Capacity-Approaching TQC-LDPC Convolutional Codes Enabling Power-Efficient Decoders

• Published in: IEEE transactions on communications 2017-01, Vol.65 (1), p.1-13
• Main Authors: Pisek, Eran, Rajan, Dinesh, Abu-Surra, Shadi, Cleveland, Joseph R.
• Format: Article
• Language: English
• Subjects: Block codes; Codes; Coding; Complexity; Complexity theory; Convolutional codes; decoder complexity; Decoders; Decoding; Dependence; Error correcting codes; IEEE802.11ad; LDPC convolutional code; MAP decoder; Maximum likelihood decoding; Mobile communication systems; Parity check codes; spatially-coupled LDPC; Systematics
• ISSN: 0090-6778; 1558-0857
• DOI: 10.1109/TCOMM.2016.2616142

In this paper, we develop a new capacity-approaching code, namely, parallel-concatenated (PC)-Low Density Parity Check (LDPC) convolutional code that is based on the parallel concatenation of trellis-based quasi-cyclic LDPC (TQC-LDPC) convolutional codes. The proposed PC-LDPC convolutional code can be derived from any QC-LDPC block code by introducing the trellis-based convolutional dependency to the code. The capacity-approaching PC-LDPC convolutional codes are encoded through parallel concatenated trellis-based QC recursive systematic convolutional (RSC) encoder (namely, QC-RSC encoder) that is also proposed in this paper. The proposed PC-LDPC convolutional code and the associated encoder retain a fine input granularity on the order of the lifting factor of the underlying block code. We also describe the corresponding trellis-based QC maximum a posteriori probability (namely, QC-MAP) decoder that efficiently decodes the PC-LDPC convolutional code. Performance and hardware implementation results show that the PC-LDPC convolutional codes with the QC-MAP decoder have two times lower complexity for a given bit-error-rate (BER), signal-to-noise ratio, and data rate, than conventional QC-LDPC block codes and LDPC convolutional codes. Moreover, the PC-LDPC convolutional code with the QC-MAP decoder outperforms the conventional QC-LDPC block codes by more than 0.5 dB for a given BER, complexity, and data rate and approaches Shannon capacity limit with a gap smaller than 1.25 dB. This low decoding complexity and the fine granularity make it feasible to efficiently implement the proposed capacity-approaching PC-LDPC convolutional code and the associated trellis-based QC-MAP decoder in next generation ultra-high data rate mobile systems.