On The Design Of Physical Layer Rateless Codes

Codes that are capable of generating any number of encoded symbols from a given number of source symbols are called rateless codes. Luby transform (LT) codes are the first practical realization of rateless codes while Raptor codes are constructed by serially concatenating LT codes with high-rate outer low-density parity-check (LDPC) codes. Although these codes were originally developed for binary erasure channel (BEC), due to their rateless feature, they are being investigated and designed for their use in noisy channels. It is known that LT codes are the irregular non-systematic rateless counterpart of low-density generator-matrix (LDGM) codes. Therefore, the first part of our work is focused on LDGM codes and their serially concatenated scheme called serially concatenated LDGM (SCLDGM) codes. Though single LDGM codes are asymptotically bad codes, the SCLDGM codes are known to perform close to the Shannon limit. We first study the asymptotic behaviour of LDGM codes using a discretized density evolution method. We then show that the DDE method can be used in two-steps to provide the detailed asymptotic performance analysis of SCLDGM codes. We also provide the detailed error-floor analysis of both the LDGM and SCLDGM codes. We also prove a necessary condition for the successful decoding of such concatenated codes under sum-product (SP) decoding in binary input additive white Gaussian noise (BIAWGN) channels. Based on this necessary condition, we then develop a DDE-based optimization approach which can be used to optimize such concatenated codes in general. We present both the asymptotic performance and simulation results of our optimized SCLDGM codes that perform within 0.26 dB to the Shannon limit in BIAWGN channels. Secondly, we focus on the asymptotic analysis and optimization design of LT and Raptor codes over BIAWGN channels. We provide the exact asymptotic performance of LT codes using the DDE method. We apply the concept of the two-step DDE method to the Raptor codes and obtain their exact asymptotic performance in BIAWGN channels. We show that the existing Raptor codes using solely the same output degree distribution can perform within 0.4 dB to the Shannon limit for various realized code-rates. We then develop a DDE-based optimization technique to optimally design such physical layer Raptor codes. Our optimized Raptor codes are shown to perform within 0.2 dB to the Shannon limit for most of the realized code-rates. We also provide the asymptotic curves, decoding thresholds, and simulation results showing that our optimized Raptor codes outperform the existing Raptor codes in BIAWGN channels. Finally, we present the asymptotic analysis and optimization design of systematic version of these codes namely systematic LT and systematic Raptor codes as well

Density Evolution and Functional Threshold for the Noisy Min-Sum Decoder

This paper investigates the behavior of the Min-Sum decoder running on noisy devices. The aim is to evaluate the robustness of the decoder in the presence of computation noise, e.g. due to faulty logic in the processing units, which represents a new source of errors that may occur during the decoding process. To this end, we first introduce probabilistic models for the arithmetic and logic units of the the finite-precision Min-Sum decoder, and then carry out the density evolution analysis of the noisy Min-Sum decoder. We show that in some particular cases, the noise introduced by the device can help the Min-Sum decoder to escape from fixed points attractors, and may actually result in an increased correction capacity with respect to the noiseless decoder. We also reveal the existence of a specific threshold phenomenon, referred to as functional threshold. The behavior of the noisy decoder is demonstrated in the asymptotic limit of the code-length -- by using "noisy" density evolution equations -- and it is also verified in the finite-length case by Monte-Carlo simulation.Comment: 46 pages (draft version); extended version of the paper with same title, submitted to IEEE Transactions on Communication

A STUDY ON WIRELESS COMMUNICATION ERROR PERFORMANCE AND PATH LOSS PREDICTION

One channel model that characterises multipath fading effect of a wireless channel is called Flat Rayleigh Fading channel model. Given the properties of Flat Rayleigh Fading channel, an equation to find the capacity of a Flat Rayleigh fading channel with hard decision decoding is derived. The difference of power requirement to achieve the Additive White Gaussian Noise (AWGN) capacity over a Flat Rayleigh Fading channel fading is found to increase exponentially with Es /N0 . Upper and lower bounds of error performance of linear block codes over a Flat Rayleigh Fading channel are also studied. With the condition that the excess delay of a channel is known earlier, it is shown that a correlator with shorter length, according to excess delay of the channel, can be constructed for use in wireless channel response measurements. Therefore, a rule of construction of a shorter length correlator is defined, involving concatenation of parts of a Constant Amplitude Zero Auto-Correlation (CAZAC) sequence. Simulation of [136,68,24] Double Circulant Code with Dorsch List Decoding is also done in order to evaluate error performance of the channel coding scheme over one of the IEEE Wireless Metropolitan Area Network (WirelessMAN) channel models, the Stanford University Interim Channel Model No. 5 (SUI-5) channel. Performance of the channel cod- ing was severely degraded over the SUI-5 channel when it is compared to its performance over the AWGN channel. Indoor path losses within three multifloor office buildings were investigated at 433 MHz, 869 MHz and 1249 MHz. The work involved series of extensive received signal strength measurements within the buildings for all of the considered frequencies. Results have shown that indoor path loss is higher within a square footprint building than indoor path loss in a rectangular building. Parameters of Log-Distance Path Loss and Floor Attenuation Factor Path Loss models have been derived from the measurement data. In addition, a new indoor path loss prediction model was derived to cater for path loss pre- diction within multifloor buildings with indoor atriums. The model performs with better prediction accuracy when compared with Log-Distance Path Loss and Floor Attenuation Factor Path Loss models.Ministry of Higher Education of Malaysia, Universiti Teknologi Malaysi

Comparative study of a time diversity scheme applied to G3 systems for narrowband power-line communications

A dissertation submitted to the Faculty of Engineering and the Built Environment, University of the Witwatersrand, Johannesburg, in ful lment of the requirements for the degree of Masters of Science in Engineering (Electrical). Johannesburg, 2016Power-line communications can be used for the transfer of data across electrical net- works in applications such as automatic meter reading in smart grid technology. As the power-line channel is harsh and plagued with non-Gaussian noise, robust forward error correction schemes are required. This research is a comparative study where a Luby transform code is concatenated with power-line communication systems provided by an up-to-date standard published by electricit e R eseau Distribution France named G3 PLC. Both decoding using Gaussian elimination and belief propagation are imple- mented to investigate and characterise their behaviour through computer simulations in MATLAB. Results show that a bit error rate performance improvement is achiev- able under non worst-case channel conditions using a Gaussian elimination decoder. An adaptive system is thus recommended which decodes using Gaussian elimination and which has the appropriate data rate. The added complexity can be well tolerated especially on the receiver side in automatic meter reading systems due to the network structure being built around a centralised agent which possesses more resources.MT201

Comparison of direct and heterodyne detection optical intersatellite communication links

The performance of direct and heterodyne detection optical intersatellite communication links are evaluated and compared. It is shown that the performance of optical links is very sensitive to the pointing and tracking errors at the transmitter and receiver. In the presence of random pointing and tracking errors, optimal antenna gains exist that will minimize the required transmitter power. In addition to limiting the antenna gains, random pointing and tracking errors also impose a power penalty in the link budget. This power penalty is between 1.6 to 3 dB for a direct detection QPPM link, and 3 to 5 dB for a heterodyne QFSK system. For the heterodyne systems, the carrier phase noise presents another major factor of performance degradation that must be considered. In contrast, the loss due to synchronization error is small. The link budgets for direct and heterodyne detection systems are evaluated. It is shown that, for systems with large pointing and tracking errors, the link budget is dominated by the spatial tracking error, and the direct detection system shows a superior performance because it is less sensitive to the spatial tracking error. On the other hand, for systems with small pointing and tracking jitters, the antenna gains are in general limited by the launch cost, and suboptimal antenna gains are often used in practice. In which case, the heterodyne system has a slightly higher power margin because of higher receiver sensitivity