Implementation aspects of a pipeline ADMM-based LP decoding of LDPC convolutional codes

The enforcement of the linear programming (LP) decoding was recently extended to LDPC convolutional codes (LDPC-CC). It was demonstrated that their convolutional structure suites the message-passing based representation of the LP problem, thanks to the application of the alternating directions method of multipliers (ADMM). In this paper, a modified formulation of the ADMM-LP problem is introduced for pipeline decoding of LDPC-CCs based on the layered schedule. Moreover, an assessment of the fixed-point format required for hardware implementation is provided to evaluate the complexity of the underlying decoding algorithm. Simulations show that an 8-bit quantization scheme yields negligible error correction performances loss of about 0.05 dB regarding the floating-precision ADMM based LDPC-CC decoder. Further, an algorithmic optimization of the Euclidean projection skipping technique, described in [1] [2], is proposed. This improved version enables to reduce the computational complexity of the decoding process without memory penalty contrary to the original formulation.