Trellis-Based QC-LDPC Convolutional Codes Enabling Low Power Decoders

Abstract

In this paper, we propose a new type of code called Trellis-based Quasi-Cyclic (TQC)-LDPC convolutional code, which is a special case of protograph-based LDPC convolutional codes. The proposed TQC-LDPC convolutional code can be derived from any QC-LDPC block code by introducing trellis-based convolutional dependency to the code. The main advantage of the proposed TQC-LDPC convolutional code is that it allows reduced decoder complexity and input granularity (which is defined as the minimum number of input information bits the code requires to generate a codeword) while maintaining the same bit error-rate as the underlying QC-LDPC block code ensemble. We also propose two related power-efficient encoding methods to increase the code rate of the derived TQC-LDPC convolutional code. The newly derived short constraint length TQC-LDPC convolutional codes enable low complexity trellis-based decoders and one such decoder is proposed and described in this paper (namely, QC-Viterbi). The TQC-LDPC convolutional codes and the QC-Viterbi decoder are compared to conventional LDPC codes and Belief Propagation (BP) iterative decoders with respect to bit-error-rate (BER), signal-to-noise ratio (SNR), and decoder complexity. We show both numerically and through hardware implementation results that the proposed QC-Viterbi decoder outperforms the BP iterative decoders by at least 1 dB for same complexity and BER. Alternatively, the proposed QC-Viterbi decoder has 3 times lower complexity than the BP iterative decoder for the same SNR and BER. This low decoding complexity, low BER, and fine granularity makes it feasible for the proposed TQC-LDPC convolutional codes and associated trellis-based decoders to be efficiently implemented in high data rate, next generation mobile systems.