self-organizing networks: state-of-the-art, challenges ...

Self-Organizing Networks: State-of-the-Art, Challenges and Perspectives Nicola Marchetti, Neeli Rashmi Prasad

Johan Johansson, Tao Cai

Center for TeleInFrastruktur Aalborg University, Denmark Email: {nm,np}@es.aau.dk

Huawei Technologies AB Kista, Sweden

Abstract—In this paper, a general overview of Self-Organizing Networks (SON), and the rationale and state-of-the-art of wireless SON are first presented. The technical and business requirements are then briefly treated, and the research challenges within the field of SON are highlighted. Thereafter, the relation between SON and Cognitive Networks (CN) is covered. At last, the application of Algorithmic Information Theory (AIT) as a possible theoretical tool to support SON in addressing the growing complexity of networks is discussed.

I. I NTRODUCTION TO S ELF -O RGANIZING N ETWORKS The phenomenon of self-organization is pervasive in many areas of life. In nature, e.g., fish organize themselves to swim in well structured swarms, ants find shortest routes to food sources, and fireflies emit light flashes in a synchronized fashion. Other examples of self-organized behavior can be observed in economy, population dynamics, psychology, and brain theory. In all the above examples, the participating entities establish an organizational structure that does not require any central coordination. Instead, the entities interact directly with each other, reacting to changes in their local environment. Typically, such self-organizing systems are very flexible, adaptive, failure-robust, and scalable [1]. Lately, with the availability and analysis of volumes of traces and statistics on the behavior of nodes, two major approaches to describe complex networks have been proposed, related to the small world and scale-free concepts. Small world is a property observed in many systems, such as in society and communication networks, and refers to the fact that entities (e.g. people or network nodes) are closer than one may think. Most entities are connected such that the average path length between them is small, the entities tend to form clusters, and the connectivity distribution peaks at an average value, and then decays exponentially. Scale-free properties are those which do not change with the size of the system, that in our case is the network. A particular scale-free property is that the connectivity distributions follow the power law form. This means that the connectivity distribution in a scale-free network tends to remain the same irrespectively of the size of the network, even at different orders of magnitude. Simply stated, the average path length between any two entities does not increase, independently of how large the network grows [2], [3]; this property is observed in many complex networks (e.g. the Internet). For Self-Organizing Networks

c 978-1-4244-6363-3/10/$26.00 2010 IEEE

Fig. 1.

SON growth and preferential attachment properties.

(SON) applied to wireless communications, the fundamental scale-free and small world properties are also set by the limited radio propagation range. Barabasi et al. [4], [5], [6], [7] used the following features of real networks to develop a scale-free network model (see Fig. 1): • •

Real networks expand continuously by the addition of new nodes (growth property); New nodes attach preferentially to nodes that are already well connected (preferential attachment property).

The properties of growth and preferential attachment lead to the scale-free property and are typically exhibited by real large networks, and this is confirmed by observations revealing that, in general, in large networks most of the nodes have very few connections, and few nodes (called hubs) have many connections [8]. The remaining part of the paper is organized as follows: in Section II one discusses wireless SON and their rationale; Section III revises the state-of-the-art, while Section IV discusses the technical and business requirements and the challenges within the wireless SON domain. The relation between SON and Cognitive Networks (CN) is treated in Section V. Afterwards, the application of Algorithmic Information Theory

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SelfConfiguration

Incidental events of intentional nature

Radio Environment SelfHealing

Incidental events of unintentional nature

SelfOptimization

Fig. 2.

Measurements

SON cycle.

(AIT) to complex SON is suggested and motivated in Section VI, while Section VII concludes the paper. II. S ELF -O RGANIZING W IRELESS N ETWORKS AND THEIR R ATIONALE The application of SON concepts to wireless networks has gained momentum recently; indeed SON are seen a key driver for improving Operation and Maintenance (OAM) as they can help to reduce the cost of installation and management by simplifying operational tasks through automated mechanisms targeting self-configuration, self-optimization and self-healing, which constitute the three main phases of the SON cycle (see Fig. 2). The significance of the circle encompassing radio environment, measurements and self-optimization in Fig. 2 will be explained later on, in Section V. The self-configuration phase is triggered by incidental events of an intentional nature, e.g. the addition of a new site or the introduction of a new service or network feature. These upgrades generally require an initial (re)configuration of a number of radio parameters or resource management algorithms, e.g. pilot powers and neighbors’ lists. These parameters have to be set prior to operations and before they can be optimized as part of the continuous self-optimization process [9]. In the self-optimization phase, intelligent methods apply to the processed measurements to derive an updated set of radio (resource management) parameters, including e.g. antenna parameters (tilt, azimuth), power settings (including pilot, control and traffic channels), neighbors’ lists (cell IDs and associated weights), and other radio resource management parameters (admission/congestion/handover control and packet scheduling) [9]. Triggered by incidental events of a non-intentional nature, such as the failure of a cell or site, self-healing methods aim to resolve the loss of coverage or capacity induced by such events to the extent possible. This is done by appropriately adjusting the parameters and algorithms in surrounding cells.

Once the actual failure has been repaired, all parameters are restored to their original settings [9]. SON are likely to have a relevant impact on Capital Expenditure (CAPEX) and Operational Expenditure (OPEX). Indeed, currently about 17% of wireless operators CAPEX is spent on engineering and installation services [10], therefore the self-configuring functions can eliminate the on-site operations for basic settings and updates, which will reduce the CAPEX. Also, since about 24% of a typical wireless operator revenue goes to network OPEX [11], the self-optimizing functions of SON can help to reduce the workload associated with site survey and network performance analysis. Moreover, the energy saving functions derived by the application of SON will reduce the costs in terms of power consumed by the equipment. On top of this, self-optimization and self-healing will help to improve the user perceived quality, by optimizing network parameters and by mitigating quality degradations. However, the main rationale for wireless SON is not the current OPEX situation, but what is probable to happen next. For several reasons, it is likely that increasingly more cells will be small in the future: • significant new spectrum becomes available in the high frequencies range; • although there have been very significant advances in spectrum efficient communication, the main capacity growth during the life-time of cellular communication is due to increased network density; • the trend to optimize towards very high peak data rates limits the range of a cell. In the predicted scenario of cells becoming smaller and increasing in number, the network’s OPEX is becoming the major cost. One part of the OPEX problem is the OAM cost, which is directly related to the need of SON. In summary, for SON applied to wireless networks, the main driver is the outlook of increased cost, primarily OPEX, for emerging networks. III. S TATE - OF - THE -A RT A. Standardization Bodies and Research Forums In 2007, Next Generation Mobile Networks (NGMN) Alliance released a white paper highlighting several operational use cases where automatic procedures may be introduced in order to enable the vendors to identify solutions for improving the operational efficiency of next generation networks, where the 3GPP network architecture has been considered [12]. Another document was released by NGMN on requirements of operators aiming to implement SON with focus on enablers, self-configuration, self-optimization, fault management, fault correction and SON-related OAM [13]. Concerning standardization, 3GPP has introduced SON items in its standardization path as required features for Long Term Evolution (LTE) deployments. In 2008, 3GPP released a document on self-configuring and self-optimizing network use cases and solutions [14]. It was a part of the standardization work on evolved UMTS Terrestrial Radio Access Network (eUTRAN), to study and specify the impact of self-organization

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on architecture, protocols and measurements. 3GPP release 8 includes the first specifications on requirements, integration with operators processes, and identification of main use cases. Release 9 is expected to define advanced features, which will introduce self-healing and self-optimization capabilities into LTE [15]. At a glance, the overall picture on SON-related standardization activities can be summarized as follows: • Standard progress: support for mobility related selfoptimization (Automatic Neighbor Relation, Mobility Robustness Optimization, Mobility Load Balancing), uplink Random Access Channel optimization, cell ID conflict resolution have been introduced in LTE releases 8 and 9. Support for energy saving and coverage-related selfoptimization is expected in release 10. • Standards focus: 3GPP focuses on interfaces, and thus on SON enabling measurements, control triggers and signaling interactions. Algorithms for control and optimization are out of the scope of the standard. • Work methodology: 3GPP and NGMN discussions are all very use-case oriented, and each use-case is discussed separately, including architecture issues. So far there has been limited effort to handle interaction between use cases. • Architecture: According to 3GPP principles and tradition, to allow inexpensive, easy upgradable and testable implementation, the UE does not host any significant SON intelligence, which is instead located in the network. The interface between the RAN and its OAM system is not an open interface (except for Home evolved Node B (HeNB)/HNB). Although there have been significant efforts to standardize parts of the interface into the next level Network Management System (NMS), in principle the choice of network architecture for SON functions (centralized vs. distributed) is a vendor’s implementation choice. Signaling support on the X2 interface among NodeBs has been introduced to allow for distributed solutions for most of the use cases addressed so far.

improves the application support, by a new information-centric paradigm in place of the old host-centric approach. These solutions embrace a full range of technologies, from fiber backbones to wireless and sensor networks. 4WARD also addresses non-technical drivers focusing on society, business and government in order to provide input to the technical work. E3 project [18] focuses on optimizing the use of radio resources and spectrum by employing cognitive radios and networks’ paradigms whose characteristic features include reconfigurability, self-adaptability, autonomous and collaborative behavior. The project studies the design of a Cognitive Radio (CR) system exploiting the capabilities of reconfigurable networks and self-adaptation to a dynamically changing environment. Collaborative CR resource management, spectrum management and self-organization with focus on network-based decisions, autonomous functionalities and algorithms focusing on terminal-based decisions are some of the research areas. Apart from the system research on requirements, features and architecture, one also studies the business research, regulation and standardization. FUTON [19], is also investigating NMS aligned with the specifications for next generation networks, optimization of heterogeneous radio resources and fault tolerance aspects. The FUTON architecture comprises of hybrid radio-optical infrastructure, a central unit and mobile/wireless terminals.

B. European Projects

The requirements to be met in order to develop the SON functionalities can be classified broadly into the following two categories: technical and business requirements. The purpose of specifying the technical requirements is to help in the development of novel algorithms and functionalities and to highlight the relevant network characteristics for selforganization. The list of the technical requirements to be addressed comprises: performance and complexity, stability, robustness, timing, interaction among SON functionalities, architecture and scalability, and required inputs. Defining the business requirements helps to consider factors related to the involved operational costs and incorporate them while developing the solutions. These requirements can be broadly classified into cost efficiency and deployment [28]. As per the important challenges for designing effective and dependable self-organization functionalities in future mobile radio networks, these include [29]:

There are and there have been several on going projects at European level within the area of SON. Here we will mention some of the most prominent. SOCRATES [16] is an FP7 project that aims to develop selforganization methods for enhancing the operation of wireless access networks, by integrating network planning, configuration and optimization into a single, mostly automated process requiring minimum manual intervention. 3GPP LTE radio interface has been chosen as the central radio technology. 4WARD [17] aims to research and develop an architecture for a Future Internet, in order to enable the co-existence of multiple networks on common platforms, through virtualization of networking resources. This will enhance the utility of networks, by making them capable of self-management and will also increase their robustness and efficiency, through leveraging diversity by using a novel transport approach. One

C. Academia and Industry There has been quite some activity on going in the field of SON within academia, see e.g. [1], [3], [20], [21], and more recently e.g. [22] and [23]; in particular the latter analyzes some methods to implement self optimization in LTE RAN system. In [23], how to make the system working in an optimized state is elaborated, especially for the co-existence of eNB, HeNB, 3G HNB etc. Several major industrial partners have recently published white papers on SON, clearly indicating that the industry looks with attention to this field [24], [25], [26], [27]. IV. R EQUIREMENTS AND C HALLENGES

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Measurement and probing: this involves issues such as determining what kind of data are required, at what rate they should be collected, and also devising techniques for collecting them. There is a tradeoff between the optimality of SON methods and the signaling cost associated for performing these processes; • Measurement/data processing: this deals with designing methods for appropriate processing of the collected measurements and also efficient handling of erroneous measurements’ reports; • Incomplete, delayed and faulty feedback: this may affect the efficiency of the self-optimization process and should be considered while designing algorithms, introducing safety margins which might degrade the performance with respect to ideal case; • Reliability of SON methods: in order to minimize human intervention, the control decisions should be reliable and operate autonomously. As mentioned above, the reduction of operational efforts and complexity are key drivers for RANs in LTE. One of the important aspects concerning this is that the system operability shall be improved under multi-vendor environment. With respect to this, it is important that measurements and performance data of different vendors share the same language. Such alignment eases network performance analysis and troubleshooting, and reduces efforts in maintaining the network at a properly working state. As we already stated, it is also of interest to minimize operational efforts by introducing self-configuring and selfoptimizing mechanisms. Especially in the early deployment phase, the configuration and optimization efforts are significant and traditionally lead to lengthy periods for getting an optimum and stable system setup. It is thus essential to have the necessary set of self-configuration and self-optimization mechanisms already available when initial deployment starts. From the discussion above, we can see that standardization is asked to define the necessary measurements, procedures and open interfaces to support better operability under multivendor environment. Such standardized functions shall also facilitate self-configuration and self-optimization. Especially the interaction between self-configuring/optimizing networks and OAM has to be considered [14]. •

V. R ELATION BETWEEN S ELF -O RGANIZING AND C OGNITIVE N ETWORKS Cognitive Networks (CN) are formed by spatially distributed nodes that are linked together through a connection topology. The nodes cooperate with each other through local interactions and adapt their states in response to both local data collected at the nodes and data received from their immediate neighbors. Information arriving at any particular node creates a ripple effect that propagates throughout the network by means of a diffusion process, which results in a form of collective intelligence leading to improved adaptation, learning, tracking, and convergence behavior with respect to non-cognitive networks. The edges linking the nodes can be assigned adjustable

Radio Environment

action: transmit signal

Power Control and Spectrum Management

RF stimuli

spectrum holes noise floor statistics traffic statistics

Fig. 3.

Radio Scene Analysis

CR cycle.

weights in accordance with the quality of the information that is exchanged over these edges; in this way, CN can adjust their topologies as well. Distributed processing techniques over such adaptive networks do not experience one of the main drawbacks of classical centralized fusion methods, i.e. the fact that central fusion approaches limit the autonomy of the network and add a critical point of failure due to the presence of a central node [30]. It has been observed in social and biological sciences studies on animal flocking behavior that while each individual agent in an animal colony is not capable of complex behavior, the combined coordination among multiple agents leads instead to the manifestation of regular patterns of behavior and swarm intelligence. In a similar manner, CN should benefit from local cooperation among the nodes, leading to enhanced performance in terms of e.g. improved learning, robustness, and convergence abilities [30]. CN can be designed to perform a variety of tasks such as detection, estimation, or resource allocation, through distributed processing. Their applications include environmental monitoring, distributed event detection, resource monitoring, target tracking, cooperation among CR searching for spectral resources, among others [30]. The cognitive cycle followed by CR (see Fig. 3 [31]) in their quest for free spectrum can be seen as a special case of a subset of the SON cycle showed in Fig. 2 (the one circled at the right-bottom of that figure), i.e. of the self-optimization phase of a SON cycle. As a matter of fact, the ubiquitous and pervasive computing and networking is becoming a clear trend in wireless communications: this is confirmed by the fact that computer processors are becoming part of more and more everyday items, which may form a wireless network. This trend corresponds to a shift from the very large to the very small, leading to disappearing electronics with the following characteristics: low-cost, miniature size and self-contained from energy perspective [32]. The ultimate goal is to achieve reliable universal

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coverage at all times and this brings to several challenges [33]: • • • •

this large amount of devices will very rapidly run out of spectrum; most devices will have limitations in energy consumption; wireless might be unreliable (bigger challenges due to the medium than in wired counterpart); from the very high heterogeneity of devices it might come incompatibility.

The above challenges in such complex networks’ scenarios can be faced only if a certain degree of self-organization is put into the system. In particular, self-optimized/cognitive networks will play a crucial role in identifying the needed spectrum of the proper quality for the several coexisting systems, devices and applications. Examples of possible scenarios for self-optimized and, in particular, cognitive networks, are [34]: •

•

•

vehicular networking (among cars, e.g. targeting accidents warnings, and within the car, e.g. establishing a network among personal devices); wireless sensor networks (applied e.g. to monitoring of humans, in the context of assisted living and medical engineering); wearable computing. VI. A PPLICATION TO A LGORITHMIC I NFORMATION T HEORY TO SON

SON can also be seen as a means to address the growing complexity of networks. SON are in nature decentralized and this implies a limited amount of information available compared to centralized networks; one key issue related to this, is how to quantify and minimize the information required and exchanged by the different subnetworks of a SON such that still self-organization processes’ output will be acceptable. Another possible situation related with SON is associated with the need to send information on the network to a third party, e.g. an OAM server. To understand the structure of a large-scale network (could be e.g. biological, social, or as in the case of this paper, technological), it might be helpful to decompose the network into smaller subunits or modules. [35] identifies the modules in which the network can be decomposed by finding an optimal compression of its topology, exploiting the regularities in its structure. It is assumed that a signaler knows the full network structure, i.e. the adjacency matrix (an unweighted and undirected network X is considered)  1 if there is a link between nodes i and j Aij = 0 otherwise (1) and wants to send as much information as possible about the network to a receiver over a channel with limited capacity. The signaler then encodes the network into modules in a way that maximizes the amount of information about the original network. In general, the problem is to determine the number of modules in the network, and to partition the nodes into that

number of modules. [35] provides a solution to this description problem based on Algorithmic Information Theory (AIT). AIT is a subfield of information theory, computer science, statistics and recursion theory, that deals with the relationship between computation, information, and randomness. One of the key concepts of AIT is Algorithmic Kolmogorov Complexity. Kolmogorov defined the complexity K of a string x as the length of its shortest description p on a universal Turing machine U , i.e. K(x) = min {l(p) : U (p) = x}. A string is simple if it can be described by a short program, like “the string of one million ones”, and is complex if there is no such short description, like for a random string whose shortest description is specifying it bit-by-bit. An important property of K is that it is nearly independent of the choice of U . Furthermore it leads to shorter codes than any other effective code. K shares many properties with Shannon’s entropy (information measure) S, but K is superior to S in many respects. To be brief, K is an excellent universal complexity measure [36]. In [35] the signaler does an encoding seeking to find a compression of the network structure so that the decoder can make the best possible estimate of the actual network. To minimize the description length of the original network X, one looks for the number of modules that minimizes the length of the modular description Y plus the conditional description length, i.e. the amount of information that would be needed to specify X exactly to a receiver who had already decoded the description Y , i.e. [35] tries to minimize the sum L(Y ) + L(X|Y )

(2)

where L(Y ) is the length in bits of the signal, and L(X|Y ) is the number of bits needed to specify which of the network estimates implied by the signal Y is actually realized. A tradeoff emerges as a consequence of the described approach, i.e. between how much of the network structure one can capture and how big is the amount of information to be exchanged, i.e. how many network modules and how long their descriptions. By abstracting the problem of finding patterns in networks to a problem of data compression, the information-theoretic view described in [35] provides a general basis for how to get the most information out of a network structure. A possible generalization in the context of wireless SON, could be to consider a weighted network instead of an unweighted one, compressing and transmitting not only the information on whether a link between two network nodes exists or not, but also what is the signal quality achieved over that link. This could help in planning a self-optimized resources’ distribution over the network, in either a distributed fashion (the subnetworks descriptions are exchanged among the subnetworks themselves) or in a centralized one (the network description is sent to an OAM server). VII. C ONCLUSION This paper intended to give a general overview of SelfOrganizing Networks (SON), their properties and application

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to wireless networks. After a general introduction to SON, the rationale of wireless SON was presented; thereafter the related state-of-the-art was reviewed from standardization, European projects, academia and industry viewpoints. Then, the requirements and research challenges within wireless SON domain were highlighted. The relations and analogies between SON and Cognitive Networks were then discussed. Afterwards, the application of Algorithmic Information Theory as a possible theoretical tool to support SON in addressing the growing complexity of networks was treated. R EFERENCES [1] C. Prehofer and C. W. Bettstetter, Self Organization in Communication Networks: Principles and Design Paradigms, IEEE Communication Magazine, July 2005. [2] S. Dixit and A. Sarma, Advances in Self-Organizing Networks, IEEE Communication Magazine, July 2005. [3] S. Dixit, E. Yanmaz and O.K. Tonguz, On the Design of Self-Organized Cellular Wireless Networks, IEEE Communication Magazine, July 2005. [4] A-L. Barabasi, R. Albert and H. Jeong, Mean-field Theory for Scale-free Random Networks, Physica A, vol. 272, 1999, pp. 17387. [5] A.-L. Barabasi and E. Bonabeau, Scale-Free Networks, Sci. Amer., vol. 288, May 2003, pp. 5059. [6] A.-L. Barabasi and R. Albert, Emergence of Scaling in Random Networks, Science, vol. 286, Oct. 1999, pp. 50912. [7] R. Albert and A.-L. Barabasi, Statistical Mechanics of Complex Networks, Rev. Mod. Physics, vol. 74, Jan. 2002, pp. 4791. [8] X. Wang and G. Chen, Complex Networks: Small-World, Scale-Free and Beyond, IEEE Circuits and Sys., vol. 3, no. 1, 2003, pp. 620. [9] L. Schmelz et al., Self-configuration, -optimisation, and -healing in wireless networks, Wireless World Research Forum Meeting 20, April 2008. [10] J.M. Celentano, Carrier Capital Expenditures, IEEE Communications Magazine, June 2008. [11] S. Shen, How to Cut Mobile Network Costs to Serve Emerging Markets, Gartner Inc., November 2005. [12] NGMN Alliance, NGMN Use Cases related to Self Organising Network, Overall Description, white paper, May 2007. [13] NGMN Alliance, NGMN Recommendation on SON and O&M Requirements, requirement specification, December 2008. [14] Self-configuring and self-optimizing network use cases and solutions, 3GPP TS 36.902, September 2008. [15] NEC Corporation, Self Organizing Network: NEC’s proposals for nextgeneration radio network management, white paper, February 2009. [16] Self-Optimisation & self-ConfiguRATion in wirelEss networkS (SOCRATES), EU FP7 project, http://www.fp7-socrates.org/?q=node/1. [17] 4WARD, EU FP7 project, http://www.4ward-project.eu/. [18] End-to-End Efficiency (E3), EU FP7 project, https://ict-e3.eu/. [19] Fibre-Optic Networks for Distributed Extendible Heterogeneous Radio Architectures and Service Provisioning (FUTON), EU FP7 project, http://www.ict-futon.eu/default.aspx. [20] D. Alderson et al., A Contrasting Look at Self-Organization in the Internet and Next Generation Communication Networks, IEEE Communigation Magazine, 2005. [21] L. Jun et al., A Novel Network Management Architecture for Self Organizing Network, International Conference on Networking, Architecture and Storage (NAS), 2007. [22] M.I. Tiwana, B. Sayrac, Z. Altman, Statistical learning for automated RRM: Application to eUTRAN mobility, IEEE ICC, 2009. [23] L. Xu, C. Sun, X. Li, C. Lim, H. He, The methods to implementate self optimisation in LTE system, IEEE ICCTA, October 2009. [24] 3G Americas, The Benefits of SON in LTE - Self-Optimizing and SelfOrganizing Networks, white paper, December 2009. [25] Motorola, Motorola LTE Self Organizing Networks - Motorola’s revolutionary SON solution for LTE OPEX reductions, white paper, 2009. [26] Nokia Siemens Networks, Introducing the Nokia Siemens Networks SON Suite - an efficient, future-proof platform for SON, white paper, October 2009. [27] Texas Instruments, A. Gatherer, P. Dent, S. Bhadra, R. Vedantham, Selfoptimizing networks (SON): doing more with less, white paper, 2009.

[28] L. Schmelz et al., Requirements for Self-Organizing Networks, SOCRATES Deliverable 2.1, FP7, March 2008. [29] J.L. Van et al., SOCRATES: Self Optimization and Self Configuration in Wireless Networks, COST 2100TD(08)422, Wroclaw, Poland, Feb 2008. [30] NSF Workshop on Distributed Processing over Cognitive Networks, http://www.ee.ucla.edu/NSF%20workshop%202009.htm [31] S. Haykin, Cognitive radio: brain-empowered wireless communications, IEEE JSAC, vol. 23, no. 2, February 2005, pp. 201220. [32] J.M. Rabaey and D.O. Pederson, A Brand New Wireless Day - What does it mean for design technology?, Ambient Society Symposium. [33] J. Rattner, Crossing the Chasm between Humans and Machines...the Next 40 Years, Intel Developer Forum. [34] C. Bettstetter, Self-Organization in Computer and Communication Networks, available online at http://www.bettstetter.com/talks/bettstetter2009-12-wien.pdf, December 2009. [35] M. Rosvall and C.T. Bergstrom, An Information-Theoretic Framework for Resolving Community Structure in Complex Networks, Proceedings of the National Academy of Sciences of the United States of America, Applied Mathematics, vol. 104, no. 18, May 2007, pp. 7327-7331. [36] Algorithmic Information Theory, available online at http://www.hutter1.net/ait.htm

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