LDPC convolutional codes versus QC LDPC block codes in communication standard scenarios

Outstanding asymptotical performance demonstrated by low-density parity-check (LDPC) convolutional codes (CC) makes them strong competitors with respect to quasi-cyclic (QC) LDPC block codes (BC) currently used in a variety of communication standards. However, typically communication standards, for example, DVB-S2 or WIMax standards impose rather serious restrictions on the structure of the employed codes. These restrictions are related to different implementation issues such as existence of low-complexity encoding and decoding, short decoding delay etc. Two scenarios are considered. In one scenario, short-delay and low-complexity constraints are taken into account. In the other scenario, the complexity requirement is relaxed. Both LDPC CCs and QC LDPC BCs with optimized degree distribution and girth profile, which enable low-complexity encoding, are constructed for these scenarios. Having both delay and complexity constraints yields QC LDPC BCs that outperform the LDPC CCs. In this scenario LDPC CCs play an important role mostly for constructing tailbiting QC LDPC BCs. On the other hand, assuming only a decoding delay constraint the LDPC CCs can be superior compared to the QC LDPC BCs at the relatively low signal-to-noise ratio region. Moreover, under practically acceptable decoding delays also the LDPC CCs with low-complexity encoding structure beat records in approaching the Shannon limit. A new LDPC CC is presented achieving the BER 10^-7 with decoding delay 96000 bits at 0.62 dB, that is, performing only about 0.43 dB from the Shannon limit.