Partial Ordered Statistics Decoding with Enhanced Error Patterns

In this contribution, KNIH algorithm and Ordered Statistic Decoding (OSD) algorithm are investigated, based on which, a novel KNIH-OSD parallel decoding scheme for LDPC codes is proposed. KNIH decoding algorithm processes certain LRPs of a received sequence, while OSD algorithm processes certain MRIPs of a received sequence. If there are too many errors in MRIPs, the OSD algorithm will fail, on the contrary, if there are too many errors in LRPs, the KNIH algorithm will fail. This contribution proposes a parallel decoding scheme based on the complementary characteristic of these two algorithms. Simulation results show that the proposed scheme is feasible and effective. Compared with OSD and KNIH algorithm, the decoding performance is improved.

This letter is concerned with a generalized ordered statistic decoding (OSD) algorithm, called locally constrained OSD (LC-OSD). Instead of order- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$t$ </tex-math></inline-formula> reprocessing on the most reliable independent bits, the LC-OSD searches for test error patterns using the serial list Viterbi algorithm (SLVA) over a trellis specified by a local parity-check matrix. We derive several early stopping criteria that can be used to reduce the number of searches. Numerical results show that the LC-OSD algorithm with the proposed stopping criteria has much lower time complexity than the original OSD but incurs negligible performance loss.

In this work, we present an improvement on low complexity serial concatenation of belief propagation (BP) - order statistic decoding (OSD) algorithm for low-density parity-check (LDPC) codes. We introduce a more reliable method to reconstruct ordered information sequence in terms of the accumulated log-likelihood ratio (LLR) transitions of variable nodes. We give a general expression for both the existing BP-OSD algorithm and our proposed new method according to a structure similar to an infinite impulse response (IIR) filter. This improved algorithm achieves noticeable performance gains with only modest increase in computation complexity.

Irregular LDPC codes can achieve better error rate performance than regular LDPC codes. However, irregular LDPC codes have higher error floors than regular LDPC codes. The Ordered Statistic Decoding (OSD) algorithm achieves approximate Maximum Likelihood (ML) decoding. ML decoding is effective to lower error floors. However, the OSD estimates satisfy the parity check equation of the LDPC code even the estimates are wrong. Hybrid decoder combining LLR-BP decoding algorithm and the OSD algorithm cannot also lower error floors, because wrong estimates also satisfy the LDPC parity check equation. We proposed the concatenated code constructed with an inner irregular LDPC code and an outer Cyclic Redundancy Check (CRC). Owing to CRC, we can detect wrong codewords from OSD estimates. Our CRC-LDPC code with hybrid decoder can lower error floors in an AWGN channel. In wireless communications, we cannot neglect the effects of the channel. The OSD algorithm needs the ordering of each bit based on the reliability. The Channel State Information (CSI) is used for deciding reliability of each bit. In this paper, we evaluate the Block Error Rate (BLER) of the CRC-LDPC code with hybrid decoder in a fast fading channel with perfect and imperfect CSIs where 'imperfect CSI' means that the distribution of channel and those statistical average of the fading amplitudes are known at the receiver. By computer simulation, we show that the CRC-LDPC code with hybrid decoder can lower error floors than the conventional LDPC code with hybrid decoder in the fast fading channel with perfect and imperfect CSIs. We also show that combining error detection with the OSD algorithm is effective not only for lowering the error floor but also for reducing computational complexity of the OSD algorithm.

Data center networks (DCNs) require a low-cost, low-power optical transceiver to handle increased traffic from generative artificial intelligence, video streaming services, and more. Improving the required signal-to-noise ratio (RSNR) by digital signal processing such as forward error correction (FEC) mitigates the requirements for electrical and optical components. The optical transceivers in DCNs exploit a low-complexity soft-decision (SD) FEC, consisting of short block-length linear error-correcting codes and a low-complexity SD decoder (SDD), such as Chase decoding and ordered statistics decoding. The low-complexity SDD efficiently approaches a maximum likelihood decoding (MLD). However, the decoding performance of MLD is limited by its finite block length. In this paper, we describe the details of our proposed channel-polarized multilevel coding with iterative decoding (CP-MLC-ID). The proposed CP-MLC-ID improves the decoding performance by extending the codeword length to weakly and indirectly connect codewords via bypassed bits. The 19.5% –OH CP-MLC-ID using 128-bit extended Bose–Chaudhuri–Hocquenghem (eBCH) and KP4 codes outperforms the concatenated eBCH and KP4 codes with a net coding gain of 0.25 and 0.40dB for the same and double the number of SDDs, respectively. We also investigate the dependency of the decoding performance on the size of a bit interleaver. The performance degradation of CP-MLC-ID using an 8-bit interleaver is about 0.1dB compared to using the large-bit interleaver. Our results indicate that even a weak connection by exclusive-OR between codewords improves the decoding performance, compared to simple concatenated codes in the DCNs.

Polar codes have been used to guarantee high reliability in communication due to their excellent performance. In this letter, we propose a guessing error pattern ordered statistic decoding (GEPOSD) algorithm to further improve the performance of short polar codes. It outperforms the widely used cyclic redundancy check-aided successive cancellation list (CA-SCL) decoding under a code length of 64. The GEPOSD algorithm utilizes a strategy based on the maximum a posteriori probability rule to select the error pattern on the most reliable independent bits. Subsequently, an error pattern set is extended using a tree search approach. To minimize computational complexity, we introduce two early stopping criteria that limit the number of error patterns tested in decoding. The simulation results show that the complexity of GEPOSD is significantly reduced compared to the original OSD algorithm.

This paper focuses on Dynamic Implementation using Array and Linked list. In the data structure concept, the list plays a major role in the allocation of data where it is a general overview of creating a node in a linked list using an array with the initialization of size. The node contains data and is interconnected to the next node in the sequence via their links which perform the search operation where the space and time complexity are not wasted in these analyses. Linked lists are a great way to store a theoretically infinite amount of data with a small and versatile amount of code. The amount of data stored increases linearly with the number of nodes in the list (space-o(n)) where linked lists are more efficient than arrays. It is observed that considering the time complexity when there is a variation in data set linked array is almost reaches close to array whenever dataset is high also linked array has better time complexity than linked list when the searching element is in middle and last. Considering the space complexity linked array is almost 2 times and 4 times less space is needed than array and linked list respectively.

Binary embedding refers to methods for embedding points in $\mathbb {R}^{d}$ into vertices in the Hamming cube of dimension ${\mathcal{O}}(d)$ , such that the normalized Hamming distance between the codes preserves a prespecified distance between vectors in the original space. A common approach to binary embedding is to use random projection , followed by one-bit quantization to produce binary codes. Of particular interest, in this letter, is sparse circulant binary embedding (SCBE), where a sparse random circulant matrix with random sampling at a rate of $1-s$ for $s\in (0, 1)$ is used for random projection. The SCBE has the space complexity ${\mathcal{O}}((1-s)d)$ , while unstructured random projection has the space complexity ${\mathcal{O}}(d^2)$ . We present an asymptotic analysis of SCBE, when $d$ approaches $\infty$ , showing that the performance of SCBE is comparable to that of binary embedding with unstructured random projection whilethe former has the space complexity ${\mathcal{O}}((1-s)d)$ and the time complexity ${\mathcal{O}}(d\log d)$ but the latter has both space and time complexities ${\mathcal{O}}(d^2)$ .

WITHDRAWN: Spearman rank correlation based bagging ensemble bayes optimal classification for genomic predictive pattern analytics

This paper proposes an enhanced guessing codeword decoding (GCD) algorithm, termed GCD with most reliable cyclic basis (MRCB-GCD), specifically tailored for BCH codes. Unlike original GCD, the proposed method selects the k consecutive bits with the highest aggregate reliability as the re-encoding basis, leveraging the cyclic structure of BCH codes. To further enhance search efficiency, a local constraint (LC) mechanism is introduced, where the extended reliable bits of length k+δ enable the algorithm to skip numerous unnecessary test error patterns (TEPs). To stop the search process, we introduce two termination criteria and prove that the proposed approach with the trivial termination criterion forms a non-exhaustive-search maximum likelihood (ML) decoding algorithm. A saddlepoint-based numerical method is developed to approximately calculate the upper bound on the performance gap to the ML decoding and estimate the average number of searches, showing the advantages of the proposed MRCB-GCD over the original GCD in terms of both decoding performance and search efficiency. Simulation results demonstrate that: 1) MRCB- GCD outperforms original GCD in both frame error rate (FER) and number of searches, 2) the LC mechanism and termination criteria further reduce the number of searches, and 3) the proposed approach achieves finite-length capacity across various code rates but without requiring Gaussian elimination.

In this paper, we present a computationally efficient method for estimating error floors of low-density parity-check (LDPC) codes over the binary symmetric channel (BSC) without any prior knowledge of its trapping sets (TSs). Given the Tanner graph $G$ of a code, and the decoding algorithm $\mathcal {D}$ , the method starts from a list of short cycles in $G$ , and expands each cycle by including its sufficiently large neighborhood in $G$ . Variable nodes of the expanded sub-graphs $\mathcal {G}_{\text{EXP}}$ are then corrupted exhaustively by all possible error patterns, and decoded by $\mathcal {D}$ operating on $\mathcal {G}_{\text{EXP}}$ . Union of support of the error patterns for which $\mathcal {D}$ fails on each $\mathcal {G}_{\text{EXP}}$ defines a subset of variable nodes that is a TS. The knowledge of the minimal error patterns and their strengths in each TSs is used to compute an estimation of the frame error rate. This estimation represents the contribution of error events localized on TSs, and therefore serves as an accurate estimation of the error floor performance of $\mathcal {D}$ at low BSC cross-over probabilities. We also discuss trade-offs between accuracy and computational complexity. Our analysis shows that in some cases the proposed method provides a million-fold improvement in computational complexity over standard Monte-Carlo simulation.

We initiate the systematic study of the energy complexity of algorithms (in addition to time and space complexity) based on Landauer's Principle in physics, which gives a lower bound on the amount of energy a system must dissipate if it destroys information. We propose energy-aware variations of three standard models of computation: circuit RAM, word RAM, and transdichotomous RAM. On top of these models, we build familiar high-level primitives such as control logic, memory allocation, and garbage collection with zero energy complexity and only constant-factor overheads in space and time complexity, enabling simple expression of energy-efficient algorithms. We analyze several classic algorithms in our models and develop low-energy variations: comparison sort, insertion sort, counting sort, breadth-first search, Bellman-Ford, Floyd-Warshall, matrix all-pairs shortest paths, AVL trees, binary heaps, and dynamic arrays. We explore the time/space/energy trade-off and develop several general techniques for analyzing algorithms and reducing their energy complexity. These results lay a theoretical foundation for a new field of semi-reversible computing and provide a new framework for the investigation of algorithms.

The classic buffer insertion algorithm of van Ginneken has time and space complexity O(n/sup 2/), where n is the number of possible buffer positions. For more than a decade, van Ginneken's algorithm has been the foundation of buffer insertion. In this paper, we present a new algorithm that computes the same optimal buffer insertion, but runs much faster. For 2-pin nets, our time complexity is O(nlogn) and space complexity is O(n). For multipin nets, our time complexity is O(nlog/sup 2/n) and space complexity is O(nlogn). The speedup is achieved by four novel techniques: predictive pruning, candidate tree, fast redundancy check, and fast merging. On industrial test cases, the new algorithms is 2-80 times faster than van Ginneken's algorithm and uses 1/4-1/500 of the memory. Since van Ginneken's algorithm and its variations are used by most existing algorithms on buffer insertion and buffer sizing, our new algorithm significantly improves the performance of all these algorithms. The predictive pruning technique has been applied to buffer cost minimization (Shi et al., 2004), and significantly improved the running time.

This paper introduces a new heuristic function with high efficiency for an optimum solving of the 8 - puzzle, this one being the double of the Chebyshev distance. The comparative study is realized among this new heuristic (Chebyshev heuristic), the Hamming h euristic and the Manhattan heuristic using A* algorithm implemented in Java. The Chebyshev heuristic function is more informed than Hamming and Manhattan heuristics. This paper also presents the necessary stages in object oriented development of an interactive software dedicated to simulate the A* search algorithm for 8 -puzzle. The modeling of the software is achieved through specific UML diagrams representing the phases of analysis, design and implementation, the system thus being described in a clear and practical manner. In order to confirm the obtained theoretical results which show that Chebyshev heuristic is more efficient, two performance criteria were used: space complexity and time complexity. The space complexity was measured by the number of generated nodes from the search tree, by the number of the expanded nodes and by the effective branching factor. The time complexity was measured by the running time. From the experimental results obtained by using the Chebyshev heuristic, improvements were obs erved regarding space and time complexity of A* algorithm versus Hamming and Manhattan heuristics.

In the original McEliece cryptosystem based on QC-LDPC codes, the decoding algorithm uses BF algorithm instead of BP algorithm, which reduces the time complexity but decreases the decoding performance. To solve this problem, we improve the original algorithm and use the Q-decoder which utilizes the correlation between the error pattern e and the matrix Q, making decoding performance much better. Finally, we analyze the security of the improved cryptosystem, finding it has a higher security level.