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

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Vin

Vou

t

u-law encoding; u = 255

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 802.3

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.