### Low-density Parity-check Codes

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Basic infomation
Authors: Robert G Gallager
Published in: IEEE Transactions On Information Theory
Year: 1962
DOI: 10.1109/TIT.1962.1057683
Citations: 3222
EI: NO
Abstract:
a low density parity check code is a code specified by a parity check matrix with the following properties each column contains a small fixed number of l 's and each row contains a small fixed number of l 's the typical minimum distance of these codes increases linearly with block length for a fixed rate and 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 fixed a simple but nonoptimum decoding scheme operating directly from the channel a posteriori probabilities is described both the equipment complexity and the data handling capacity in bits per second of this decoder increase approximately linearly with block length for and 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 some experimental results show that the actual probability of decoding error is much smaller than this theoretical bound
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