An improved decoding algorithm for finite-geometry LDPC codes (original) (raw)

A decoding algorithm for finite-geometry LDPC codes

IEEE Transactions on Communications, 2005

In this paper, we develop a new low-complexity algorithm to decode low-density parity-check (LDPC) codes. The developments are oriented specifically toward low-cost, yet effective, decoding of (high-rate) finite-geometry (FG) LDPC codes. The decoding procedure updates iteratively the hard-decision received vector in search of a valid codeword in the vector space. Only one bit is changed in each iteration, and the bit-selection criterion combines the number of failed checks and the reliability of the received bits. Prior knowledge of the signal amplitude and noise power is not required. An optional mechanism to avoid infinite loops in the search is also proposed. Our studies show that the algorithm achieves an appealing tradeoff between performance and complexity for FG-LDPC codes.

Two bit-flipping decoding algorithms for low-density parity-check codes

IEEE Transactions on Communications, 2009

In this letter, a low complexity decoding algorithm for binary linear block codes is applied to low-density paritycheck (LDPC) codes and improvements are described, namely an extension to soft-decision decoding and a loop detection mechanism. For soft decoding, only one real-valued addition per code symbol is needed, while the remaining operations are only binary as in the hard decision case. The decoding performance is considerably increased by the loop detection. Simulation results are used to compare the performance with other known decoding strategies for LDPC codes, with the result that the presented algorithms offer excellent performances at smaller complexity.

Two-Bit Bit Flipping Decoding of LDPC Codes

In this paper, we propose a new class of bit flipping algorithms for low-density parity-check (LDPC) codes over the binary symmetric channel (BSC). Compared to the regular (parallel or serial) bit flipping algorithms, the proposed algorithms employ one additional bit at a variable node to represent its "strength." The introduction of this additional bit increases the guaranteed error correction capability by a factor of at least 2. An additional bit can also be employed at a check node to capture information which is beneficial to decoding. A framework for failure analysis of the proposed algorithms is described. These algorithms outperform the Gallager A/B algorithm and the minsum algorithm at much lower complexity. Concatenation of twobit bit flipping algorithms show a potential to approach the performance of belief propagation (BP) decoding in the error floor region, also at lower complexity.

A novel high-throughput, low-complexity bit-flipping decoder for LDPC codes

2017 International Conference on Advanced Technologies for Communications (ATC), 2017

This paper presents a new high-throughput, lowcomplexity Bit Flipping (BF) decoder for Low-Density Parity-Check (LDPC) codes on the Binary Symmetric Channel (BSC), called Probabilistic Parallel Bit Flipping (PPBF). The advantage of PPBF comes from the fact that, no global operation is required during the decoding process and from that, all of the computations could be parallelized and localized at the computing units. Also in PPBF, the probabilistic feature in flipping the Variable Node (VN) is incorporated for all satisfaction level of its CN neighbors. This type of probabilistic incorporation makes PPBF more dynamic to correct some error patterns which are unsolvable by other BF decoders. PPBF offers a faster decoding process with an equivalent error correction performance to the Probabilistic Gradient Descent Bit Flipping (PGDBF) decoder, which is better than all so-far introduced BF decoders in BSC channel. A hardware implementation architecture of PPBF is also presented in this paper with detailed circuits for the probabilistic signal generator and processing units. The implementation of PPBF on FPGA confirms that, the PPBF complexity is much lower than that of the PGDBF and even lower than the one of the deterministic Gradient Descent Bit Flipping (GDBF) decoder. The good decoding performance along with the high throughput and low complexity lead PPBF decoder to become a brilliant candidate for the next generation of communication and storage standards.

Improved Bit-Flipping Decoding of Low-Density Parity-Check Codes

IEEE Transactions on Information Theory, 2005

In this correspondence, a new method for improving hard-decision bit-flipping decoding of low-density parity-check (LDPC) codes is presented. Bits with a number of unsatisfied check sums larger than a predetermined threshold are flipped with a probability 1 which is independent of the code considered. The probability is incremented during decoding according to some rule. With a proper choice of the initial , the proposed improved bit-flipping (BF) algorithm achieves gain not only in performance, but also in average decoding time for signal-to-noise ratio (SNR) values of interest with respect to = 1.

IJERT-Bit Flipping Decoders for LDPC Codes: A Short Survey

International Journal of Engineering Research and Technology (IJERT), 2020

https://www.ijert.org/bit-flipping-decoders-for-ldpc-codes-a-short-survey https://www.ijert.org/research/bit-flipping-decoders-for-ldpc-codes-a-short-survey-IJERTV9IS110120.pdf In the domain of wireless communication systems, Error Control Coding schemes are one of the widely relied upon or responsible methodology for securing the integrity and authenticity of the data transmission process. In the last decade, due to the advent of modern communication standards and their wide range of services, there has been a resurgence of interest and support in the research community towards the conception of efficient and versatile error control coding techniques. Recent developments in the wireless communication-based technologies have witnessed the pliable nature of low-density parity-check (LDPC) codes and their contributions which cannot be overstated. As of now, the decoding schemes based on LDPC codes have emerged as one of the most promising and efective coding scheme for addressing several key problems of reliable data communication. In this article, comprehensive overview on the on some well-known LDPC hard decision decoding algorithms is provided. In addition, simulations carried out on various LDPC decoding algorithms based on their performance is also presented. Finally, at the end of this review, the scope for future prospects are forecasted through discussions.

IJERT-BER Performance Comparison of Bit Flipping Algorithms used for Decoding of LDPC Codes

International Journal of Engineering Research and Technology (IJERT), 2015

https://www.ijert.org/ber-performance-comparison-of-bit-flipping-algorithms-used-for-decoding-of-ldpc-codes https://www.ijert.org/research/ber-performance-comparison-of-bit-flipping-algorithms-used-for-decoding-of-ldpc-codes-IJERTV4IS051311.pdf In this paper the Bit Error Rate (BER) performance of different bit flipping algorithms used for decoding of Low Density Parity Check (LDPC) code is compared. These algorithms mainly depend on inversion function. Through simulation results the Noisy Gradient Descent Bit flipping (NGDBF) algorithm is proved to be best till date. This algorithm provides the best BER performance, for Smoothed Noisy Gradient Descent Bit flipping (SM-NGDBF) algorithm we can obtain BER 4.86×10-4 at 3.5db. The Multi Noisy Gradient Descent Bit flipping (M-NGDBF) algorithm requires the least number of iterations than the other algorithms proposed for decoding a codeword.

A novel bit flipping decoder for systematic LDPC codes

IEICE Electronics Express, 2017

In this letter, a novel bit flipping decoding of systematic LDPC codes is proposed. Unsuccessfully decoded codeword is efficiently redecoded by the candidate information bit flipping (CIBF) decoder using cyclic redundancy check (CRC) information at the end of each iteration. We adopt the CIBF decoder to the LDPC decoding additionally and that makes it possible to reduce the power consumption up to 12.7% because of the reduced average number of iterations and to improve the frame error rate (FER) performance. Based on the hardware cost analysis in the CMOS cell library, the additional hardware cost of the CIBF decoder is negligible compared with the conventional LDPC decoder.

Low-density parity check ( LDPC ) codes : A new era in coding

2015

“Low Density” comes from the characteristic of their parity-check matrix that contains small number of 1’s in comparison to the amount of 0’s in them. This sparseness of parity check matrix guarantees two features: First, ‘a decoding complexity’ which increases only linearly with the code length and second, ‘a minimum distance’ which also increases linearly with the code length. These codes are practical implementation of Shannon noisy coding theorem[1]. LDPC codes are similar to other linear block codes. Actually, every existing code can be successfully implemented with the LDPC iterative decodSukhleen Bindra Narang, Kunal Pubby*, Hashneet Kaur Department of Electronics Technology, Guru Nanak Dev University, Amritsar, (INDIA) E-mail: kunalpubby02@gmail.com

Majority Logic Decoding Of Euclidean GeometryLow Density Parity Check (EG-LDPC) Codes

International Journal of Innovative Research in Computer and Communication Engineering, 2014

Error detection in memory applications was proposed to accelerate the majority logic decoding of difference set low density parity check codes. This is useful as majority logic decoding can be implemented serially with simple hardware but requires a large decoding time. For memory applications, this increases the memory access time. The method detects whether a word has errors in the first iterations of majority logic decoding, and when there are no errors the decoding ends without completing the rest of the iterations. Since most words in a memory will be error free, the average decoding time is greatly reduced. In this brief, the application of a similar technique to a class of Euclidean geometry low density parity check (EG-LDPC) codes that are one step majority logic decodable. The results obtained show that the method is also effective for EG-LDPC codes. Extensive simulation results are given to accurately estimate the probability of error detection for different code sizes and...