Low-density parity-check codes

@article{citeulike:474700, 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<tex>j geq 3</tex>of l's and each row contains a small fixed number<tex>k \&gt; j</tex>of l's. The typical minimum distance of these codes increases linearly with block length for a fixed rate and fixed<tex>j</tex>. 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<tex>j</tex>. 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<tex>j \&gt; 3</tex>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.}, author = {Gallager, R. }, citeulike-article-id = {474700}, journal = {Information Theory, IEEE Transactions on}, number = {1}, pages = {21--28}, posted-at = {2006-01-21 23:52:48}, priority = {2}, title = {Low-density parity-check codes}, url = {http://ieeexplore.ieee.org/xpls/abs\_all.jsp?arnumber=1057683}, volume = {8}, year = {1962} }

TY - JOUR ID - citeulike:474700 L3 - citeulike-article-id:474700 N2 - 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<tex>j geq 3</tex>of l's and each row contains a small fixed number<tex>k &gt; j</tex>of l's. The typical minimum distance of these codes increases linearly with block length for a fixed rate and fixed<tex>j</tex>. 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<tex>j</tex>. 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<tex>j &gt; 3</tex>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. IS - 1 JF - Information Theory, IEEE Transactions on EP - 28 TI - Low-density parity-check codes VL - 8 SP - 21 AU - Gallager, R PY - 1962/// UR - http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1057683 ER -