A Non-Asymptotic Approach to the Analysis of Communication Networks: From Error Correcting Codes to Network Properties

This dissertation has its focus on two different topics: 1. non-asymptotic analysis of polar codes as a new paradigm in error correcting codes with very promising features, and 2. network properties for wireless networks of practical size. In its first part, we investigate properties of polar codes that can be potentially useful in real-world applications. We start with analyzing the performance of finite-length polar codes over the binary erasure channel (BEC), while assuming belief propagation (BP) as the decoding method. We provide a stopping set analysis for the factor graph of polar codes, where we find the size of the minimum stopping set. Our analysis along with bit error rate (BER) simulations demonstrates that finite-length polar codes show superior error floor performance compared to the conventional capacity-approaching coding techniques. Motivated by good error floor performance, we introduce a modified version of BP decoding while employing a guessing algorithm to improve the BER performance. Each application may impose its own requirements on the code design. To be able to take full advantage of polar codes in practice, a fundamental question is which practical requirements are best served by polar codes. For example, we will see that polar codes are inherently well-suited for rate-compatible applications and they can provably achieve the capacity of time-varying channels with a simple rate-compatible design. This is in contrast to LDPC codes for which no provably universally capacity-achieving design is known except for the case of the erasure channel. This dissertation investigates different approaches to applications such as UEP, rate-compatible coding, and code design over parallel sub-channels (non-uniform error correction). Furthermore, we consider the idea of combining polar codes with other coding schemes, in order to take advantage of polar codes\u27 best properties while avoiding their shortcomings. Particularly, we propose, and then analyze, a polar code-based concatenated scheme to be used in Optical Transport Networks (OTNs) as a potential real-world application The second part of the dissertation is devoted to the analysis of finite wireless networks as a fundamental problem in the area of wireless networking. We refer to networks as being finite when the number of nodes is less than a few hundred. Today, due to the vast amount of literature on large-scale wireless networks, we have a fair understanding of the asymptotic behavior of such networks. However, in real world we have to face finite networks for which the asymptotic results cease to be valid. Here we study a model of wireless networks, represented by random geometric graphs. In order to address a wide class of the network\u27s properties, we study the threshold phenomena. Being extensively studied in the asymptotic case, the threshold phenomena occurs when a graph theoretic property (such as connectivity) of the network experiences rapid changes over a specific interval of the underlying parameter. Here, we find an upper bound for the threshold width of finite line networks represented by random geometric graphs. These bounds hold for all monotone properties of such networks. We then turn our attention to an important non-monotone characteristic of line networks which is the Medium Access (MAC) layer capacity, defined as the maximum number of possible concurrent transmissions. Towards this goal, we provide a linear time algorithm which finds a maximal set of concurrent non-interfering transmissions and further derive lower and upper bounds for the cardinality of the set. Using simulations, we show that these bounds serve as reasonable estimates for the actual value of the MAC-layer capacity

Segmented GRAND: Combining Sub-patterns in Near-ML Order

The recently introduced maximum-likelihood (ML) decoding scheme called guessing random additive noise decoding (GRAND) has demonstrated a remarkably low time complexity in high signal-to-noise ratio (SNR) regimes. However, the complexity is not as low at low SNR regimes and low code rates. To mitigate this concern, we propose a scheme for a near-ML variant of GRAND called ordered reliability bits GRAND (or ORBGRAND), which divides codewords into segments based on the properties of the underlying code, generates sub-patterns for each segment consistent with the syndrome (thus reducing the number of inconsistent error patterns generated), and combines them in a near-ML order using two-level integer partitions of logistic weight. The numerical evaluation demonstrates that the proposed scheme, called segmented ORBGRAND, significantly reduces the average number of queries at any SNR regime. Moreover, the segmented ORBGRAND with abandonment also improves the error correction performance

From Polar to Reed-Muller Codes:Unified Scaling, Non-standard Channels, and a Proven Conjecture

The year 2016, in which I am writing these words, marks the centenary of Claude Shannon, the father of information theory. In his landmark 1948 paper "A Mathematical Theory of Communication", Shannon established the largest rate at which reliable communication is possible, and he referred to it as the channel capacity. Since then, researchers have focused on the design of practical coding schemes that could approach such a limit. The road to channel capacity has been almost 70 years long and, after many ideas, occasional detours, and some rediscoveries, it has culminated in the description of low-complexity and provably capacity-achieving coding schemes, namely, polar codes and iterative codes based on sparse graphs. However, next-generation communication systems require an unprecedented performance improvement and the number of transmission settings relevant in applications is rapidly increasing. Hence, although Shannon's limit seems finally close at hand, new challenges are just around the corner. In this thesis, we trace a road that goes from polar to Reed-Muller codes and, by doing so, we investigate three main topics: unified scaling, non-standard channels, and capacity via symmetry. First, we consider unified scaling. A coding scheme is capacity-achieving when, for any rate smaller than capacity, the error probability tends to 0 as the block length becomes increasingly larger. However, the practitioner is often interested in more specific questions such as, "How much do we need to increase the block length in order to halve the gap between rate and capacity?". We focus our analysis on polar codes and develop a unified framework to rigorously analyze the scaling of the main parameters, i.e., block length, rate, error probability, and channel quality. Furthermore, in light of the recent success of a list decoding algorithm for polar codes, we provide scaling results on the performance of list decoders. Next, we deal with non-standard channels. When we say that a coding scheme achieves capacity, we typically consider binary memoryless symmetric channels. However, practical transmission scenarios often involve more complicated settings. For example, the downlink of a cellular system is modeled as a broadcast channel, and the communication on fiber links is inherently asymmetric. We propose provably optimal low-complexity solutions for these settings. In particular, we present a polar coding scheme that achieves the best known rate region for the broadcast channel, and we describe three paradigms to achieve the capacity of asymmetric channels. To do so, we develop general coding "primitives", such as the chaining construction that has already proved to be useful in a variety of communication problems. Finally, we show how to achieve capacity via symmetry. In the early days of coding theory, a popular paradigm consisted in exploiting the structure of algebraic codes to devise practical decoding algorithms. However, proving the optimality of such coding schemes remained an elusive goal. In particular, the conjecture that Reed-Muller codes achieve capacity dates back to the 1960s. We solve this open problem by showing that Reed-Muller codes and, in general, codes with sufficient symmetry are capacity-achieving over erasure channels under optimal MAP decoding. As the proof does not rely on the precise structure of the codes, we are able to show that symmetry alone guarantees optimal performance

Publications of the Jet Propulsion Laboratory 1976

The formalized technical reporting, released January through December 1975, that resulted from scientific and engineering work performed, or managed, by the Jet Propulsion Laboratory is described and indexed. The following classes of publications are included: (1) technical reports; (2) technical memorandums; (3) articles from bi-monthly Deep Space Network (DSN) progress report; (4) special publications; and (5) articles published in the open literature. The publications are indexed by: (1) author, (2) subject, and (3) publication type and number. A descriptive entry appears under the name of each author of each publication; an abstract is included with the entry for the primary (first-listed) author. Unless designated otherwise, all publications listed are unclassified

On generalized LDPC codes for ultra reliable communication

Ultra reliable low latency communication (URLLC) is an important feature in future mobile communication systems, as they will require high data rates, large system capacity and massive device connectivity [11]. To meet such stringent requirements, many error-correction codes (ECC)s are being investigated; turbo codes, low density parity check (LDPC) codes, polar codes and convolutional codes [70, 92, 38], among many others. In this work, we present generalized low density parity check (GLDPC) codes as a promising candidate for URLLC. Our proposal is based on a novel class of GLDPC code ensembles, for which new analysis tools are proposed. We analyze the trade-o_ between coding rate and asymptotic performance of a class of GLDPC codes constructed by including a certain fraction of generalized constraint (GC) nodes in the graph. To incorporate both bounded distance (BD) and maximum likelihood (ML) decoding at GC nodes into our analysis without resorting to multi-edge type of degree distribution (DD)s, we propose the probabilistic peeling decoding (P-PD) algorithm, which models the decoding step at every GC node as an instance of a Bernoulli random variable with a successful decoding probability that depends on both the GC block code as well as its decoding algorithm. The P-PD asymptotic performance over the BEC can be efficiently predicted using standard techniques for LDPC codes such as Density evolution (DE) or the differential equation method. We demonstrate that the simulated P-PD performance accurately predicts the actual performance of the GLPDC code under ML decoding at GC nodes. We illustrate our analysis for GLDPC code ensembles with regular and irregular DDs. This design methodology is applied to construct practical codes for URLLC. To this end, we incorporate to our analysis the use of quasi-cyclic (QC) structures, to mitigate the code error floor and facilitate the code very large scale integration (VLSI) implementation. Furthermore, for the additive white Gaussian noise (AWGN) channel, we analyze the complexity and performance of the message passing decoder with various update rules (including standard full-precision sum product and min-sum algorithms) and quantization schemes. The block error rate (BLER) performance of the proposed GLDPC codes, combined with a complementary outer code, is shown to outperform a variety of state-of-the-art codes, for URLLC, including LDPC codes, polar codes, turbo codes and convolutional codes, at similar complexity rates.Programa Oficial de Doctorado en Multimedia y ComunicacionesPresidente: Juan José Murillo Fuentes.- Secretario: Matilde Pilar Sánchez Fernández.- Vocal: Javier Valls Coquilla

Partially Coupled Codes for TB-based Transmission

In this thesis, we mainly investigate the design of partially coupled codes for transport block (TB) based transmission protocol adopted in 4G/5G mobile network standards. In this protocol, an information sequence in a TB is segmented into multiple code blocks (CBs) and each CB is protected by a channel codeword independently. It is inefficient in terms of transmit power and spectrum efficiency because any erroneous CB in a TB leads to the retransmission of the whole TB. An important research problem related to this TB-based transmission is how to improve the TB error rate (TBER) performance so that the number of retransmissions reduces. To tackle this challenge, we present a class of spatial coupling techniques called partial coupling in the TB encoding operation, which has two subclasses: partial information coupled (PIC) and partial parity coupling (PPC). To be specific, the coupling is performed such that a fraction of the information/parity sequence of one component code at the current CB is used as the input of the component encoder at the next CB, leading to improved TBER performance. One of the appealing features of partial coupling (both PIC and PPC) is that the coupling can be applied to any component codes without changing their encoding and decoding architectures, making them compatible with the TB-based transmission protocol. The main body of this thesis consists of two parts. In the first part, we apply both PIC and PPC to turbo codes. We investigate various coupling designs and analysis the performance of the partially coupled turbo codes over the binary erasure channel via density evolution (DE). Both simulation results and DE analysis show that such a class of codes can approach channel capacity with a large blocklength. In the second part, we construct PIC-polar codes. We show that PIC can effectively improve the error performance of finite-length polar codes by utilizing the channel polarization phenomenon. The DE-based performance analysis is also conducted. For both turbo codes and polar codes, we have shown that the partially coupled codes have significant performance gain over their uncoupled counterpart, demonstrating the effectiveness of the partial coupling

On Transmission System Design for Wireless Broadcasting

This thesis considers aspects related to the design and standardisation of transmission systems for wireless broadcasting, comprising terrestrial and mobile reception. The purpose is to identify which factors influence the technical decisions and what issues could be better considered in the design process in order to assess different use cases, service scenarios and end-user quality. Further, the necessity of cross-layer optimisation for efficient data transmission is emphasised and means to take this into consideration are suggested. The work is mainly related terrestrial and mobile digital video broadcasting systems but many of the findings can be generalised also to other transmission systems and design processes. The work has led to three main conclusions. First, it is discovered that there are no sufficiently accurate error criteria for measuring the subjective perceived audiovisual quality that could be utilised in transmission system design. Means for designing new error criteria for mobile TV (television) services are suggested and similar work related to other services is recommended. Second, it is suggested that in addition to commercial requirements there should be technical requirements setting the frame work for the design process of a new transmission system. The technical requirements should include the assessed reception conditions, technical quality of service and service functionalities. Reception conditions comprise radio channel models, receiver types and antenna types. Technical quality of service consists of bandwidth, timeliness and reliability. Of these, the thesis focuses on radio channel models and errorcriteria (reliability) as two of the most important design challenges and provides means to optimise transmission parameters based on these. Third, the thesis argues that the most favourable development for wireless broadcasting would be a single system suitable for all scenarios of wireless broadcasting. It is claimed that there are no major technical obstacles to achieve this and that the recently published second generation digital terrestrial television broadcasting system provides a good basis. The challenges and opportunities of a universal wireless broadcasting system are discussed mainly from technical but briefly also from commercial and regulatory aspectSiirretty Doriast