Data Encoding and Decoding Professor: Dr. Miguel Alonso Jr.

Outline u-law encoding Encoding Formats NRZ RZ Bi-phase and Miller Alphanumeric Encoding Coding Principles Code Error Detection and Correction

U-law Encoding before PCM Useful for when the analog signal is to vary throughout its entire range. i.e. the signal will change from a very strong to a very weak signal Solution: u-law companding Vout = Vmax * ln(1+u*Vin/Vmax) / ln (1+u)‏ u defines the amount of compression u = 0, no compression Early Bell systems u=100, for a 7 bit PCM code

Encoding Formats For transmitting PCM codes short distances, typically 5 Volts represents a logic 1, and 0 volts represents a logic 0 But for transmission over long distances through wire, or through fiber optic lines or RF (radio frequencies), the binary data must be encoded so that the highs and lows are easily detected Systems are typically serial, either Synchronous – clocking information needs to be added Asynchronous – no clocking information necessary

Commonly used digital signal encoding formats NRZ – non return to zero RZ – return to zero Phase-encoded and delay encoded Multilevel binary

NRZ Easiest to implement Data does not return to zero during an interval or frame No – self synchronization, synchronization must be added NRZ-L (level)‏ 1 – high level 0 – low level NRZ-M (mark)‏ 1 – transition at the beginning of the interval 0 – no transition NRZ-S (space)‏ 1 – no transition 0 – transition at the beginning of the interval

RZ Same limitations and disadvantages of NRZ RZ (unipolar)‏ 1 – transition at the beginning of the interval 0 – no transition RZ(bi-polar)‏ 1 – positive transition in the first half of the interval 0 – negative transition in the first half of the interval RZ-AMI (alternate – mark inversion)‏ 1 – transition with the clock interval alternating in direction 0 – no transition

Bi-phase and Miller Codes No – DC component and self synchronizing Biphase – M (bi-phase mark)‏ 1 - transition in the middle of the clock interval 0 – no transition in the middle of the clock interval Note: always a transition at the beginning of the clock interval Biphase – L /Manchester ((ethernet standard IEEE LAN)‏ 1 – transition from high to low in the middle of the clock interval 0 – transition from low to high in the middle of the clock interval

Biphase – S 1 – no transition in the middle of the clock interval 0 - transition in the middle of the clock interval Note: there is always a transition at the beginning of the clock interval Differential Manchester 1 – transition in the middle of the clock interval 0 – transition at the beginning of the clock interval Miller/delay modulation 1 – transition in the middle of the clock inteval 0 – no transition at the end of the clock interval unless followed by a zero

Alpha-Numeric Coding ASCII (American Standard Code for Information Exchange)‏ 128 possible combinations ( 7 bits)‏ 1 parity bit ( used for error detection LSB transmitted first First 3 bits indicate number, letter, or character Lower 4 bits are BCD progression

BCD (Binary coded decimal)‏ EBCDIC ( Extended Binary-Coded Decimal Interchange Code)‏ Hexadecimal Numbering System

Coding Principles Hamming Distance: Minimum distance between each defined state Error Detection and Correction based on Dmin Dmin – 1 errors can be detected if Dmin is even, then Dmin/2 – 1 errors can be corrected if Dmin is odd, the 1/2*(Dmin -1) errors can be corrected

Error detection Parity A single bit is added to each code representation if # of 1's is even, even parity if odd, odd parity Parity Generator/Checker: XOR Gates 1 for odd parity, 0 for even parity 0 for no errors if used as a checker

Error Handling ARQ Automatic Request for Retransmission Symbol Substitution Most Systems use ARQ ACK (positive acknowledgment is sent back to the transmitter if no error is detected)‏ NAK (negative acknowledgment is sent back if an error is detected and the the transmitter repeats that block of data.