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Upper bounds on the rate of LDPC codes

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4 Author(s)
Burshtein, D. ; Dept. of Electr. Eng.-Syst., Tel Aviv Univ., Israel ; Krivelevich, M. ; Litsyn, S. ; Miller, G.

We derive upper bounds on the rate of low-density parity-check (LDPC) codes for which reliable communication is achievable. We first generalize Gallager's (1963) bound to a general binary-input symmetric-output channel. We then proceed to derive tighter bounds. We also derive upper bounds on the rate as a function of the minimum distance of the code. We consider both individual codes and ensembles of codes.

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Information Theory, IEEE Transactions on  (Volume:48 ,  Issue: 9 )