A Mysterious Message

Imagine that at some point in the future, you are working at a SETI search. After years of listening to static, you finally detect a narrow-band signal. The signal consists of a long, repetitive chain of long and short pulses. Remembering way back to your college days, you realize that this must be some sort of binary code. You decide to call the short pulses '0' and the long pulses '1'.

You then find that the overall pattern looks like the following:

121 bits, repeating twice

00000000000000000100000000010100000
00100010000010000010001010100010001
00000100000100010000000101000000000
1000000000000000

77 bits, repeating twice

00000010000000001010000000100010000
01010001000001000100000001010000000
0010000

35 bits, repeating twice

00001000001010001110100010100000100

finally...

000111010000101

Can you decode this message? What is the sender trying to describe / say / show?