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In block codes (channel coding), in practice, how is the message length ($k$) fixed? If $k$ is large, the practical implementation of it requires huge memory if look up table approach is adopted.

What is the disadvantage with short $k$'s? Code rate will degrade?

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There are a few rules of thumb:

  • For a fixed code rate $r = \frac{k}{n}$, the amount of gain you observe from applying coding typically increases as you increase the block size $n$. Accordingly, the complexity of decoding the larger blocks is often larger.

  • If you decrease the number of information symbols in the block $k$ and keep $n$ fixed, the code rate decreases. This will result in higher coding gain, but lower information throughput for a given channel symbol rate.

  • If you increase the number of information symbols in the block $k$ and keep $n$ fixed, the code rate increases. This will result in lower coding gain, but higher information throughput for a given channel symbol rate.

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