2 point about Shannon entropy, and error-coding reducing possible information density

The question as you have it formulated currently has "no" for an answer. If the loss of coherent information means you cannot correct the errors, then obviously the loss of coherent information means you cannot correct any errors.

In non-quantum coding, it is possible to generate error correcting codes that are capable of correcting $a$-bit errors per $n$ bits (obviously, $a \lt n$), and of detecting $b$-bit errors per $n$ bits, ($a \lt b \lt n$), while greater than $b$ erroneous bits would be a catastrophic undetectable and uncorrectable error. These error-correcting codes depend on sending redundant information, decreasing the information content or the information content below the maximal Shannon information density possible on that communication stream. There is no way around having to reduce information density to increase the quality of the transmission.

Hamming codes allow for 1-bit error correction, 2-bit detection; Reed-Solomon codes are used to perform error correction on audio compact-discs. While your comment says you "meant not PERFECT error correction", your question still says "to provide for perfect error correction". Perhaps you could edit your question to provide more rigorous mathematical definitions and ask explicitly exactly what you mean.

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The question as you have it formulated currently has "no" for an answer. If the loss of coherent information means you cannot correct the errors, then obviously the loss of coherent information means you cannot correct any errors.

In non-quantum coding, it is possible to generate error correcting codes that are capable of correcting $a$-bit errors per $n$ bits (obviously, $a \lt n$), and of detecting $b$-bit errors per $n$ bits, ($a \lt b \lt n$), while greater than $b$ erroneous bits would be a catastrophic undetectable and uncorrectable error.