Approaching the DT Bound Using Linear Codes in the Short Blocklength Regime

The dependence-testing (DT) bound is one of the
strongest achievability bounds for the binary erasure channel
(BEC) in the finite block length regime. In this paper, we show that
maximum likelihood decoded regular low-density parity-check
(LDPC) codes with at least 5 ones per column almost achieve
the DT bound. Specifically, using quasi-regular LDPC codes with
block length of 256 bits, we achieve a rate that is less than 1% away
from the rate predicted by the DT bound for a word error rate
below 10^−3. The results also indicate that the maximum-likelihood
solution is computationally feasible for decoding block codes over
the BEC with several hundred bits.