Matthew C. Davey's research while affiliated with University of Cambridge and other places
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Publications (8)
A new block code is introduced which is capable of correcting multiple insertion, deletion and substitution errors. The code consists of non-linear inner codes, which we call `watermark' codes, concatenated with low-density parity-check codes over non-binary elds. The inner code allows probabilistic resynchronisation and provides soft outputs for t...
Gallager codes with large block length and low rate (e.g., N ≃ 10,000–40,000, R ≃ 0.25–0.5) have been shown to have record-breaking performance for low signal-to-noise applications. In this paper we study Gallager codes at the other end of the spectrum. We first explore the theoretical properties of binary Gallager codes with very high rates and ob...
We present a pair of Gallager codes with rate R=1/3 and transmitted blocklength N=1920 as candidates for the proposed international standard for cellular telephones.
| A new block code is introduced which is capable of correcting multiple insertion, deletion and substitution errors present in a single block. An inner code resilient to synchronisation errors provides soft inputs to an outer code capable of correcting substitution errors. The decoder does not require knowledge of the block boundaries. Many coding...
The low-density parity check codes whose performance is closest to the Shannon limit are “Gallager codes” based on irregular graphs. We compare alternative methods for constructing these graphs and present two results. First, we find a “super-Poisson” construction which gives a small improvement in empirical performance over a random construction....
Binary Low Density Parity Check (LDPC) codes have been shown to have near Shannon limit performance when decoded using a probabilistic decoding algorithm. The analogous codes defined over finite fields GF (q) of order q ? 2 show significantly improved performance. We present the results of Monte Carlo simulations of the decoding of infinite LDPC Co...
Binary Low Density Parity Check (LDPC) codes have been shown to have near Shannon limit performance when decoded using a probabilistic decoding algorithm. The analogous codes defined over finite fields GF (q) of order q ? 2 show significantly improved performance. We present the results of Monte Carlo simulations of the decoding of infinite LDPC Co...
Binary Low Density Parity Check (LDPC) codes have been shown to have near Shannon limit performance when decoded using a probabilistic decoding algorithm. The analogous codes defined over finite fields GF (q) of order q ? 2 show significantly improved performance. We present the results of Monte Carlo simulations of the decoding of infinite LDPC Co...
Citations
... In NB-LDPC decoders, the direct application of the Belief Propagation (BP) [5] algorithm leads to O(q 2 ) complexity and is thus prohibitive for q > 16 . A considerable amount of work has then been dedicated to reduce the complexity of decoding algorithms and their associated architectures ( [6][7][8][9][10][11], among others), with a special focus on the Check Node (CN) processing which is the major bottleneck in NB-LDPC decoders. ...
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... After decades of continuous research, it has become the coding scheme of data channel in 5G technology. The most prominent ones are the Quasi-cyclic LDPC codes [5], [6] proposed by Myung et al. and the Optimization-based decoding algorithms for LDPC convolutional codes in communication systems [7] proposed by Banu et al. and the Comparison of constructions of irregular Gallager codes [8] proposed by Mackay et al. Compared with the length of the check matrix-H, there are a few non-zero number in its ranks, that is, the number of ''0'' is much more than the VOLUME 10, 2022 This work is licensed under a Creative Commons Attribution 4.0 License. ...
... Existed algorithms also focus on one aspect or both. Those LDPC decoding algorithms endeavoring to node update include sum product algorithm (SPA) [4,5], min sum algorithm (MSA) [6] and normalized min sum (NMS) algorithm [7].The informed scheduling for BP is a hot topic in LDPC decoding algorithm, because it dramatically influences both FER performance and convergence speed. As the original scheduling of BP decoding, flooding algorithm was based on parallel decoding scheduling [8]. ...
... Therefore, it can be realized relatively easily with a physical circuit. Furthermore, since Gallager first proposed LDPC codes in the 1960s [30], this class of classical code has shown good performance approaching the channel capacity [31][32][33][34][35]. Subsequently, its quantum versions has been investigated [22,23]. ...
Reference: Quantum Coding via Quasi-Cyclic Block Matrix
... • Polar code with successive cancellation (SC) decoder and 4-PSK. Reed-Solomon codes have been introduced in [18] in 1960, LDPC codes in [19] in 1962 and non-binary LPDC codes in [20] in 1998. The LDPC codes proposed in the competition are based on [21,22], respectively. ...
... Since DNA molecules use four nucleotide bases (i.e., adenine (A), thymine (T), cytosine (C), and guanine (G)) to store genetic information [7], DNA is a quadratic channel corrupted by insertions, deletions, and substitutions. To correct synchronization (i.e., insertion and deletion) errors, Matthew C. Davey proposed the concatenated watermark code scheme [8], and Daniel Marco proposed the concatenated marker code scheme [9]. To correct DNA channel errors, a modified concatenated watermark code scheme and a modified concatenated marker code scheme were proposed in [10,11], respectively. ...
... Marker codes [36] and Watermark codes [19] each use concatenation of codes to allow for correction of insertions and deletions. However, these codes are generally not suitable in biological applications as they maintain a specific structure [13], which causes difficulty for biological constraints as noted in Section 2.1. ...
Reference: Effective decoders for DNA codes
