Page 342 - Satellite Communications, Fourth Edition

322 Chapter Eleven

TABLE 11.2 m, n, k for some
Hamming Codes
m n k
2 3 1
3 7 4
4 15 11
5 31 26
6 63 57
7 127 120

It will be seen that the code rate r k/n approaches unity as m
c
increases, which leads to more efficient coding. However, only a single
error can be corrected with Hamming codes.

11.3.2 BCH codes
BCH stands for the names of the inventors, Bose, Chaudhuri, and
Hocquenghen. These codes can correct up to t errors, and where m is any
m
positive integer, the permissible values are n 2 1 and k n mt.
The integers m and t are arbitrary, which gives the code designer con-
siderable flexibility in choice. Proakis and Salehi (1994) give an exten-
sive listing of the parameters for BCH codes, from which the values in
Table 11.3 have been obtained. As usual, the code rate is r k/n.
c

11.3.3 Reed-Solomon codes
The codes described so far work well with errors that occur randomly
rather than in bursts. However, there are situations where errors do
occur in bursts; that is, a number of bits that are close together may

Table 11.3 Some parameters
for BCH codes
n k t
7 4 1
15 11 1
15 7 2
15 5 3
31 26 1
31 21 2
31 16 3
31 11 5
31 6 7