Clyde A. Lettsome, Ph.D., P.E.

*Wireless Digital Communication and Coding Techniques

*Agenda

*Digital Communication Overview

*Digital Modulation Techniques

*Frequency Shift Keying

*Binary Phase Shift Keying

*Code Error Detection and Correction Methods

*Parity

*Cyclical Redundancy Check

*Block Error Detection and Correction

*Hamming Code

*Reed Solomon

*Channel Access Methods

*Time Division Multiple Access (TDMA)

*Code Division Multiple Access (CDMA)

*Digital Communications

Overview

*Digital Communications

Overview

Satellite, Television, Radio Broadcast

Data Storage, Hard drives, USB drives

CD, MP3, MPegWireless Routers, Cellular networks, Bluetooth

Digital Communications is

Everywhere

*Why Digital Communications?

*Reduced bandwidth if modulated on an analog carrier

*Noise Immunity

*Errors may be detected

*Errors may be corrected

*Easily manipulate to improve transmission

*Time Division Multiple Access (TDMA)

*Code Division Multiple Access (CDMA)

*Digital Communications

Overview

Convert to Binary

Data Encoding Modulation

DemodulationData

Decoding

Convert to Original Form

Transmission Medium

Storage Device

Transmission Medium

Storage Device

System dependent

*Digital Modulation Techniques

*Digital Modulation

Techniques: FSK

*Frequency Shift Keying (FSK) - transmission method in which the modulating wave shifts between two predetermined frequencies.

*Figure from Modern Communications by Beasley & Miller

*Digital Modulation Techniques: BPSK

*Binary Phase Shift Keying (BPSK) - transmission method in which the modulating wave shifts between two phases 180o out of phase.

*Figure from Modern Communications by Beasley & Miller

*Error Detection and Correction

*What if a bit(s) is(are) messed up during transmission or storage?

*Examples: atmospheric noise, intrinsic noise, scratches on CDs, single-event upsets, etc.

*Digital coding has many advantages over analog coding

*Immunity to noise

*Errors can be detected and corrected

*Error Detection and Correction

Methods

*Common Error Processing Techniques

*Error detection –Retransmit the block

*Parity

*Cyclic Redundancy Check

*Block Codes

*Error correction – Fix errors at the receiver

via FEC – Forward Error Correction (Adding more coding bits increases the correction capability but reduces throughput.)

*Block Codes

*Hamming Code

*Reed Solomon

*Error Detection: Parity

*Arguably the most common method of error detection.

*A single bit called parity bit is added to each transmitted code.

*Parity bit makes the code either be even or odd

*Even parity makes the total number of ones even

*Odd parity makes the total number of ones odd

*Example: Code [1001]

*Even parity transmitted code: [1001|0]

*Odd parity transmitted code: [1001|1]

*Error Detection: Parity

*Will detect error only if an unexpected parity is received*Odd parity transmitted code: [1001|1] *Received code indicates error [1101|1]*Received code does not indicate error [1111|1]

*Good for random errors (single bit errors but not for burst errors (multiple consecutive errors)*Used with ASCII

*Error Detection: CRC

*Effectively detect 99.95 % errors.

*Block of data (D) is combined with a frame check sequence (F) to compose a frame to be transmitted (T).

*The Frame check sequence is developed by mathematically dividing the block of data by a predetermined divisor (P).

*On the receiver side the transmitted frame (T) is divided by the divisor (P). If the remainder is zero then no error is detected.

*Error Detection: CRC

Example: Develop a (7,4) cyclic code from a transmitter where the data to be transmitted(D) = [1100] and divisor (P) =[1011].

1100/1011 = 1110 <-[D]/[P]

1011

1110

1011

1010

1011

010 <-Remainder (Block Check Code)

Transmitted(T) = [D R] = [1100010]

*Error Detection: CRC

Decoding in the receiver

1100010 /1011 = 1110 <-[T]/[P]

1011

1110

1011

1011

1011

00 <-Remainder

*Error Correction: Block Error Correction

Code

*The Hamming distance is the number of bits that are different between allowed transmitted code words*d(code block, received block)

*d(00000,00100) = 1

*d(00111,00100) = 2

*The greater the Hamming distance the more errors need to be corrected.

*Error Detection: Simple Block Code

*Example: Block code example*Let 0 be represented by 00. *Let 1 be represented by 11.

*The code block is two bits long.*The number of bits that are different between

each allowed code word is 2. Therefore the Hamming distance is 2. *If 01 or 10 is received at the receiver then a

bit error occurred.*This code can detect one bit error per

block but cannot correct a bit error

*Error Correction: Block Error Correction

Code

*Example: Block code example*Let 0 be represented by 00000. *Let 1 be represented by 00111.

*The code block is five bits long.*The number of bits that are different between each

allowed code word is 3. Therefore the Hamming distance is 3. *If 00110, 00101, or 00011 is received at the

receiver then a bit error occurred.*This code can detect up to three bit error

per block and can correct one bit bit error

*Error Correction: Hamming Code

*Hamming code correct single bit errors

*Example: Consider D=[1001] the minimum number of parity bits is 3.

(2n ≥ m+n+1 where m is the length of D and n is the smallest of parity bits that makes the relationship true)

*Let P1 = (2,4,5), P2 = (4,5,6), P3 = (5,6,2) and use odd parity.

P1 1 P2 0 0 1 P3

1 2 3 4 5 6 7

0 1 0 0 0 1 1 Transmitted

*Error Correction: Reed Solomon

*Detects and corrects bursts of errors

*Utilizes Interleaving

*Used in extensively CDs and Cell Phone Transmission

0 1 0 <- 1st Word

0 0 1 <- 2nd Word

0 1 1 <- 3rd Word

*Channel Access Methods

*Time Division Multiple Access

*Example: TDMA Example

*Cell phone A and cell phone B, A would be given a certain amount of time to transmit.

*After that time B is transmitted and the process is repeated

*(ABABABABAB……)

*Code Division Multiple Access

*Example: CDMA Example of a computer network

* If the system router transmits 01101001, both endpoints receive the information. However, endpoint 1 knows the router is communicating with it because the XNOR and sum of the data equals 4 or 0.

0110|1001 <- Transmitted

0110|1001 <- Stored Codeword

1111|1111 <- 4|4

Endpoint 1 (computer)Let 0 equal 0110Let 1 equal 1001

Endpoint 2 (computer)Let 0 equal 0011Let 1 equal 1100