Block Codes-0

EEL 6509 Wireless Communications- Block Codes
Dr. John M. Shea

Overview




Binary Block Codes

Error Correcting Codes

Binary BCH Codes

Error Probabilities for Binary Block Codes

Error Detecting Codes

Cyclic Redundancy Check (CRC) Codes

Nonbinary Block Codes

Reed-Solomon Codes

Example t=2 code over GF(23)

\begin{eqnarray*}n&=&2^3-1=7\\
k&=& 7 -2(2)=3
\end{eqnarray*}


(7,3) code

Message symbols: 3 symbols from GF(23) = 3 (3 bit symbols) = 9 bits

Coded symbols: 7 (3 bit symbols) = 21 bits

29 = 512 code words
221 = 2 million possible received words

(In comparison, the (7,3) binary code has 8 codewords and 128 possible received words.)

For the (7,3) RS code,

\begin{displaymath}\frac{2^{3 \cdot 3}}{2^{3 \cdot 7 }} = \frac{1}{4096} \mbox{ of
binary words are valid codewords} \end{displaymath}

For the (7,3) binary code,


\begin{displaymath}\frac{2^{3}}{2^{7}} = \frac{1}{16} \mbox{ of
binary words are valid codewords} \end{displaymath}

Block Codes in Wireless Communications

System

Error Correcting Code Error Detecting Code

AMPS - US Analog Cellular System

   

forward blank & burst (40,28) BCH  

reverse blank & burst (48,36) BCH  

IS-54 - US Digital Cellular System

   

voice channel (convolutional) 7-bit CRC
  digital verification color code (12,8) Hamming  

GSM

   
  voice (conv.) 3-bit CRC on most-
      important bits
  control (conv.) 40-bit CRC

IS-95 - CDMA Cellular System

   
  various (conv.) 16, 12, 10, 8, 6-bit CRC codes

Digital European Cordless Telephone (DECT)

(none) 16-bit CRC

SINCGARS Military Frequency Hop Radio

Reed-Solomon  

IEEE 802.11 Wireless LAN

?? 16-bit CRC

Bluetooth

   
  Header rate-1/3 repetition 8-bit CRC
  Data (15,10) shortened Hamming code 16-bit CRC

NASA Voyager Satellite

(255,223) Reed-Solomon code  
    (with conv. code)  



Information for this table collected from [3]-[5].

Bibliography

1
B. Sklar, Digital Communications: Fundamentals and Applications.
Englewood Cliffs, New Jersey: Prentice Hall, 1988.

2
S. Lin and D. J. Costello, Error Control Coding: Fundamentals and Applications.
New Jersey: Prentice-Hall, 1983.

3
T. S. Rappaport, Wireless Communications: Principles and Practice.
New Jersey: Prentice Hall, 1996.

4
V. K. Garg, IS-95 CDMA and cdma2000: Cellular/PCS Systems Implementation.
Upper Saddle River, New Jersey: Prentice Hall, 2000.

5
S. B. Wicker and V. K. Bhargava, eds., Reed-Solomon Codes and Their Applications.
Piscataway, New Jersey: IEEE Press, 1994.

About this document ...

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The translation was initiated by John Shea on 2001-04-04


John Shea
2001-04-04