Spatially-Coupled Precoded Rateless Codes with Bounded Degree Achieve the Capacity of BEC under BP decoding

Raptor codes are known as precoded rateless codes that achieve the capacity of BEC. However the maximum degree of Raptor codes needs to be unbounded to achieve the capacity. In this paper, we prove that spatially-coupled precoded rateless codes achieve the capacity with bounded degree under BP decoding

Spatially-Coupled Precoded Rateless Codes

Raptor codes are rateless codes that achieve the capacity on the binary erasure channels. However the maximum degree of optimal output degree distribution is unbounded. This leads to a computational complexity problem both at encoders and decoders. Aref and Urbanke investigated the potential advantage of universal achieving-capacity property of proposed spatially-coupled (SC) low-density generator matrix (LDGM) codes. However the decoding error probability of SC-LDGM codes is bounded away from 0. In this paper, we investigate SC-LDGM codes concatenated with SC low-density parity-check codes. The proposed codes can be regarded as SC Hsu-Anastasopoulos rateless codes. We derive a lower bound of the asymptotic overhead from stability analysis for successful decoding by density evolution. The numerical calculation reveals that the lower bound is tight. We observe that with a sufficiently large number of information bits, the asymptotic overhead and the decoding error rate approach 0 with bounded maximum degree

ALOHA Random Access that Operates as a Rateless Code

Various applications of wireless Machine-to-Machine (M2M) communications have rekindled the research interest in random access protocols, suitable to support a large number of connected devices. Slotted ALOHA and its derivatives represent a simple solution for distributed random access in wireless networks. Recently, a framed version of slotted ALOHA gained renewed interest due to the incorporation of successive interference cancellation (SIC) in the scheme, which resulted in substantially higher throughputs. Based on similar principles and inspired by the rateless coding paradigm, a frameless approach for distributed random access in slotted ALOHA framework is described in this paper. The proposed approach shares an operational analogy with rateless coding, expressed both through the user access strategy and the adaptive length of the contention period, with the objective to end the contention when the instantaneous throughput is maximized. The paper presents the related analysis, providing heuristic criteria for terminating the contention period and showing that very high throughputs can be achieved, even for a low number for contending users. The demonstrated results potentially have more direct practical implications compared to the approaches for coded random access that lead to high throughputs only asymptotically.Comment: Revised version submitted to IEEE Transactions on Communication

Precoded Integer-Forcing Universally Achieves the MIMO Capacity to Within a Constant Gap

An open-loop single-user multiple-input multiple-output communication scheme is considered where a transmitter, equipped with multiple antennas, encodes the data into independent streams all taken from the same linear code. The coded streams are then linearly precoded using the encoding matrix of a perfect linear dispersion space-time code. At the receiver side, integer-forcing equalization is applied, followed by standard single-stream decoding. It is shown that this communication architecture achieves the capacity of any Gaussian multiple-input multiple-output channel up to a gap that depends only on the number of transmit antennas.Comment: to appear in the IEEE Transactions on Information Theor

Efficient Termination of Spatially-Coupled Codes

Spatially-coupled low-density parity-check codes attract much attention due to their capacity-achieving performance and a memory-efficient sliding-window decoding algorithm. On the other hand, the encoder needs to solve large linear equations to terminate the encoding process. In this paper, we propose modified spatially-coupled codes. The modified (\dl,\dr,L) codes have less rate-loss, i.e., higher coding rate, and have the same threshold as (\dl,\dr,L) codes and are efficiently terminable by using an accumulator

Lossy Source Coding via Spatially Coupled LDGM Ensembles

We study a new encoding scheme for lossy source compression based on spatially coupled low-density generator-matrix codes. We develop a belief-propagation guided-decimation algorithm, and show that this algorithm allows to approach the optimal distortion of spatially coupled ensembles. Moreover, using the survey propagation formalism, we also observe that the optimal distortions of the spatially coupled and individual code ensembles are the same. Since regular low-density generator-matrix codes are known to achieve the Shannon rate-distortion bound under optimal encoding as the degrees grow, our results suggest that spatial coupling can be used to reach the rate-distortion bound, under a {\it low complexity} belief-propagation guided-decimation algorithm. This problem is analogous to the MAX-XORSAT problem in computer science.Comment: Submitted to ISIT 201

FREE SPACE OPTICS LINKS AFFECTED BY OPTICAL TURBULENCE: CHANNEL MODELING, MEASUREMENTS AND CODING TECHNIQUES FOR ERROR MITIGATION

FSO is an optical wireless line-of-sight communication system able to offer good broadband performance, electromagnetic interference immunity, high security, license-free operation, low power consumption, ease of relocation, and straightforward installation. It represents a modern technology, significantly functional when it is impossible, expensive or complex to use physical connections or radio links. Unfortunately, since the transmission medium in a terrestrial FSO link is the air, these communications are strongly dependent on various atmospheric phenomena (e.g., rain, snow, optical turbulence and, especially, fog) that can cause losses and fading. Therefore, in worst-case conditions, it could be necessary to increase the optical transmission power, although, at the same time, it is needed to comply to safety regulations. The effects of the already mentioned impairments are: scattering (i.e., Rayleigh and Mie) losses, absorption and scintillation. The first two can be described by proper attenuation coefficients and increase if the atmospheric conditions get worst. As regards scintillation, it is a random phenomenon, appreciable even under clear sky. Because of scintillation, in FSO links, the irradiance fluctuates and could drop below a threshold under which the receiver is not able to detect the useful signal. In this case, communications suffer from erasure errors, which cause link outages. This phenomenon becomes relevant at high distance, but it can also be observed in 500m-long FSO links. Moreover, the optical turbulence intensity can change of an order of magnitude during the day: it reaches its maximum around midday (when the temperature is the highest) and, conversely, it is lower during the night. In order to reduce or eliminate these impairments, different methods (both hardware and software) were studied and reported in literature. Hardware solutions focus on aperture averaging effects to reduce irradiance fluctuations, in particular by using a bigger detector or multi-detector systems. On the other hand, software techniques mostly focus on transmission codes. Rateless codes are an innovative solution, suitable for channels affected by erasure or burst errors. They add a redundant coding (also settable on the fly) to the source data, allowing the receiver to successfully recover the whole payload that, otherwise, would be corrupted or partially lost. To test rateless codes, recovery capabilities in FSO channels, detailed information about the occurring signal fading are needed: in particular, its depth, temporal duration and statistics. For this reason, I have implemented a time-correlated channel model able to generate an irradiance time-series at the receiver side, at wide range of turbulence conditions (from weak to strong). The time-series represents a prediction of temporal irradiance fluctuations caused by scintillation. In this way, I was able to test the recovery capabilities of several types of rateless codes. I have performed measurement campaigns in order to characterize Free Space Optics links affected by the optical turbulence. In particular, I have used three different setups placed in the Laboratory of Optics of the University of Palermo and in the Optical Communication Laboratory of the Northumbria University. Thanks to an in-depth post-processing of the collected data, I was able to extract useful information about the FSO link quality and the turbulence strength, thus proving the effectiveness of the Gamma-Gamma model under several turbulence conditions. In Chapter 1, I will introduce the theory of optical wireless communications and, in particular, of Free Space Optics communications. In detail, I will describe the advantages and the impairments that characterize this kind of communication and discuss about its applications. In Chapter 2, the adopted channel models are presented. In particular, these models are able to predict irradiance fluctuations at the detector in Free Space Optics links and were designed for terrestrial and space-to-ground communications at different link specifications, turbulence conditions and temporal covariance. Firstly, a brief description of the employed irradiance distribution and of the irradiance covariance functions is presented. The details of the above mentioned channel model implementation and the performance are then described. Finally, in order to detail the channel model features, several examples of irradiance fluctuation predictions are depicted. In Chapter 3, the details of a measurement campaign, focused on the analysis of optical turbulence effects in a FSO link, will be treated. Three different measurement setups composed of different typologies of laser sources, detectors and turbulent channels will be described. Data post-processing will be discussed. Moreover, a performance evaluation of the terrestrial channel model described in Chapter 2 will be discussed. In Chapter 4, rateless codes will be presented. These codes introduce a redundancy by means of repair symbols, associated to the source data, and, in case of losses, they are able to recover the source data without any need for retransmission. They can also manage large amounts of data and offer very interesting features for erasure channels and multicast/broadcast applications. Three different classes of rateless codes will be described and, in particular: Luby Transform, Raptor and RaptorQ codes. Moreover, the performance of the rateless codes in Free Space Optics links will be investigated. The implemented simulators are based on the channel models presented in Chapter 2 and focus on the study of rateless codes recovery capabilities when erasure errors due to fadings occur. The results on the performance of three rateless codes typologies, in two different FSO links, will be illustrated. All the research work was supported by the European Space Agency (grant no. 5401001020). Experimental activities were performed in collaboration with the Optical Communications Research Group of the Northumbria University and within the COST IC1101 European Action

New Codes on Graphs Constructed by Connecting Spatially Coupled Chains

A novel code construction based on spatially coupled low-density parity-check (SC-LDPC) codes is presented. The proposed code ensembles are described by protographs, comprised of several protograph-based chains characterizing individual SC-LDPC codes. We demonstrate that code ensembles obtained by connecting appropriately chosen SC-LDPC code chains at specific points have improved iterative decoding thresholds compared to those of single SC-LDPC coupled chains. In addition, it is shown that the improved decoding properties of the connected ensembles result in reduced decoding complexity required to achieve a specific bit error probability. The constructed ensembles are also asymptotically good, in the sense that the minimum distance grows linearly with the block length. Finally, we show that the improved asymptotic properties of the connected chain ensembles also translate into improved finite length performance.Comment: Submitted to IEEE Transactions on Information Theor