Near DT Bound Achieving Linear Codes in the Short Blocklength Regime

The dependence-testing (DT) bound is one of the strongest achievability bounds for the binary erasure channel for the finite blocklength 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. We specifically design a quasi-regular LDPC code with 256 bits that delivers 99.4% of the rate predicted by the DT bound for a residual block error rate below 0.001. The results also indicate that the maximum-likelihood solution is computational feasible for decoding block codes over the binary erasure channel with several hundred bits.