Iterative Construction of Regular LDPC Codes from Independent Tree-Based Minimum Distance Bounds

An independent tree-based method for lower bounding the minimum distance of low-density parity-check (LDPC) codes is presented. This lower-bound is then used as the decision criterion during the iterative construction of regular LDPC codes. The new construction algorithm results in LDPC codes with greater girth and improved minimum-distance bounds when compared to regular LDPC codes constructed using the progressive edge-growth (PEG) construction and the approximate cycle extrinsic message degree (ACE)-constrained PEG construction. Simulation results of codes constructed with the new method show improved performance on the additive white Gaussian noise channel at moderate signal-to-noise ratios

On Lowering the Error Floor of Short-to-Medium Block Length Irregular Low Density Parity Check Codes

Edited version embargoed until 22.03.2019 Full version: Access restricted permanently due to 3rd party copyright restrictions. Restriction set on 22.03.2018 by SE, Doctoral CollegeGallager proposed and developed low density parity check (LDPC) codes in the early 1960s. LDPC codes were rediscovered in the early 1990s and shown to be capacity approaching over the additive white Gaussian noise (AWGN) channel. Subsequently, density evolution (DE) optimized symbol node degree distributions were used to significantly improve the decoding performance of short to medium length irregular LDPC codes. Currently, the short to medium length LDPC codes with the lowest error floor are DE optimized irregular LDPC codes constructed using progressive edge growth (PEG) algorithm modifications which are designed to increase the approximate cycle extrinsic message degrees (ACE) in the LDPC code graphs constructed. The aim of the present work is to find efficient means to improve on the error floor performance published for short to medium length irregular LDPC codes over AWGN channels in the literature. An efficient algorithm for determining the girth and ACE distributions in short to medium length LDPC code Tanner graphs has been proposed. A cyclic PEG (CPEG) algorithm which uses an edge connections sequence that results in LDPC codes with improved girth and ACE distributions is presented. LDPC codes with DE optimized/’good’ degree distributions which have larger minimum distances and stopping distances than previously published for LDPC codes of similar length and rate have been found. It is shown that increasing the minimum distance of LDPC codes lowers their error floor performance over AWGN channels; however, there are threshold minimum distances values above which there is no further lowering of the error floor performance. A minimum local girth (edge skipping) (MLG (ES)) PEG algorithm is presented; the algorithm controls the minimum local girth (global girth) connected in the Tanner graphs of LDPC codes constructed by forfeiting some edge connections. A technique for constructing optimal low correlated edge density (OED) LDPC codes based on modified DE optimized symbol node degree distributions and the MLG (ES) PEG algorithm modification is presented. OED rate-½ (n, k)=(512, 256) LDPC codes have been shown to have lower error floor over the AWGN channel than previously published for LDPC codes of similar length and rate. Similarly, consequent to an improved symbol node degree distribution, rate ½ (n, k)=(1024, 512) LDPC codes have been shown to have lower error floor over the AWGN channel than previously published for LDPC codes of similar length and rate. An improved BP/SPA (IBP/SPA) decoder, obtained by making two simple modifications to the standard BP/SPA decoder, has been shown to result in an unprecedented generalized improvement in the performance of short to medium length irregular LDPC codes under iterative message passing decoding. The superiority of the Slepian Wolf distributed source coding model over other distributed source coding models based on LDPC codes has been shown

Superposition Mapping & Related Coding Techniques

Since Shannon's landmark paper in 1948, it has been known that the capacity of a Gaussian channel can be achieved if and only if the channel outputs are Gaussian. In the low signal-to-noise ratio (SNR) regime, conventional mapping schemes suffice for approaching the Shannon limit, while in the high SNR regime, these mapping schemes, which produce uniformly distributed symbols, are insufficient to achieve the capacity. To solve this problem, researchers commonly resort to the technique of signal shaping that mends the symbol distribution, which is originally uniform, into a Gaussian-like one. Superposition mapping (SM) refers to a class of mapping techniques which use linear superposition to load binary digits onto finite-alphabet symbols that are suitable for waveform transmission. Different from conventional mapping schemes, the output symbols of a superposition mapper can easily be made Gaussian-like, which effectively eliminates the necessity of active signal shaping. For this reason, superposition mapping is of great interest for theoretical research as well as for practical implementations. It is an attractive alternative to signal shaping for approaching the channel capacity in the high SNR regime. This thesis aims to provide a deep insight into the principles of superposition mapping and to derive guidelines for systems adopting it. Particularly, the influence of power allocation to the system performance, both w.r.t the achievable power efficiency and supportable bandwidth efficiency, is made clear. Considerable effort is spent on finding code structures that are matched to SM. It is shown that currently prevalent code design concepts, which are mostly derived for coded transmission with bijective uniform mapping, do not really fit with superposition mapping, which is often non-bijective and nonuniform. As the main contribution, a novel coding strategy called low-density hybrid-check (LDHC) coding is proposed. LDHC codes are optimal and universally applicable for SM with arbitrary type of power allocation

Improving Group Integrity of Tags in RFID Systems

Checking the integrity of groups containing radio frequency identification (RFID) tagged objects or recovering the tag identifiers of missing objects is important in many activities. Several autonomous checking methods have been proposed for increasing the capability of recovering missing tag identifiers without external systems. This has been achieved by treating a group of tag identifiers (IDs) as packet symbols encoded and decoded in a way similar to that in binary erasure channels (BECs). Redundant data are required to be written into the limited memory space of RFID tags in order to enable the decoding process. In this thesis, the group integrity of passive tags in RFID systems is specifically targeted, with novel mechanisms being proposed to improve upon the current state of the art. Due to the sparseness property of low density parity check (LDPC) codes and the mitigation of the progressive edge-growth (PEG) method for short cycles, the research is begun with the use of the PEG method in RFID systems to construct the parity check matrix of LDPC codes in order to increase the recovery capabilities with reduced memory consumption. It is shown that the PEG-based method achieves significant recovery enhancements compared to other methods with the same or less memory overheads. The decoding complexity of the PEG-based LDPC codes is optimised using an improved hybrid iterative/Gaussian decoding algorithm which includes an early stopping criterion. The relative complexities of the improved algorithm are extensively analysed and evaluated, both in terms of decoding time and the number of operations required. It is demonstrated that the improved algorithm considerably reduces the operational complexity and thus the time of the full Gaussian decoding algorithm for small to medium amounts of missing tags. The joint use of the two decoding components is also adapted in order to avoid the iterative decoding when the missing amount is larger than a threshold. The optimum value of the threshold value is investigated through empirical analysis. It is shown that the adaptive algorithm is very efficient in decreasing the average decoding time of the improved algorithm for large amounts of missing tags where the iterative decoding fails to recover any missing tag. The recovery performances of various short-length irregular PEG-based LDPC codes constructed with different variable degree sequences are analysed and evaluated. It is demonstrated that the irregular codes exhibit significant recovery enhancements compared to the regular ones in the region where the iterative decoding is successful. However, their performances are degraded in the region where the iterative decoding can recover some missing tags. Finally, a novel protocol called the Redundant Information Collection (RIC) protocol is designed to filter and collect redundant tag information. It is based on a Bloom filter (BF) that efficiently filters the redundant tag information at the tag’s side, thereby considerably decreasing the communication cost and consequently, the collection time. It is shown that the novel protocol outperforms existing possible solutions by saving from 37% to 84% of the collection time, which is nearly four times the lower bound. This characteristic makes the RIC protocol a promising candidate for collecting redundant tag information in the group integrity of tags in RFID systems and other similar ones

Conception Avancée des codes LDPC binaires pour des applications pratiques

The design of binary LDPC codes with low error floors is still a significant problem not fully resolved in the literature. This thesis aims to design optimal/optimized binary LDPC codes. We have two main contributions to build the LDPC codes with low error floors. Our first contribution is an algorithm that enables the design of optimal QC-LDPC codes with maximum girth and mini-mum sizes. We show by simulations that our algorithm reaches the minimum bounds for regular QC-LDPC codes (3, d c ) with low d c . Our second contribution is an algorithm that allows the design optimized of regular LDPC codes by minimizing dominant trapping-sets/expansion-sets. This minimization is performed by a predictive detection of dominant trapping-sets/expansion-sets defined for a regular code C(d v , d c ) of girth g t . By simulations on different rate codes, we show that the codes designed by minimizing dominant trapping-sets/expansion-sets have better performance than the designed codes without taking account of trapping-sets/expansion-sets. The algorithms we proposed are based on the generalized RandPEG. These algorithms take into account non-cycles seen in the case of quasi-cyclic codes to ensure the predictions.La conception de codes LDPC binaires avec un faible plancher d’erreurs est encore un problème considérable non entièrement résolu dans la littérature. Cette thèse a pour objectif la conception optimale/optimisée de codes LDPC binaires. Nous avons deux contributions principales pour la construction de codes LDPC à faible plancher d’erreurs. Notre première contribution est un algorithme qui permet de concevoir des codes QC-LDPC optimaux à large girth avec les tailles minimales. Nous montrons par des simulations que notre algorithme atteint les bornes minimales fixées pour les codes QC-LDPC réguliers (3, d c ) avec d c faible. Notre deuxième contribution est un algorithme qui permet la conception optimisée des codes LDPC réguliers en minimisant les trapping-sets/expansion-sets dominants(es). Cette minimisation s’effectue par une détection prédictive des trapping-sets/expansion-sets dominants(es) définies pour un code régulier C(d v , d c ) de girth gt . Par simulations sur des codes de rendement différent, nous montrons que les codes conçus en minimisant les trapping-sets/expansion-sets dominants(es) ont de meilleures performances que les codes conçus sans la prise en compte des trapping-sets/expansion-sets. Les algorithmes que nous avons proposés se basent sur le RandPEG généralisé. Ces algorithmes prennent en compte les cycles non-vus dans le cas des codes quasi-cycliques pour garantir les prédictions