We consider automorphism ensemble decoding (AED) of quasi-cyclic (QC) low-density parity-check (LDPC) codes. Belief propagation (BP) decoding on the conventional factor graph is equivariant to the quasi-cyclic automorphisms and therefore prevents gains by AED. However, by applying small modifications to the parity-check matrix at the receiver side, we can break the symmetry without changing the code at the transmitter. This way, we can leverage a gain in error-correcting performance using an ensemble of identical BP decoders, without increasing the worst-case decoding latency. The proposed method is demonstrated using LDPC codes from the CCSDS, 802.11n and 5G standards and produces gains of 0.2 to 0.3 dB over conventional BP decoding. Compared to the similarly performing saturated BP (SBP), the proposed algorithm reduces the average decoding latency by more than eight times.
We consider automorphism ensemble decoding (AED) of quasi-cyclic (QC) low-density parity-check (LDPC) codes. Belief propagation (BP) decoding on the conventional factor graph is equivariant to the quasi-cyclic automorphisms and therefore prevents gains by AED. However, by applying small modifications to the parity-check matrix at the receiver side, we can break the symmetry without changing the code at the transmitter. This way, we can leverage a gain in error-correcting performance using an ensemble of identical BP decoders, without increasing the worst-case decoding latency. The proposed method is demonstrated using LDPC codes from the CCSDS, 802.11n and 5G standards and produces gains of 0.2 to 0.3 dB over conventional BP decoding. Compared to the similarly performing saturated BP (SBP), the proposed algorithm reduces the average decoding latency by more than eight times.
To alleviate the suboptimal performance of belief propagation (BP) decoding of short low-density parity-check (LDPC) codes, a plethora of improved decoding algorithms has been proposed over the last two decades. Many of these methods can be described using the same general framework, which we call ensemble decoding: A set of independent constituent decoders works in parallel on the received sequence, each proposing a code-word candidate. From this list, the maximum likelihood (ML) decision is designated as the decoder output. In this paper, we qualitatively and quantitatively compare different realizations of the ensemble decoder, namely multiple-bases belief propagation (MBBP), automorphism ensemble decoding (AED), scheduling ensemble decoding (SED), noise-aided ensemble decoding (NED) and saturated belief propagation (SBP). While all algorithms can provide gains over traditional BP decoding, ensemble methods that exploit the code structure, such as MBBP and AED, typically show greater performance improvements.
With the increasing demands on future wireless systems, new design objectives become eminent. Low-density parity-check codes together with belief propagation (BP) decoding have outstanding performance for large block lengths. Yet, for future wireless systems, good decoding performance for short block lengths is mandatory, a regime in which BP decoding typically shows a significant gap to maximum likelihood decoding. Automorphism ensemble decoding (AED) is known to reduce this gap effectively and, in addition, enables an easy trade-off between latency, throughput, and complexity. Recently, generalized AED (GAED) was proposed to increase the set of feasible automorphisms suitable for ensemble decoding. By construction, GAED requires a preprocessing step within its constituent paths that results in information loss and potentially limits the gains of GAED. In this work, we show that the preprocessing step can be merged with the Tanner graph of BP decoding, thereby improving the performance of the constituent paths. Finally, we show that the improvement of the individual paths also enhances the overall performance of the ensemble.
Belief-propagation (BP) decoding of short and moderate-length low-density parity-check (LDPC) codes is limited by finite-length graph effects: a single decoder trajectory can become trapped or oscillatory even when an alternative trajectory would decode the received word. Existing ensemble-BP decoders create the required diversity through multiple parity-check matrices, automorphisms, modified schedules, subcodes, or altered update rules. We introduce row-boosted ensemble (RBE) decoding as a minimal decoder-side diversity mechanism: all ensemble members share the same parity-check matrix and the same BP kernel, and differ only in a small set of parity-check rows whose outgoing messages are boosted. On the 5G~NR BG1 (144,96) code, RBE with 32 members lowers the frame-error rate of BP with 20 iterations (BP-20) from 1.6×10−2 to 1.6×10−3 at Eb/N0=4.0dB, outperforming saturated-min-sum and affine subcode ensembles of equal size. Increasing the ensemble size yields additional gains, indicating that RBE provides a scalable performance-complexity tradeoff. The gains transfer across 5G~NR block lengths and rates, to non-5G short LDPC codes, and across flooding and layered schedules.
Low-density parity-check (LDPC) codes together with belief propagation (BP) decoding yield exceptional error correction capabilities in the large block length regime. Yet, there remains a gap between BP decoding and maximum likelihood decoding for short block length LDPC codes. In this context, ensemble decoding schemes yield both reduced latency and good error rates. In this paper, we propose subcode ensemble decoding (SCED), which employs an ensemble of decodings on different subcodes of the code. To ensure that all codewords are decodable, we use the concept of linear coverings and explore approaches for sampling suitable ensembles for short block length LDPC codes. Monte-Carlo simulations conducted for three LDPC codes demonstrate that SCED improves decoding performance compared to stand-alone decoding and automorphism ensemble decoding. In particular, in contrast to existing schemes, e.g., multiple bases belief propagation and automorphism ensemble decoding, SCED does not require the NP-complete search for low-weight dual codewords or knowledge of the automorphism group of the code, which is often unknown.
This paper presents a different decoding techniques for Quasi-Cyclic (QC) Low Density Parity Check (LDPC) code. QC-LDPC code is proposed to reduce the complexity of the Low Density Parity Check code while obtaining the similar performance. The encoding and decoding processes of these codes are easy to simplify and implement. The algorithm used for encoding and decoding are based on matrices and implemented on MATLAB for simulation results. In this paper decoding technique QC-LDPC is introduced and compare the performance of LDPC and QC-LDPC. The decoding techniques is conducted by different algorithms such as Bit Flipping (BF), Belief Propagation (BP) Log, Belief Propagation (BP) Probabilistic (Prob), Belief Propagation (BP) Log Simple.
In this paper, we propose an optimized belief propagation (OBP) based progressive edge-growth (PEG) method for constructing quasi-cyclic low density parity check (QC-LDPC) codes. In this proposed method, Tanner graphs are built by progressively appending the check nodes rather than the variable nodes. Moreover, this OBP-PEG method considers three new constraint conditions to select the QC-LDPC code sets constructed by the PEG method. Compared with the PEG-based QC-LDPC decoders, the proposed OBP-PEG decoders decrease the number of the input ports of check-node processer by up to 25%, accelerates the convergence speed by up to 11.7% in layered decoding process, and improves the success probability by up to ten times in constructing fast-convergence QC-LDPC codes.