Network Coding/Cryptography for

Wireless Network Security over

Galois Field TheoryAlyaa Al Barrak

School of Science and Technology

Supervisors

Prof. Kamal Bechkoum

Dr. Ali Al Sherbaz Dr. Robin Crockett

Outline

What is a Network?

What is a Network Coding?

Aim of our research.

It’s a group of two or more network devices (Computers, Mobiles, TVs and so on) connected together, so they can communicate with each other to transmit and share data.

What is a Network?

Message

Sender/ Receiver Receiver/ Sender

Node Node

Wireless Network Architecture:

Tx RxTx Rx

Tx RxTx Rxantenna antenna

MISOMulti Input Single output Wireless network

MIMOMulti Input Multi output Wireless network

SISO Single Input Single Output wireless network

SIMOSingle Input Multi output Wireless network

H 0 1 0 0 1 0 0 0

E 0 1 0 0 0 1 0 1

L 0 1 0 0 1 1 0 0

L 0 1 0 0 1 1 0 0

O 0 1 0 0 1 1 1 1

Data Transmission Example

HELLO

ASCII “American Standard Code for Information Interchange

Message

Noise

H 0 1 0 0 1 0 0 0

Sender ReceiverRequest To resend the Message

till receive it correct (Delay time)

Node Node

H 0 1 0 0 1 0 0 0

E 0 1 0 0 0 1 0 1

H 0 1 0 0 1 0 0 0

O 0 1 0 0 1 1 1 1

L 0 1 0 0 1 1 0 0

Network coding points out to each node taking its received packets, computing a linear combination over a finite field, and forwarding the result to another node till reach the final destination.In our research there will be two types of coding: Error detection code, and Error correction code.

What is a Network Coding?

b7 b6 b5 b4 b3 b2 b1 b0

8-Bit per packet

Original Packet (word)

b8 b7 b6 b5 b4 b3 b2 b1 b0

8-Bit per packet

Code Packet (code word)

Party Bit (P)

9-Bit per packet

overhead

Types of parity bitEven parity: numbers on “ 1 bits” even.

Odd parity: numbers of “1 bits” odd.

0 1 0 0 1 1 0 0 1

Logical operation XORP=

Data Bits

b8 b7 b6 b5 b4 b3 b2 b1 b0

P

0 or 1

P1 1 0 0 1 1 0 0 0

Data Bits P

1 1 0 0 1 1 0 0 1P

0 1 0 0 1 1 0 0 0P

Data Bits Data Bits

Sender

Receiver

Coding(Using Mathematical Model)

Ex:

Data Transmission With Network Coding

Source Encoder

Channel Encoder

Channel

Decoding (Using Mathematical Model)Ex:

Source Decoder Channel Decoder

Error Detection

Find error locations

ErrorsCorrection

Packet

2.3 KB packet size (WIFI)

50%-30%Overhead50%-70%

Data per packet(payload)

The aim is to find new or modified mathematical model using Galois Filed (GF) to minimize the

overhead and maximize the error correction as much as possible in the SISO and apply it on the

MIMO which is a challenge.

Thanks for your Attention

Q & A