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

Abstract

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.