Extended Golay Code

National Instruments has partnered with Prentice Hall to bring you large portions of in-depth technical topics from several PTR RF and Communications books, including Digital Communications: Fundamentals and Applications, 2nd Edition. This series of content is designed for a broad range of audiences, from experts who want to review a specific topic to students who need easy-to-understand documentation for their projects.

For the complete list of RF topics, please visit the RF and Communications Resource Main Page.

6.8.2 Extended Golay Code

One of the more useful block codes is the binary (24, 12) extended Golay code,

which is formed by adding an overall parity bit to the perfect (23, 12) code, known

as the Golay code. This added parity bit increases the minimum distance d_min from

7 to 8 and produces a rate ½ code, which is easier to implement (with regard to system

clocks) than the rate 12/23 original Golay code. Extended Golay codes are

considerably more powerful than the Hamming codes described in the preceding

section. The price paid for the improved performance is a more complex decoder, a

lower code rate, and hence a larger bandwidth expansion.

Since d_min = 8 for the extended Golay code, we see from Equation (6.44) that

the code is guaranteed to correct all triple errors. The decoder can additionally be

designed to correct some but not all four-error patterns. Since only 16.7% of the

four-error patterns can be corrected, the decoder, for the sake of simplicity, is usually

designed to only correct three-error patterns [5]. Assuming hard decision decoding,

the bit error probability for the extended Golay code can be written as a

function of the channel symbol error probability p from Equation (6.46), as follows:

The plot of Equation (6.77) is shown in Figure 6.21; the error performance of the

extended Golay code is seen to be significantly better than that of the Hamming

codes. Combining Equations (6.77), (6.74), and (6.75), we can relate P_B versus

E_b/N₀ for coherently demodulated BPSK with extended Golay coding over a

Gaussian channel. The result is plotted in Figure 6.22.

Relevant NI products

Customers interested in this topic were also interested in the following NI products:

• RF and Communication Hardware and Software
  
• Other Modular Instruments (digital multimeters, digitizers, switching, etc...)
• LabVIEW Graphical Programming Environment

For the complete list of tutorials, return to the NI RF and Communications Fundamentals Main page.

Buy the Book

Purchase Digital Communications from Prentice Hall Professional through this link and receive the following:

• Between 15% and 30% Off
• Free Shipping and Handling

1 ratings | 1.00 out of 5

Print

Reader Comments | Submit a comment »