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Wireless Systems - Lecture. Network coding techniques. Elena Fasolo PhD Student - SIGNET Group fasoloel@dei.unipd.it. March, 7 th 2004. Definition of network coding (NC).

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Remote Systems - Lecture Network coding methods Elena Fasolo PhD Student - SIGNET Group fasoloel@dei.unipd.it March, 7 th 2004

Definition of system coding (NC) Pioneering work : [1] R. Ahlswede, N. Cai, S.- Y. R. Li, and R.W. Yeung, "Organize data stream," IEEE Trans. on Information Theory , vol. 46, no. 4, July 2000. Enhances the execution in information broadcasting Most appropriate setting: all to all correspondences DEFINITION Network coding is a specific in-system information handling method that adventures the qualities of the remote medium (specifically, the communicate correspondence channel) keeping in mind the end goal to build the limit or the throughput of the system

Communication systems TERMINOLOGY Communication organize = limited coordinated chart Acyclic correspondence arrange = organize with no direct cyclic Source hub = hub with no approaching edges (square) Channel = quiet correspondence connect for the transmission of an information unit for every unit time (edge) WX has limit equivalent to 2

The sanctioned illustration (I) Without system coding Simple store and forward Multicast rate of 1.5 bits for each time unit

The standard case (II) With system coding X-OR is one of the least difficult type of information coding Multicast rate of 2 bits for every time unit Disadvantages Coding/unraveling plan must be settled upon previously

b 1 C A r B NC and remote interchanges (a) Problem: send b 1 from A to B and b 2 from B to An utilizing hub C as a transfer An and B are not in correspondence extend ( r ) Without system coding, 4 transmissions are required. With system coding, just 3 transmissions are required (b) (c) b 2 b 2 b 1 C B A B A

Linear system coding When we allude to straight system coding [2], we mean that: The o utput stream at a given hub is gotten as a direct blend of its information streams. The coefficients of the blend are, by definition, chose from a limited field Coding can be executed at low computational cost Moreover, the data crossing a non source hub has the accompanying property : The substance of any data streaming out of an arrangement of non source hubs can be gotten from the gathered data that has flown into the arrangement of hubs [2] S.- Y. R. Li, R. W. Yeung, and N. Cai, "Direct system Coding", IEEE Trans. on Information Theory , vol. 49, no. 2, Feb. 2003.

Theoretical model for direct NC Graph ( V,E ) having unit limit edges Sender s in V , set of recipients T= { t,… } in V Source hub of h images Intermediate hub Destination hub

Linear coding stage Transmitted image Local encoding vector Global encoding vector

- 1 Decoding stage Node t can recuperate the source images x 1 , . . . , x h the length of the network G t , framed by the worldwide encoding vectors, has (full) rank h .

Inverting G t G t will be invertible with high likelihood if neighborhood encoding vectors are arbitrary and the field size is adequately substantial [3] P = 1 - |F| (where |F| is the cardinality of the limited field of coefficients) Example : If field measure = 2 16 and |E| = 2 8 then G t will be invertible with likelihood ≥ 1−2 −8 = 0.996 [3] R. Koetter,M.Medard, "An arithmetical way to deal with system coding", IEEE/ACM Trans. on Networking , Nov.2003

Theory versus Hone Theory: Symbols stream synchronously all through system Edges have unit (or known whole number) limits Centralized and full learning of topology, which is utilized to figure encoding and unraveling capacities Practice: Information ventures nonconcurrently in parcels Packets subject to irregular deferrals and misfortunes Edge limits frequently obscure, time-shifting Difficult to get concentrated learning, or to organize dependable communicate of capacities Need for basic arrangements, pertinent by and by

Practical Random NC Main thought [4] : Select the direct coefficients in a limited field of perfect size haphazardly Send the encoding vector inside similar bundle Packetization : Header expels requirement for brought together information of chart topology and encoding/deciphering capacities Nodes stores inside their cradles the got bundles Buffering : Allows offbeat parcels landings & flights with subjectively fluctuating rates, delay, misfortune [4] P. A. Chou, T.Wu, and K. Jain, "Functional system coding", in 51st Allerton Conf. Correspondence, Control and Computing , Oct. 2003.

Practical Algorithm Each hub gets parcels which are a straight blends of source bundles and it stores them into a lattice Each hubs conveys parcels acquired as an arbitrary direct mix of parcels put away in its cushion If the network of a hub has full rank (h) or a submatrix with full rank (r < h) exists, the hub can interpret h (or r) bundles in the meantime

Innovative bundles or not When a hub gets a parcel, it chooses whether to store the bundle or dispose of it Innovative bundle : it expands the present rank of the framework Non imaginative parcel : it doesn\'t build the rank of the grid. It implies that the parcel contains repetitive data and it is not expected to unravel the source bundles Hence, non inventive parcels are dropped

Need to synchronize All parcels identified with same source vectors x 1 ,… , x h are said to be in similar era; h is the era estimate All parcels in same era are labeled with same era number (one byte - mod 256 - is adequate) Generations are valuable to consider the distinctions in information sorts, era moments, needs, and so on . Eras

Packet Format At source hubs At the intermediated hubs

Transmission opportunity: produce parcel edge Random Combination edge Buffer Arriving bundles (jitter, misfortune, variable rate) Asynchronous transmission edge NODE Summarizing

0 an ij Observations about the interpreting stage Block deciphering : Collect h or more bundles, want to alter G t Early unraveling (prescribed): Perform Gaussian end after each RX bundle At each hub, distinguish & dispose of non-imaginative parcels G t has a tendency to be lower triangular, so it is ordinarily conceivable to disentangle x 1 ,… , x k with less more than k bundles Much shorter translating delay than square deciphering Approximately consistent, autonomous of piece length h It can be decoded

Costs and advantages Cost : Overhead of transmitting h additional images per bundle Example: h = 50 and field estimate = 2 8 overhead ≈ 50/1400 ≈ 3% Benefits : Receivers can unravel regardless of the possibility that Network topology & encoding capacities are obscure Nodes & edges included & evacuated in specially appointed way Packet misfortune, hub & interface disappointments with obscure areas Local encoding vectors are time-changing & irregular

Energy proficient telecom with NC [5] RING NETWORK All hubs are senders; all hubs are recipients T nc = # transmissions expected to communicate with system coding T w = # transmissions without system coding Lemma: T nc/T w ≥ ½ Without NC = 6 transmissions (T w ≥ n - 2 ) With NC = T nc ≥ (n – 1)/2 Achievable by physical piggybacking [5] J. Widmer, C. Fragouli, and J.- Y. L. Boudec, "Low–complexity energy–efficient broadcasting in remote ad–hoc systems usign arrange coding", in Proc.IEEE Information Theory Workshop , Oct. 2004.

Energy proficient telecom with NC GRID NETWORK Consider framework organize (toroidal) n = m 2 hubs Lemma : T nc/T w ≥ ¾ Without NC = T w ≥ n 2/3 With NC = T nc ≥ n 2/4 Achievable by physical piggybacking

Broadcasting in arbitrary systems [6] At every hub v in the diagram is related a sending component , d v . Source hub v transmits its source images (or parcels) max{ 1, | d v | } times. An extra time with likelihood p = d v - max{ 1, | d v | } if p > 0 . At the point when a hub gets a creative image (parcel), it communicates a direct mix over the traverse of the got coding vectors int(d v ) times And TX a further duplicate with likelihood p = d v – int(d v ) if p > 0 Two heuristics : d v = k/|N(v)| d v = k/min |N2(v)| where N2(v) are the quantity of 2-bounces neighbors [6] C. Fragouli, J. Widmer, and J.- Y. L. Boudec, "A system coding way to deal with vitality proficient telecom", Proceedings of INFOCOM06 , April 2006.

Simulation comes about All to all correspondence situation Energy utilization: number of transmissions and gatherings expected to assemble all the required parcels Delay: number of time units expected to interpret all the required bundles

NC in multicast interchanges

Summary Network Coding can be utilized as a part of practice Packetization Buffering Generation Network Coding is being connected to Internet, Live communicate, stockpiling, informing, peer2peer record sharing ("eMULE without bounds"), … Wireless specially appointed, portable, and sensor systems Many open issues

Wireless Systems - Lecture Thank you!