I'm looking for a kind of error correction code or solution that can correct my codeword in this case:
My message holds $k$ bits, and $2k$ bits codeword (rate is $1/2$) is produced by the generator matrix, e.g. $k=5$, so it yields $10$ bits codeword $\rm 1001100111$. If the codeword is erased for some reason and it becomes $\rm 1xx1x00xx1$ (similar to the codeword transmitted through Binary Erasure Channel, and $\rm x$ is unknown, either '$0$' or '$1$'), can I still correct all the "$\rm x$ bits" in such situation as bit error rate is $1/2$?
I have read about some error correction code, such as block code, convolutional code and LDPC and got the following questions:
All these ECC have pratical application in communication, so do they still work when BER is close to $1/2$ (I think BER is impossible so high)?
Are there any feasible solution to my case? In fact, my message is $30$ bits and I can introduce another $30$ bits redundancy as parity bits. Can I still correct my codeword even if its half bits are erased where the recipient knows which bits he didn't receive properly?
What's the limit of ECC? If it can't correct half bits of codeword that are erased, how many bits can it correct at most?
Any guides or suggestions are appreciated!