EBP-GEXIT Charts for M-ary AWGN Channel for Generalized LDPC and Turbo Codes
Arti Yardi, Tarik Benaddi, Charly Poulliat, and Iryna Andriyanova

TL;DR
This paper introduces a method to estimate the MAP threshold of various sparse-graph codes over M-ary AWGN channels using an approximation of the EBP-GEXIT function, extending previous results to non-binary channels.
Contribution
It extends the EBP-GEXIT analysis to non-binary channels and provides a practical way to estimate MAP thresholds for multiple code families, including LDPC and turbo codes.
Findings
BP threshold of spatially-coupled SC-TC saturates to the MAP threshold
Extended GEXIT charts effectively estimate MAP thresholds in non-binary channels
The method applies to LDPC, generalized LDPC, doubly generalized LDPC, and turbo codes.
Abstract
This work proposes a tractable estimation of the maximum a posteriori (MAP) threshold of various families of sparse-graph code ensembles, by using an approximation for the extended belief propagation generalized extrinsic information transfer (EBP-GEXIT) function, first proposed by Measson et al. We consider the transmission over non-binary complex-input additive white Gaussian noise channel and extend the existing results to obtain an expression for the GEXIT function. We estimate the MAP threshold by applying the Maxwell construction to the obtained approximate EBP-GEXIT charts for various families of low-density parity-check (LDPC), generalized LDPC, doubly generalized LDPC, and serially concatenated turbo codes (SC-TC). When codewords of SC-TC are modulated using Gray mapping, we also explore where the spatially-coupled belief propagation (BP) threshold is located with respect to…
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Taxonomy
TopicsError Correcting Code Techniques · Advanced Wireless Communication Techniques · Advanced MIMO Systems Optimization
