  A low-complexity soft-decision concatenated FEC scheme, consisting of an
inner LDPC code and an outer staircase code is proposed. The inner code is
tasked with reducing the bit error probability below the outer-code threshold.
The concatenated code is obtained by optimizing the degree distribution of the
inner-code ensemble to minimize estimated data-flow, for various choices of
outer staircase codes. A key feature that emerges from this optimization is
that it pays to leave some inner codeword bits completely uncoded, thereby
greatly reducing a significant portion of the decoding complexity. The
trade-off between required SNR and decoding complexity of the designed codes is
characterized by a Pareto frontier. Computer simulations of the resulting codes
reveals that the net coding-gains of existing designs can be achieved with up
to 71\% reduction in complexity. A hardware-friendly quasi-cyclic construction
is given for the inner codes, which can realize an energy-efficient decoder
implementation, and even further complexity reductions via a layered
message-passing decoder schedule.
