We develop improved algorithms to construct good low-density parity-check codes that approach the Shannon limit very closely. For rate 1/2, the best code found has a threshold within 0.0045 dB of the Shannon limit of the binary-input additive white Gaussian noise channel. Simulation results with a somewhat simpler code show that we can achieve within 0.04 dB of the Shannon limit at a bit error rate of 10/sup -6/ using a block length of 10/sup 7/.
['Sae-Young Chung', 'G.D. Forney', 'Thomas Richardson', 'Rüdiger L. Urbanke']
On the design of low-density parity-check codes within 0.0045 dB of the Shannon limit