Digital to Digital Encoding

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Stephanie Clara Gray
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1 MODULATION AND ENCODING Data must be transformed into signals to send them from one place to another Conversion Schemes Digital-to-Digital Analog-to-Digital Digital-to-Analog Analog-to-Analog Digital to Digital Encoding representation of digital information by a digital signal Types Unipolar Polar Bipolar

2 Unipolar Encoding simplest yet primitive; uses only one level of value; straight forward & inexpensive to implement. Unipolar encoding is less desirable because of: Presence of DC component average amplitude of a unipolar encoded signal is nonzero (creating a DC); it cannot travel to a media that can t handle DC. Synchronization occurs in unipolar encoding when the receiver can t determine the beginning and ending of each bit thereby distorting the timing of the signal. Polar Encoding Uses 2 levels (+ or -) of amplitude Types: Non return to Zero (NRZ) level of signal is always either (+) or (-) Forms of NRZ transmission: NRZ-L the level of signal is dependent upon the state of the bit; positive voltage means 0; negative means the bit is 1. NRZ-I an inversion of the voltage level represents a 1 bit. It is transition between a (+) and a (-) voltage, not the voltage themselves, that represents a 1 bit. A 0 bit represents no change.

3 Polar Encoding Return to Zero (RZ) uses 3 values: positive, negative or zero. Advantage: assurance of synchronization Disadvantage: requires 2 signal changes to encode one bit, occupying more BW. Biphase provides the best solution for synchronization problems; the signal changes at the middle of the bit interval but does not return to zero. Implemented by Manchester encoding the transition at the middle of the bit is used for both synchronization & bit representation. Differential Manchester the transition at the middle of the bit is used only for synchronization. Bipolar Encoding Uses 3 voltage levels like the RZ; zero level is used to represent binary 0; the 1s are represented by alternating (+) & (-) voltages. Types: Alternate Mark Inversion (AMI) simplest type of bipolar encoding; A zero voltage represents binary zero; 1s are represented by alternating (+) & (-) voltages. By inverting on each occurrence of a 1, bipolar AMI accomplishes two things: first, DC component is zero and second, a long sequence of 1s stays synchronized. No mechanism to ensure synchronization of a long string of one s.

4 Bipolar Encoding Bipolar 8 Zero Substitution ( B8ZS) convention adopted in N. America to provide synchronization of long strings of 0s. forces artificial signal changes, called violations, w/ in the Ø string. Anytime eight 0s occur in succession, B8ZS introduces changes in the pattern based on the polarity of the previous 1. High- Density Bipolar 3 (HDB3) used in Japan & Europe in HDB3, if 4 0 s come one after another, we change the pattern in one of four ways based on the polarity pf the previous 1 and the no. of 1s since the last substitution. Analog to Digital Conversion PULSE AMPLITUDE MODULATION (PAM) first step in analog- to- digital conversion; foundation of PCM PULSE CODE MODULATION (PCM) made up of 4 processes: sampling, quantization; binary encoding & digital- to- digital encoding Quantization method of assigning integral values in a specific range to sampled instances. Nyquist theorem The sampling rate must be at least two times the highest frequency.

5 Transmission of Digital Signal Parallel Transmission Using n wires to send n bits Main feature is speed but costly Serial Mode Bits are sent one after the other Types: Asynchronous: information is translated by agreedupon patterns (based on grouping bit streams); Use of start and stop bits with optional parity bit Synchronous: bit streams are combined into longer frames, synchronization characters are added instead of start and stop bits Digital to Analog Conversion process of changing one of the characteristics of an analog signal based on the information in a digital signal. Bit rate no. of bits transmitted per second. Baud - no. of signal units per second. *Baud is less than or equal to the bit rate. Types: Amplitude Shift Keying (ASK) the strength of the carrier signal is varied to represent binary 1 and 0. highly susceptible to noise and interference; modulating method most affected by noise. On-off keying (OOK) most popular ASK technique; known to some as digital AM.

6 Digital to Analog Conversion Frequency Shift Keying (FSK) - frequency of carrier signal is varied to represent binary 1 and 0. Phase Shift Keying (PSK) phase of the carrier is varied to represent binary 1 and 0. BPSK or (2-PSK) QPSK or (4- PSK) 8-PSK Quadrature Amplitude Modulation (QAM) means combining ASK & PSK in such a way that we have maximum contrast b/w each bit, dibit, tribit, etc. 4- QAM 8-QAM 16- QAM Digital to Analog Conversion Modulation Units Bits Bit rate Baud (rate) ASK, FSK, BPSK Bit 1 N N 4-PSK, 4-QAM Dibit 2 2N N 8-PSK, 8-QAM Tribit 3 3N N Bit / Baud 16-QAM Quadbit 4 4N N Comparison 32-QAM Pentabit 5 5N N 64-QAM Hexabit 6 6N N 128-QAM Septabit 7 7N N 256-QAM Octabit 8 8N N Example: A constellation diagram consists of 8 equally spaced points on a circle. If the bit rate is 4800 bps, find the baud. Find the bit rate for a 16-QAM signal with a band equal to 1000 baud. Find the baud for a 72 kbps, 64-QAM signal.

7 Telephone Modems Modem Standards: V.32 modem: uses trellis-coded modulation (essentially QAM with redundant bit), 32-QAM V.32 bis modem: uses 128 QAM (7 bits with 1 bit for error control) V.90: a bit rate of 56kbps (33.6kbps upload) V.92: a bit rate of 56kbps (48kbps upload) Analog-to to-analog Conversion Representation of analog information by an analog signal Types: Amplitude Modulation: the modulating signal becomes the envelope to the carrier Bandwidth: 2 x BW m Frequency Modulation: as the amplitude of the information signal changes, the frequency of the carrier signal changes correspondingly Bandwidth: 10 x BW m Phase Modulation: used in some systems as an alternative to FM

8 Error Detection and Correction Data can be corrupted during transmission. For reliable communication, errors must be detected and corrected Types of Errors Single Bit Multiple Bit Burst Error Detection: uses the concept of redundancy which means adding extra bits for detecting errors at the destination Error Detection Methods Parity check Simple Parity Check: a parity bit is added to every data unit so that the total number of 1s in a unit becomes even/odd. Two Dimensional Parity Check: a block of bits is divided into rows and a redundant bit is added to the whole block Performance: two-dimensional parity check increases the likelihood of detecting burst errors Cyclic Redundancy Check: based on binary division Performance: CRC can detect all burst errors that affect an odd # of bits; can detect all burst errors of length less than or equal to the degree of the polynomial; can detect, with a high probability, burst errors of length greater than the degree of the polynomial

9 Error Detection Methods Parity check Cyclic Redundancy Check: a polynomial is used to represent the divisor Properties of a CRC divisor: (1) It should not be divisible by x; (2) It should be divisible by (x+1). Checksum: used by higher layer protocols; uses binary addition Performance: detects all errors involving an odd number of bits, as well as most errors involving an even number of bits. But anytime a bit inversion is balanced by an opposite bit inversion in the corresponding digit of another data segment, the error is invisible Error Correction Handled in two ways: When an error is discovered, the receiver can have the sender retransmit the entire data unit A receiver can use an error-correcting code, which automatically corrects certain errors. In theory, it is possible to correct any binary code errors automatically. Error correction is limited to one-, two- or three-bit errors

10 Single Bit Error Correction Redundancy Bits Additional bits necessary to cover all possible error locations 2 r m + r + 1 Hamming Code Can be applied to data units of any length and uses the relationship between data and redundancy bits Each r bit is the VRC bit for one combination of data bits wherein each data bit may be included in more than one VRC calculation Burst Error Correction The number of redundancy bits required to make these corrections is dramatically higher than that required for single-bit errors To correct double-bit errors, we must take into consideration that the two bits can be a combination of any two bits in the entire sequence. The Hamming code strategy must be redesigned to be applicable for multiple bit correction.

Chapter 5 Analog Transmission

5-1 DIGITAL-TO-ANALOG CONVERSION Chapter 5 Analog Transmission Digital-to-analog conversion is the process of changing one of the characteristics of an analog signal depending on the information in digital