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- W4386075180 abstract "It is well-known that a linearly coded vector over an erasure channel can be decoded uniquely if the sub-generator matrix formed by the unerased columns has full row rank. This property is generalized in this paper to a necessary and sufficient condition for an information bit to be retrieved uniquely from a received vector with erasures. We show that an information bit of a linear code can be uniquely decodable if and only if its corresponding row of the sub-generator matrix is linearly independent from the other rows. Then we prove that, for semi-random linear codes over binary-input output-symmetric (BIOS) memoryless channels, the information bits associated with the random part of the generator matrices can be decoded with arbitrarily small error probability as the codelength increases. This in turn is applied to prove the coding theorem for time-invariant convolutional codes." @default.
- W4386075180 created "2023-08-23" @default.
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- W4386075180 date "2023-06-25" @default.
- W4386075180 modified "2023-10-16" @default.
- W4386075180 title "On Reliably Decodable Information Bits of Linear Codes" @default.
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- W4386075180 doi "https://doi.org/10.1109/isit54713.2023.10206534" @default.
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