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Generalized LDPC codes with low-complexity decoding and fast convergence

Dawit Simegn, Dmitry Artemasov, Kirill Andreev, Pavel Rybin, Alexey Frolov

TL;DR

This work introduces CW-GLDPC codes built from dual Cordaro–Wagner component codes and develops two low-complexity decoders, Hartmann–Rudolph SP and Min-Sum, framed by a latent-variable interpretation of the CW-GLDPC constraint nodes. A quantized protograph density-evolution framework is used to optimize the PCM for MS decoding, and a genetic-algorithm-driven search tunes the graph structure. Through extensive comparisons with 5G LDPC codes, CW-GLDPC demonstrates comparable performance at 50 iterations while achieving faster convergence and substantially better performance at 10 iterations, highlighting its potential for low-latency, high-reliability communications. The latent-variable perspective clarifies the decoding dynamics and scheduling choices, underscoring practical gains in decoding speed and robustness for CW-GLDPC-based systems.

Abstract

We consider generalized low-density parity-check (GLDPC) codes with component codes that are duals of Cordaro-Wagner codes. Two efficient decoding algorithms are proposed: one based on Hartmann-Rudolph processing, analogous to Sum-Product decoding, and another based on evaluating two hypotheses per bit, referred to as the Min-Sum decoder. Both algorithms are derived using latent variables and an appropriate message-passing schedule. A quantized, protograph-based density evolution procedure is used to optimize GLDPC codes for Min-Sum decoding. Compared to 5G LDPC codes, the proposed GLDPC codes offer similar performance at 50 iterations and significantly better convergence and performance at 10 iterations.

Generalized LDPC codes with low-complexity decoding and fast convergence

TL;DR

This work introduces CW-GLDPC codes built from dual Cordaro–Wagner component codes and develops two low-complexity decoders, Hartmann–Rudolph SP and Min-Sum, framed by a latent-variable interpretation of the CW-GLDPC constraint nodes. A quantized protograph density-evolution framework is used to optimize the PCM for MS decoding, and a genetic-algorithm-driven search tunes the graph structure. Through extensive comparisons with 5G LDPC codes, CW-GLDPC demonstrates comparable performance at 50 iterations while achieving faster convergence and substantially better performance at 10 iterations, highlighting its potential for low-latency, high-reliability communications. The latent-variable perspective clarifies the decoding dynamics and scheduling choices, underscoring practical gains in decoding speed and robustness for CW-GLDPC-based systems.

Abstract

We consider generalized low-density parity-check (GLDPC) codes with component codes that are duals of Cordaro-Wagner codes. Two efficient decoding algorithms are proposed: one based on Hartmann-Rudolph processing, analogous to Sum-Product decoding, and another based on evaluating two hypotheses per bit, referred to as the Min-Sum decoder. Both algorithms are derived using latent variables and an appropriate message-passing schedule. A quantized, protograph-based density evolution procedure is used to optimize GLDPC codes for Min-Sum decoding. Compared to 5G LDPC codes, the proposed GLDPC codes offer similar performance at 50 iterations and significantly better convergence and performance at 10 iterations.
Paper Structure (10 sections, 25 equations, 6 figures, 1 table)

This paper contains 10 sections, 25 equations, 6 figures, 1 table.

Table of Contents

  1. Introduction
  2. Code Construction
  3. Component code
  4. CW-GLDPC codes
  5. Decoding algorithms
  6. SP algorithm
  7. MS algorithm
  8. Decoding with use of latent variables
  9. Parity check matrix optimization
  10. Numerical results

Figures (6)

  • Figure 1: Generalized LDPC structure for six variable nodes and two generalized parity checks having degrees $5$ and $4$.
  • Figure 2: Correspondence between the GLDPC parity check matrix $\mathbf{\Gamma}$ and a parity check matrix $\mathbf{H}$ of the equivalent binary code.
  • Figure 3: Graphical representation of the rule \ref{['eq:hr_update_final']}.
  • Figure 4: Simulation results for scenario A.
  • Figure 5: Simulation results for scenario B.
  • ...and 1 more figures