B. P. Lathi, Zhi Ding - Modern Digital and Analog Communication Systems-Oxford University Press (2009)

14.13 MATLAB Exercises 863
Exl4 3
r =
1 0 1 0 1 1 1
Syndrome Error Pattern
1 0 1 1 0 0 0 0 0 0
1 1 1 0 1 0 0 0 0 0
1 1 0 0 0 1 0 0 0 0
0 1 1 0 0 0 1 0 0 0
1 0 0 0 0 0 0 1 0 0
0 1 0 0 0 0 0 0 1 0
0 0 1 0 0 0 0 0 0 1
syndrome
1 0 0
error =
0 0 0 0 1 0 0
cword =
1 0 1 0 0 1 1
COMPUTER EXERCISE 14.2
In a more realistic example, we will use the Hamming (7,4) code to encode a long binary message bit
sequence. The coded bits will be transmitted in polar signaling over an additive white Gaussian noise
(AWGN) channel. The channel outputs will be detected using a hard-decision function sgn. The channel
noise will lead to hard-decision errors. The detector outputs will be decoded using the Hamming (7,4)
decoder that is capable of correcting 1 bit error in each codeword of length 7.
This result is compared against the uncoded polar transmission. To be fair, the average Eb/ JI/ ratio
for every information bit is made equal for both cases. MATLAB program Sim7 4Harnming . mis given;
the resulting BER comparison is shown in Fig. 14.25.
% Matlab Program <Sim7 4Harnming .m>
% Simulation of the Hamming (7,4) code performance
% under polar signaling in AWGN channel and performance
% comparison with uncoded polar signaling
clf; clear sigcw BER_uncode BER_coded
G= [l O O O 1 0 1 % Code Generator
0 1 0 0 1 1 1
0 0 1 0 1 1 0
0 0 0 1 0 1 1] ;
H= [l 1 1 0 1 0 0 % Parity Check Matrix
0 1 1 1 0 1 0