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The lifetime capacity can be arbitrarily large. One may change the weight of the ternary symbols from 1/3, 1/3, 1/3 to 1/2, 1/4, 1/4 (favouring the symbol with blank bits). This reduces the entropy of the ternary symbol from $log_2(3)$ to $\frac{3}{2}$. What it also does is reducing the capacity loss between generations, to a factor of $\frac{5}{3}$ Thus, ...


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You mentioned in a comment that your messages are very short, only 7-10 bits long. Another option is to explicitly construct a code, with encoding and decoding done via a lookup table rather than by an algorithm or a formula. For instance, suppose you have $K=7$-bit messages, that you will encode to a $N=30$-bit codeword that will be written onto the tape, ...


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