Parity-check density versus performance of binary linear block codes over memoryless symmetric channels

@article{Sason2003ParitycheckDV,
  title={Parity-check density versus performance of binary linear block codes over memoryless symmetric channels},
  author={Igal Sason and R{\"u}diger L. Urbanke},
  journal={IEEE Transactions on Information Theory},
  year={2003},
  volume={49},
  pages={1611-1635}
}
We derive lower bounds on the density of parity-check matrices of binary linear codes which are used over memoryless binary-input output-symmetric (MBIOS) channels. The bounds are expressed in terms of the gap between the rate of these codes for which reliable communications is achievable and the channel capacity; they are valid for every sequence of binary linear block codes if there exists a decoding algorithm under which the average bit-error probability vanishes. For every MBIOS channel, we… CONTINUE READING
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