A modification to the usual iterative decoding algorithm for LDPC codes, called bounded angle iterative (BA-I) decoding, is introduced. The modified decoder erases codewords detected during iterations that fall outside a maximum decoding angle with respect to the received observation. The new algorithm is applicable in scenarios that demand a very low undetected error rate but require short LDPC codes that are too vulnerable to undetected errors when the usual iterative decoding algorithm is used. BA-I decoding provides a means of reducing the maximum undetected error rate for short LDPC codes significantly, by incorporating a simple extra condition into the iterative decoder structure without redesigning the code. The reduction in undetected error rate comes at a price of increasing the threshold signal-to-noise ratio (SNR) required for achieving a good overall error rate, but this increase in channel threshold can be minimized by allowing the decoderpsilas maximum decoding angle to vary with SNR.
A modification to the usual iterative decoding algorithm for LDPC codes, called bounded angle iterative (BA-I) decoding, is introduced. The modified decoder erases codewords detected during iterations that fall outside a maximum decoding angle with respect to the received observation. The new algorithm is applicable in scenarios that demand a very low undetected error rate but require short LDPC codes that are too vulnerable to undetected errors when the usual iterative decoding algorithm is used. BA-I decoding provides a means of reducing the maximum undetected error rate for short LDPC codes significantly, by incorporating a simple extra condition into the iterative decoder structure without redesigning the code. The reduction in undetected error rate comes at a price of increasing the threshold signal-to-noise ratio (SNR) required for achieving a good overall error rate, but this increase in channel threshold can be minimized by allowing the decoderpsilas maximum decoding angle to vary with SNR.
Low-density parity-check (LDPC) codes have become a standard in modern communication systems thanks to their near-optimal error correction performance, which approaches Shannon's channel capacity as block length increases. However, in scenarios requiring short block lengths with low undetected frame error rate (UFER)-such as command and control data transmission in satellite communications-using only iterative decoders fails to achieve a balance between undetected and total frame error rates (FERs). This thesis addresses these challenges by investigating post-decoding error detection methods that enhance iterative LDPC decoding to achieve target FERs for both total and undetected errors. Specifically, we work with (128, 64) LDPC codes and explore two novel post-decoding techniques: bounded angle iterative decoding and single bit flip (SBF) list decoding, a variation of SBF decoding. These methods are applied to the iterative LDPC decoder output to manage the trade-off between total and undetected FERs effectively. Our results demonstrate that bounded angle iterative decoding effectively reduces UFER in codes with a large minimum distance with maintaining an acceptable increase in total frame error rate (TFER). Meanwhile, SBF list decoding mitigates the UFER increase introduced by standard SBF decoding, while retaining the significant TFER improvement that SBF decoding offers.
For short to moderate block-length LDPC codes, a large number of uncorrected error frames causes the increase of average number of iterations in the region of low SNR(Signal-to-Noise Ratio) and the oscillation of some variable nodes degrades the error performance in the region of medium to high SNR. In order to reduce the average number of iterations in the region of low SNR and improve error performance in the region of medium to high SNR, an iterative decoding algorithm with channel adaptation is proposed. The decoding method with pre-decision making based on error patterns of check-sum and weighted average message is adopted in this algorithm. Through the primary role of early decision method on reducing average iterations at low SNR and weighted average message on reducing error frames at medium to high SNR, iterative decoding with channel adaptation is realized and high efficient decoding is achieved. Simulation results show that, with the proposed algorithm, the average number of iterations is reduced in the region of low SNR without noticeable error performance degradation, and the error performance is improved in the region of medium to high SNR without obvious increase of the number of iterations compared with standard BP algorithm.
The paper presents a novel approach to reduce the bit error rate (BER) in iterative belief propagation (BP) decoding of low density parity check (LDPC) codes. The behavior of the BP algorithm is first investigated as a function of number of decoder iterations, and it is shown that typical uncorrected error patterns can be classified into 3 categories: oscillating, nearly-constant, or random-like, with a predominance of oscillating patterns at high Signal-to-Noise (SNR) values. A proposed decoder modification is then introduced based on tracking the number of failed parity check equations in the intermediate decoding iterations, rather than relying on the final decoder output (after reaching the maximum number of iterations). Simulation results with a rate ¿ (1024,512) progressive edge-growth (PEG) LDPC code show that the proposed modification can decrease the BER by as much as 10-to-40%, particularly for high SNR values.
This paper considers a modified iterative version of the two-stage hybrid algorithm for decoding low-density parity- check (LDPC) codes. The hybrid-decision scheme is a decoding scheme used that combines two iterative decoding algorithms for decoding LDPC codes. This scheme is suitable for many applications such as audio and video transmission that are sensitive to time. The hybrid-decision scheme mixes between the characteristics of the soft-decision decoding scheme and the hard- decision decoding scheme to reduce the computational complexity of the whole decoding algorithm. The modification proposed in this paper is applied to the implementation-efficient reliability ratio weighted bit-flipping (IERRWBF) algorithm which represents hard-decision scheme in the hybrid algorithm. This modification is capable of achieving better performance than that of the hybrid decoding algorithm with reducing the number of iterations required at each SNR and approaching more to the performance of the SPA. This reduction is more observable as the maximum number of iterations assigned for the algorithm increases or as the code length increases with improving the error performance as proved by simulation results.
In this digital era, modern communication systems play an essential part in nearly every aspect of life, with examples ranging from mobile networks and satellite communications to Internet and data transfer. Unfortunately, all communication systems in a practical setting are noisy, which indicates that we can either improve the physical characteristics of the channel or find a possible systematical solution, i.e. error control coding. The history of error control coding dates back to 1948 when Claude Shannon published his celebrated work “A Mathematical Theory of Communication”, which built a framework for channel coding, source coding and information theory. For the first time, we saw evidence for the existence of channel codes, which enable reliable communication as long as the information rate of the code does not surpass the so-called channel capacity. Nevertheless, in the following 60 years none of the codes have been proven closely to approach the theoretical bound until the arrival of turbo codes and the renaissance of LDPC codes. As a strong contender of turbo codes, the advantages of LDPC codes include parallel implementation of decoding algorithms and, more crucially, graphical construction of codes. However, there are also some drawbacks to LDPC codes, e.g. significant performance degradation due to the presence of short cycles or very high decoding latency. In this thesis, we will focus on the practical realisation of finite-length LDPC codes and devise algorithms to tackle those issues.
Firstly, rate-compatible (RC) LDPC codes with short/moderate block lengths are investigated on the basis of optimising the graphical structure of the tanner graph (TG), in order to achieve a variety of code rates (0.1 < R < 0.9) by only using a single encoder-decoder pair. As is widely recognised in the literature, the presence of short cycles considerably reduces the overall performance of LDPC codes which significantly limits their application in communication systems. To reduce the impact of short cycles effectively for different code rates, algorithms for counting short cycles and a graph-related metric called Extrinsic Message Degree (EMD) are applied with the development of the proposed puncturing and extension techniques. A complete set of simulations are carried out to demonstrate that the proposed RC designs can largely minimise the performance loss caused by puncturing or extension.
Secondly, at the decoding end, we study novel decoding strategies which compensate for the negative effect of short cycles by reweighting part of the extrinsic messages exchanged between the nodes of a TG. The proposed reweighted belief propagation (BP) algorithms aim to implement efficient decoding, i.e. accurate signal reconstruction and low decoding latency, for LDPC codes via various design methods. A variable factor appearance probability belief propagation (VFAP-BP) algorithm is proposed along with an improved version called a locally-optimized reweighted (LOW)-BP algorithm, both of which can be employed to enhance decoding performance significantly for regular and irregular LDPC codes. More importantly, the optimisation of reweighting parameters only takes place in an offline stage so that no additional computational complexity is required during the real-time decoding process.
Lastly, two iterative detection and decoding (IDD) receivers are presented for multiple-input multiple-output (MIMO) systems operating in a spatial multiplexing configuration. QR decomposition (QRD)-type IDD receivers utilise the proposed multiple-feedback (MF)-QRD or variable-M (VM)-QRD detection algorithm with a standard BP decoding algorithm, while knowledge-aided (KA)-type receivers are equipped with a simple soft parallel interference cancellation (PIC) detector and the proposed reweighted BP decoders. In the uncoded scenario, the proposed MF-QRD and VM-QRD algorithms are shown to approach optimal performance, yet require a reduced computational complexity. In the LDPC-coded scenario, simulation results have illustrated that the proposed QRD-type IDD receivers can offer near-optimal performance after a small number of detection/decoding iterations and the proposed KA-type IDD receivers significantly outperform receivers using alternative decoding algorithms, while requiring similar decoding complexity.
This paper deals with the method of undetected error probability estimation for a low-density parity-check (LDPC) code under any given iterative decoding algorithm. We propose such modification of a given iterative decoding algorithm, that almost preserves a decoding failure exponent and decoding complexity of this algorithm. We obtain the upper bound on the undetected error probability for the modified algorithm. We show how to use the proposed method to estimate the undetected error probability of LDPC code under the belief propagation (BP) algorithm at the end of this paper.