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International Symposium on Turbo Codes and Iterative Information Processing

Layered Decoding of Quantum LDPC Codes

Julien Du Crest, Francisco García-Herrero, Mehdi Mhalla, Valentin Savin, Javier Valls

Published Sep 4, 2023• 11 citations
Publisher

Abstract

We address the problem of doing message passing based decoding of quantum LDPC codes under hardware latency limitations. We propose a novel way to do layered decoding that suits quantum constraints and outperforms flooded scheduling, the usual scheduling on parallel architectures. A generic construction is given to construct layers of hypergraph product codes. In the process, we introduce two new notions, t-covering layers which is a generalization of the usual layer decomposition, and a modified scheduling called random order scheduling. Numerical simulations show that the random ordering is of independent interest as it helps relieve the high error floor typical of message passing decoders on quantum codes for both layered and serial decoding without the need of post-processing.

DOI
10.1109/istc57237.2023.10273477

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We address the problem of doing message passing based decoding of quantum LDPC codes under hardware latency limitations. We propose a novel way to do layered decoding that suits quantum constraints and outperforms flooded scheduling, the usual scheduling on parallel architectures. A generic construction is given to construct layers of hypergraph product codes. In the process, we introduce two new notions, t-covering layers which is a generalization of the usual layer decomposition, and a modified scheduling called random order scheduling. Numerical simulations show that the random ordering is of independent interest as it helps relieve the high error floor typical of message passing decoders on quantum codes for both layered and serial decoding without the need of post-processing.
We address the problem of performing message-passing-based decoding of quantum LDPC codes under hardware latency limitations. We propose a novel way to do layered decoding that suits quantum constraints and outperforms flooded scheduling, the usual scheduling on parallel architectures. A generic construction is given to construct layers of hypergraph product codes. In the process, we introduce two new notions, t-covering layers which is a generalization of the usual layer decomposition, and a new scheduling called random order scheduling. Numerical simulations show that the random ordering is of independent interest as it helps relieve the high error floor typical of message-passing decoders on quantum codes for both layered and serial decoding without the need for post-processing.
In this paper, we present a layered decoding algorithm for non-binary LDPC codes. Differing from the flooding message-passing schedule in conventional designs, the proposed scheme updates check node messages in serial. Furthermore, since fully serial decoding will lead to long latency, the locally-parallel globally-serial schedule is adopted. Basically the check nodes can be divided into several groups, i.e. layers. The layers are processed one by one while the check nodes in each layer are processed in parallel. Simulation results show that the proposed algorithm not only brings some improvement in error correcting performance but also gives some advantage in VLSI implementation of efficient partially parallel decoders.
In this paper, we propose an extended layered decoding approach for low density parity check (LDPC) codes. Compared to conventional layered decoding algorithms, the proposed approach has no constraint in the column weight of each layer. Hence, it enables more flexibility in high-throughput LDPC decoder design with layered decoding. Simulations on structured and random LDPC codes show that the proposed decoding method achieves significantly faster convergence and slightly better error correction performance than the conventional two phase massage passing sum-product algorithm. We also propose an efficient highly parallel decoder architecture for generic quasi-cyclic LDPC codes to facilitate the practical application of the proposed decoding scheme.
In recent years coarsely quantized LDPC decoding using a flooding schedule has been extensively studied. However, there exist few works addressing coarse quantization for a layered schedule, which enables improved convergence speed of the message passing algorithm. The layered schedule can especially be beneficial for high throughput applications like fiber optical systems. This paper presents innovative layered decoding approaches, where the information bottleneck method is used for the design of different coarsely quantized decoder architectures. The varieties of investigated node implementations include lookup tables, computational domain techniques as well as reduced complexity approximations. All structures are designed offline using a layered discrete density evolution method. The performance of multiple node architectures is investigated in terms of evolution of mutual information in the design phase and in terms of error rates. We focus in this paper on regular quasi-cyclic codes. Our simulations running on GPUs also allow insights into the error floor behavior.
Layered decoding of Low Density Parity Check (LDPC) codes has been shown to give faster convergence and use less storage than the conventional Two Phase Message Passing (TPMP) algorithm in decoding such codes. To achieve higher throughput, multiple rows of the parity check matrix may be decoded in parallel, as in the Parallel-Turbo Decoding Message Passing (P-TDMP) algorithm. However, contention for globally shared memory permits only a subset of rows to be decoded in parallel thus limiting overall throughput. This paper uses a near optimal scheduling algorithm, based on graph colouring, to overcome memory contention, allowing processing of multiple rows without code modification, resulting in significant throughput gains over the standard P-TDMP algorithm. For the LDPC codes studied, throughput gains compared to the P-TDMP algorithm, of between ten and fifteen are shown to be possible.
The convergence speed of layered message-passing decoding (LMPD) is faster than that of standard two phase message passing (TPMP) decoding. We propose to use dynamic scheduling and early termination to reduce computational complexity for a modified LMPD algorithm which was proposed for quasi-cyclic low-density parity-check (QC-LDPC) codes. We dynamically skip or redo the decoding operations for some layers based on appropriate criteria. An early termination strategy which is efficient in hardware implementation is also proposed in this paper. The modified MPD using these two techniques simultaneously can reduce the computational complexity with similar error performance as compared to the case of not using these two techniques.