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 2*k bits codeword (rate is 1/2) is produced by the generator matrix, e.g. k=5, so it yields 10 bits codeword 1001100111. If the codeword is erased for some reason and it becomes 1xx1x00xx1 (similar to the codeword transmitted through Binary Erasure Channel, and x is unknown, either '0' or '1'), can I still correct all the "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 half bits are corrupted?
Any guides or suggestions are appreciated!