On Reliably Decodable Information Bits of Linear Codes | IEEE Conference Publication | IEEE Xplore

On Reliably Decodable Information Bits of Linear Codes


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...Show More

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.
Date of Conference: 25-30 June 2023
Date Added to IEEE Xplore: 22 August 2023
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Conference Location: Taipei, Taiwan

References

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