clock.
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Polar Encoding Polar encoding uses two voltage levels (positive and negative). By using two levels , the average voltage level is reduced and the dc component problem may be alleviated( if balance)
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NRZ: NRZ-L The level of the signal is dependent upon the state of the bit. A positive voltage means 0, while negative means 1. Has lack of synchronization , when the data contain a long stream of 0s or 1s.
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NRZ: NRZ-I In NRZ-I , the signal is inverted if a 1 is encountered. It is the transition between a +ve and a –ve voltage , not the voltage itself. A 0 bit is represented by no change NRZ-I is superior to NRZ-L due to synchronization each time a 1 bit is encountered.
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RZ encoding To ensure synchronization, there must be a signal change (transition) for each bit RZ uses three values +ve, zero and –ve The signal changes during each bit A1-bit is represented by transition from +ve to zero A 0-bit by –ve to zero
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Bi phase: Manchester encoding The transition at the middle of the bit is used for both synchronization and bit representation. It has not Dc component It achieves the same level of synchronization as RZ but with only two levels and less B-W
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Bipolar AMI (Alternate Mark Inversion) Encoding Bit 0 represents by zero voltage Bit 1s are represented by alternating +ve and –ve voltages
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Contd.. In bipolar encoding AMI , we use three levels: positive, zero, and negative as RZ. Has DC component AMI has a lack of synchronization when there is a stream of sequential zeros.
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Hamming distance The Hamming distance between two words is the number of differences between corresponding bits. The minimum Hamming distance is the smallest Hamming distance between all possible pairs in a set of words.
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Contd.. Let us find the Hamming distance between twopairs of words. The Hamming distance d(000, 011) is 2 becauseThe Hamming distance d(10101, 11110) is 3because
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Contd.. We first find all Hamming distances. The dmin in this case is 3.
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Contd.. To guarantee the detection of up to s errors in all cases, the minimum Hamming distance in a block code must be dmin = s + 1. To guarantee correction of up to t errors in all cases, the minimum Hamming distance in a block code must be dmin = 2t + 1.
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Example A code scheme has a Hamming distance dmin = 4. What is the error detection and correction capability of this scheme?SolutionThis code guarantees the detection ofup to three errors (s = 3), but it cancorrect up to one error. In other words, ifthis code is used for error correction,part of its capability is wasted. Errorcorrection codes need to have an odd
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LINEAR BLOCK CODES Almost all block codes used today belong to a subset called linear block codes. A linear block code is a code in which the exclusive OR (addition modulo-2) of two valid code words creates another valid codeword.
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Contd.. A simple parity-check code is a single-bit error-detecting code in which n = k + 1 with dmin = 2. Even parity (ensures that a codeword has an even number of 1’s) and Odd parity (ensures that there are an odd number of 1’s in the codeword)
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Cyclic Codes Cyclic codes are special linear block codes with one extra property. In a cyclic code, if a codeword is cyclically shifted (rotated), the result is another codeword.
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