Question

If we have to receive a data from sender as a chunk of bits (say 8 bits).

But, the transferring is unreliable which result in bit-lost. (Not bit-flip)
That mean, any bit in the chunk can be absent and receiver would receive only 7 bits.

I studied some error-correction coding, such as ‘Hamming code’. But, the code is designed to recover fliped-bit not lost-bit in this situation.

Answer 1

If you are happy with a low entropy code and you can detect an end-of-message, you can simply send each bit twice.

This code can recover from any number of deletions that happen in different runs:

On receiving, find all odd-sized runs and extend them by one bit. If you end up with less than the expected count of bits, you are unable to recover from multiple deletion.

If you want to ensure a fixed error rate that can be recovered, use bit-stuffing.

Example:

0110

encoded as:
00 11 11 00

a double error occurs:
0x 11 x1 00

received:
011100

'0' and '111' are odd-sized runs. Fix:
00111100

we have 8 bits, and have recovered from a double error.
decode:
0110

Example 2:

0101

encoded as
00110011

transmitted as
0xxx0011

received as
00011

corrected as
000011

decoded as
001

which is shorter than expected. A transmission error has occured.

Example 3 (bit stuffing after a run of 3 bits):

0000 1111

stuffed as
00010 11101

sent as
0000001100 1111110011