A STUDY OF LINEAR ERROR CORRECTING CODES

Since Shannon's ground-breaking work in 1948, there have been two main development streams of channel coding in approaching the limit of communication channels, namely classical coding theory which aims at designing codes with large minimum Hamming distance and probabilistic coding which places the emphasis on low complexity probabilistic decoding using long codes built from simple constituent codes. This work presents some further investigations in these two channel coding development streams. Low-density parity-check (LDPC) codes form a class of capacity-approaching codes with sparse parity-check matrix and low-complexity decoder Two novel methods of constructing algebraic binary LDPC codes are presented. These methods are based on the theory of cyclotomic cosets, idempotents and Mattson-Solomon polynomials, and are complementary to each other. The two methods generate in addition to some new cyclic iteratively decodable codes, the well-known Euclidean and projective geometry codes. Their extension to non binary fields is shown to be straightforward. These algebraic cyclic LDPC codes, for short block lengths, converge considerably well under iterative decoding. It is also shown that for some of these codes, maximum likelihood performance may be achieved by a modified belief propagation decoder which uses a different subset of 7^ codewords of the dual code for each iteration. Following a property of the revolving-door combination generator, multi-threaded minimum Hamming distance computation algorithms are developed. Using these algorithms, the previously unknown, minimum Hamming distance of the quadratic residue code for prime 199 has been evaluated. In addition, the highest minimum Hamming distance attainable by all binary cyclic codes of odd lengths from 129 to 189 has been determined, and as many as 901 new binary linear codes which have higher minimum Hamming distance than the previously considered best known linear code have been found. It is shown that by exploiting the structure of circulant matrices, the number of codewords required, to compute the minimum Hamming distance and the number of codewords of a given Hamming weight of binary double-circulant codes based on primes, may be reduced. A means of independently verifying the exhaustively computed number of codewords of a given Hamming weight of these double-circulant codes is developed and in coiyunction with this, it is proved that some published results are incorrect and the correct weight spectra are presented. Moreover, it is shown that it is possible to estimate the minimum Hamming distance of this family of prime-based double-circulant codes. It is shown that linear codes may be efficiently decoded using the incremental correlation Dorsch algorithm. By extending this algorithm, a list decoder is derived and a novel, CRC-less error detection mechanism that offers much better throughput and performance than the conventional ORG scheme is described. Using the same method it is shown that the performance of conventional CRC scheme may be considerably enhanced. Error detection is an integral part of an incremental redundancy communications system and it is shown that sequences of good error correction codes, suitable for use in incremental redundancy communications systems may be obtained using the Constructions X and XX. Examples are given and their performances presented in comparison to conventional CRC schemes

Codes on Graphs and More

Modern communication systems strive to achieve reliable and efficient information transmission and storage with affordable complexity. Hence, efficient low-complexity channel codes providing low probabilities for erroneous receptions are needed. Interpreting codes as graphs and graphs as codes opens new perspectives for constructing such channel codes. Low-density parity-check (LDPC) codes are one of the most recent examples of codes defined on graphs, providing a better bit error probability than other block codes, given the same decoding complexity. After an introduction to coding theory, different graphical representations for channel codes are reviewed. Based on ideas from graph theory, new algorithms are introduced to iteratively search for LDPC block codes with large girth and to determine their minimum distance. In particular, new LDPC block codes of different rates and with girth up to 24 are presented. Woven convolutional codes are introduced as a generalization of graph-based codes and an asymptotic bound on their free distance, namely, the Costello lower bound, is proven. Moreover, promising examples of woven convolutional codes are given, including a rate 5/20 code with overall constraint length 67 and free distance 120. The remaining part of this dissertation focuses on basic properties of convolutional codes. First, a recurrent equation to determine a closed form expression of the exact decoding bit error probability for convolutional codes is presented. The obtained closed form expression is evaluated for various realizations of encoders, including rate 1/2 and 2/3 encoders, of as many as 16 states. Moreover, MacWilliams-type identities are revisited and a recursion for sequences of spectra of truncated as well as tailbitten convolutional codes and their duals is derived. Finally, the dissertation is concluded with exhaustive searches for convolutional codes of various rates with either optimum free distance or optimum distance profile, extending previously published results

Peak to average power ratio reduction and error control in MIMO-OFDM HARQ System

Currently, multiple-input multiple-output orthogonal frequency division multiplexing (MIMOOFDM) systems underlie crucial wireless communication systems such as commercial 4G and 5G networks, tactical communication, and interoperable Public Safety communications. However, one drawback arising from OFDM modulation is its resulting high peak-to-average power ratio (PAPR). This problem increases with an increase in the number of transmit antennas. In this work, a new hybrid PAPR reduction technique is proposed for space-time block coding (STBC) MIMO-OFDM systems that combine the coding capabilities to PAPR reduction methods, while leveraging the new degree of freedom provided by the presence of multiple transmit chairs (MIMO). In the first part, we presented an extensive literature review of PAPR reduction techniques for OFDM and MIMO-OFDM systems. The work developed a PAPR reduction technique taxonomy, and analyzed the motivations for reducing the PAPR in current communication systems, emphasizing two important motivations such as power savings and coverage gain. In the tax onomy presented here, we include a new category, namely, hybrid techniques. Additionally, we drew a conclusion regarding the importance of hybrid PAPR reduction techniques. In the second part, we studied the effect of forward error correction (FEC) codes on the PAPR for the coded OFDM (COFDM) system. We simulated and compared the CCDF of the PAPR and its relationship with the autocorrelation of the COFDM signal before the inverse fast Fourier transform (IFFT) block. This allows to conclude on the main characteristics of the codes that generate high peaks in the COFDM signal, and therefore, the optimal parameters in order to reduce PAPR. We emphasize our study in FEC codes as linear block codes, and convolutional codes. Finally, we proposed a new hybrid PAPR reduction technique for an STBC MIMO-OFDM system, in which the convolutional code is optimized to avoid PAPR degradation, which also combines successive suboptimal cross-antenna rotation and inversion (SS-CARI) and iterative modified companding and filtering schemes. The new method permits to obtain a significant net gain for the system, i.e., considerable PAPR reduction, bit error rate (BER) gain as compared to the basic MIMO-OFDM system, low complexity, and reduced spectral splatter. The new hybrid technique was extensively evaluated by simulation, and the complementary cumulative distribution function (CCDF), the BER, and the power spectral density (PSD) were compared to the original STBC MIMO-OFDM signal

Towards reliable communication in LTE-A connected heterogeneous machine to machine network

Machine to machine (M2M) communication is an emerging technology that enables heterogeneous devices to communicate with each other without human intervention and thus forming so-called Internet of Things (IoTs). Wireless cellular networks (WCNs) play a significant role in the successful deployment of M2M communication. Specially the ongoing massive deployment of long term evolution advanced (LTE-A) makes it possible to establish machine type communication (MTC) in most urban and remote areas, and by using LTE-A backhaul network, a seamless network communication is being established between MTC-devices and-applications. However, the extensive network coverage does not ensure a successful implementation of M2M communication in the LTE-A, and therefore there are still some challenges. Energy efficient reliable transmission is perhaps the most compelling demand for various M2M applications. Among the factors affecting reliability of M2M communication are the high endto-end delay and high bit error rate. The objective of the thesis is to provide reliable M2M communication in LTE-A network. In this aim, to alleviate the signalling congestion on air interface and efficient data aggregation we consider a cluster based architecture where the MTC devices are grouped into number of clusters and traffics are forwarded through some special nodes called cluster heads (CHs) to the base station (BS) using single or multi-hop transmissions. In many deployment scenarios, some machines are allowed to move and change their location in the deployment area with very low mobility. In practice, the performance of data transmission often degrades with the increase of distance between neighboring CHs. CH needs to be reselected in such cases. However, frequent re-selection of CHs results in counter effect on routing and reconfiguration of resource allocation associated with CH-dependent protocols. In addition, the link quality between a CH-CH and CH-BS are very often affected by various dynamic environmental factors such as heat and humidity, obstacles and RF interferences. Since CH aggregates the traffic from all cluster members, failure of the CH means that the full cluster will fail. Many solutions have been proposed to combat with error prone wireless channel such as automatic repeat request (ARQ) and multipath routing. Though the above mentioned techniques improve the communication reliability but intervene the communication efficiency. In the former scheme, the transmitter retransmits the whole packet even though the part of the packet has been received correctly and in the later one, the receiver may receive the same information from multiple paths; thus both techniques are bandwidth and energy inefficient. In addition, with retransmission, overall end to end delay may exceed the maximum allowable delay budget. Based on the aforementioned observations, we identify CH-to-CH channel is one of the bottlenecks to provide reliable communication in cluster based multihop M2M network and present a full solution to support fountain coded cooperative communications. Our solution covers many aspects from relay selection to cooperative formation to meet the user’s QoS requirements. In the first part of the thesis, we first design a rateless-coded-incremental-relay selection (RCIRS) algorithm based on greedy techniques to guarantee the required data rate with a minimum cost. After that, we develop fountain coded cooperative communication protocols to facilitate the data transmission between two neighbor CHs. In the second part, we propose joint network and fountain coding schemes for reliable communication. Through coupling channel coding and network coding simultaneously in the physical layer, joint network and fountain coding schemes efficiently exploit the redundancy of both codes and effectively combat the detrimental effect of fading conditions in wireless channels. In the proposed scheme, after correctly decoding the information from different sources, a relay node applies network and fountain coding on the received signals and then transmits to the destination in a single transmission. Therefore, the proposed schemes exploit the diversity and coding gain to improve the system performance. In the third part, we focus on the reliable uplink transmission between CHs and BS where CHs transmit to BS directly or with the help of the LTE-A relay nodes (RN). We investigate both type-I and type-II enhanced LTE-A networks and propose a set of joint network and fountain coding schemes to enhance the link robustness. Finally, the proposed solutions are evaluated through extensive numerical simulations and the numerical results are presented to provide a comparison with the related works found in the literature

Exploiting Spatio-Temporal Coherence for Video Object Detection in Robotics

This paper proposes a method to enhance video object detection for indoor environments in robotics. Concretely, it exploits knowledge about the camera motion between frames to propagate previously detected objects to successive frames. The proposal is rooted in the concepts of planar homography to propose regions of interest where to find objects, and recursive Bayesian filtering to integrate observations over time. The proposal is evaluated on six virtual, indoor environments, accounting for the detection of nine object classes over a total of ∼ 7k frames. Results show that our proposal improves the recall and the F1-score by a factor of 1.41 and 1.27, respectively, as well as it achieves a significant reduction of the object categorization entropy (58.8%) when compared to a two-stage video object detection method used as baseline, at the cost of small time overheads (120 ms) and precision loss (0.92).</p

LIPIcs, Volume 261, ICALP 2023, Complete Volume

LIPIcs, Volume 261, ICALP 2023, Complete Volum

Voyager spacecraft phase B, task D. Volume 2 - Spacecraft design and performance Final report

Systems engineering, structural design, and performance data on recommended Voyager spacecraft configuratio