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Status: Unchecked ×Keyword: parity check matrix ×Clear all

3 claims from 1 paper

1. Computer Science › Error Correcting Code Techniques

   Low-density parity-check codes

   Gallager · IEEE Transactions on Information Theory · 1962

   Gallager defines low-density parity-check codes, describes their distance and error properties, and presents a simple decoding scheme whose complexity grows roughly linearly with block length.

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   1. Unchecked“The typical minimum distance of these codes increases linearly with block length for a fixed rate and fixedj.”
   2. UncheckedFor low-density parity-check codes on a quiet symmetric binary channel, typical decoding error shrinks exponentially as block length grows, with rate and j fixed.“When used with maximum likelihood decoding on a sufficiently quiet binary-input symmetric channel, the typical probability of decoding error decreases exponentially with block length for a fixed rate and fixedj.”
   3. Unchecked“Forj > 3and a sufficiently low rate, the probability of error using this decoder on a binary symmetric channel is shown to decrease at least exponentially with a root of the block length.”