ChannelCoding, Slides of Digital Communication Systems

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ChannelCoding

Hafiz Malik

Dept. of Electrical & Computer Engineering

The University of Michigan-Dearborn

[email protected]

http://www-perosnal-engin.umd.umich.edu/~hafiz

Channel Coding

• class of signal transformations

designed to improve communication

performance by enabling the

transmitted signals to better

withstand channel distortions such as

noise, interference, and fading.

• Channel coding can be divided into

two major classes:

1. Waveform coding by signal design
2. Structured sequences by adding redundancy

Structured Sequences

• (^) deals with transforming sequences into “better sequences” by adding structured redundancy (or redundant bits). The redundant bits are used to detect and correct errors hence improves overall performance of the communication system.
• (^) Examples:
• (^) Linear codes
• (^) Hamming codes
• (^) BCH codes
• (^) Cyclic codes
• (^) Reed-Solomon codes
• (^) Non-Linear codes
• (^) Convolution codes
• (^) Turbo codes

Waveform Coding

4-ary Amplitude

• (^) Each symbol sends 2 bits
• (^) Deciding which level is

correct gets harder due to

fading and noise

• (^) RCV needs better SNR to

achieve accuracy

11 01 10 00

Orthogonal Signals

• Definition

• This means that the signals are

perpendicular to each other in M-dim

space

• For a correlative receiver, this means

that each incoming signal can be

compared with a model of the signal

and the best match is the symbol

that was sent

    (^0 ) T b i j C i j p t p t dt i j ^   (^)   

Multi-Phase

• (^) Binary Phase Shift Keying (BPSK) 1: (t)= p(t) cos(ct) 0: (t)= p(t)cos(ct
• (^) M-ary PSK Re Im x x

cos

k c

p t p t t k

M

Re Im x x x x x (^) x x x

Quadrature Amplitude Modulation (QAM)

• (^) Amplitude-phase shift keying (APK)     (^)          cos sin cos k k c k c k c k p t p t a t b t p t r t         2 2 tan k k k k k k b r a b a        (^)     ri i

M-ary Comments

• As M increases, it is harder to make

good decisions, more power is used

• But, more information is packed into

a symbol so data rates can be

increased

• Generally, higher data rates require

more power (shorter distances,

better SNR) to get good results

How do we compare

performance?

• Symbols have different meanings, so

what does the probability of error, PE

mean?

• If a detection error is made, then

more than one bit is wrong

• DCS can be faster at the price of

being less sensitive

16

Formula for detecting error

Let d2, d4, d6, d8, d10, d12, d14, d16 be all the even values in the credit card number. Let d1, d3, d5, d7, d9, d11, d13, d15 be all the odd values in the credit card number. Let n be the number of all the odd digits which have a value that exceeds four Credit card has an error if the following is true: (d1 + d3 + d5 + d7 + d9 + d11 + d13 + d15) x 2 + n + (d2 + d4 + d6 + d8 + d10 + d12 + d14 + d16)

17

Detect Error On Credit Card

d 1 d 2 d 3 … d 5 d 6 n = 3

19

Credit Card Summary

The test performed on the credit card number is called a parity check equation. The last digit is a function of the other digits in the credit card. This is how credit card numbers are generated by Visa and Mastercard. They start with an account number that is 15 digits long and use the parity check equation to find the value of the 16 th digit. “This method allows computers to detect 100% of single-position errors and about 98% of other common errors” ( For All Practical Purposes p.

Examples

• ISBN (international standard book

number)

• UPC (universal product codes)

• (^) 12-digit sequence
• (^0) 16000 66610 8