This paper appears in: Information Theory, IRE Transactions on
Publication Date: January 1962
Volume: 8,
Issue: 1
On page(s): 21-28
ISSN: 0096-1000
Digital Object Identifier: 10.1109/TIT.1962.1057683
Current Version Published: 2003-01-06
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 numberj geq 3of l's and each row contains a small fixed numberk > jof l's. The typical minimum distance of these codes increases linearly with block length for a fixed rate and fixedj. 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. 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. 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. Some experimental results show that the actual probability of decoding error is much smaller than this theoretical bound.
Index
Terms
Available to subscribers and IEEE members.
References
Available to subscribers and IEEE members.
Citing Documents
Available to subscribers and IEEE members.
Cart
