Cryptography Reference
In-Depth Information
Figure 6.3 - The parallel concatenation of non-recursive systematic codes is a poor code
concerning the information sequences of weight 1. In this example, the redundancy
symbols
Y
1
and
Y
2
each contain only three 1.
Figure 6.4 - Parallel concatenation of extended Hamming codes (global rate: 1/3). On
the right: a pattern of errors of input weight 1 and total weight 7.
The asymptotic gain has therefore not been extraordinarily increased by means
of the concatenation (0,67 dB precisely), and a great reduction in the coding
rate has occurred. If we wish to keep the same global rate of 1/2, a part of the
redundancy must be punctured. We can choose, for example, not to transmit
the 16 symbols present in the last two columns and the last two lines of the
table of Figure 6.4(a). The MHD then drops to the value 3, that is, less than
the MHD of the elementary code. The PC is therefore of no interest in this case.
