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Linear Programming (LP) decoding is emerging as an attractive alternative todecode Low-Density Parity-Check (LDPC) codes. However, the earliest LP decodersproposed for binary and nonbinary LDPC codes are not suitable for use atmoderate and large code lengths. To overcome this problem, Vontobel et al.developed an iterative Low-Complexity LP (LCLP) decoding algorithm for binaryLDPC codes. The variable and check node calculations of binary LCLP decodingalgorithm are related to those of binary Belief Propagation (BP). The presentauthors generalized this work to derive an iterative LCLP decoding algorithmfor nonbinary linear codes. Contrary to binary LCLP, the variable and checknode calculations of this algorithm are in general different from that ofnonbinary BP. The overall complexity of nonbinary LCLP decoding is linear inblock length; however the complexity of its check node calculations isexponential in the check node degree. In this paper, we propose a modified BCJRalgorithm for efficient check node processing in the nonbinary LCLP decodingalgorithm. The proposed algorithm has complexity linear in the check nodedegree. We also introduce an alternative state metric to improve the run timeof the proposed algorithm. Simulation results are presented for $(504, 252)$and $(1008, 504)$ nonbinary LDPC codes over $\mathbb{Z}_4$.

Trellis-Based Check Node Processing for Low-Complexity Nonbinary LP Decoding