Near-Capacity Network Coding for Cooperative Multi-UserCommunicationsHung Viet Nguyen1, Soon Xin Ng1, Jo ao Luiz Rebelatto2, Yonghui Li3and Lajos Hanzo11School of Electronics and Computer Science, University of Southampton, SO17 1BJ, United Kingdom.2Dept. of Electrical Engineering, Federal University of Santa Catarina, Florian opolis, SC, 88040-900, Brazil.3School of Electrical & Information Engineering, University of Sydney, Sydney, NSW, 2006, Australia.Emails:1{hvn08r,sxn,lh}@ecs.soton.ac.uk;2jlrebelatto@eel.ufsc.br;3lyh@ee.usyd.edu.auAbstractInthis contribution, weinvestigateNear-CapacityMulti-user Network-coding (NCMN) based systems using an Irregular Convo-lutional Code, a Unity-Rate Code and M-ary Phase-Shift Keying. In theNCMNbasedsystems, weconsideramultiusernetworkinwhichtheusers cooperatively transmit independent information to a common basestation (BS). Extrinsic Information Transfer (EXIT) charts were used fordesigning the proposed NCMN scheme. The design principles presentedinthiscontributioncanbeextendedtoavast rangeof NCMNbasedsystems using arbitrary channel coding schemes.I. INTRODUCTIONNetworkcodingisarecentlyintroducedparadigmconceivedforefcientlydisseminatingdatainmulticastwirelessnetworks,wherethe data ows arriving from multiple sources are combined to achievecompression and hence to increase the achievable throughput, as wellastoreducethedelayimposedandtoenhancetheerror-resilience[1][3]. Therelaynodes storetheincomingpackets intheir ownbuffer and then transmit the linear combinations of these packets. Thecoefcients used for creating the linear combination may be randomnumbersdenedoveralargeniteeld[4],orthosegleanedfromparity-check matrices of error control codes [5], [6].Generalised Dynamic Network Codes (GDNC) were proposedin [6], [7] byinterpretingthe designproblemof networkcodeasbeingequivalent tothat ofdesigninglinearblockcodesdenedoverGF(q)forerasurecorrection.Theauthorsof[6],[7]extendedtheoriginal DiversityNetworkCode(DNC) concept presentedin[8], which had been named Dynamic Network Code in [9], byallowing each user to broadcast several (as opposed to a singlein [8], [9]) information frames (IFs) of its own during the broadcastphase via orthogonal channels. Similarly, during the cooperativephases, each user transmits an arbitrary number of nonbinary linearcombinations tothe base station(BS) usingorthogonal channels,andthese nonbinarylinear combinations are consideredas parityframes (PFs). In [6], [7], the authors investigated GDNCs assuminganidealisedor so-calledperfect channel codingscheme, whichwas denedas thecodethat is capableof operatingright at theContinuous-input Continuous-output Memoryless Channels (CCMC)capacity. TheFrameErrorRatio(FER)performanceoftheGDNCscheme was determined in [6] by calculating the rank of the matrixcharacterising GDNCs. This method, which we refer to as the PurelyRank-Based Method (PRBM), always provides an optimistic estimateof the attainable FER performance of GDNCs.T uchler and Hagenauer proposed the employment of IrregularConvolutional Codes (IrCCs) [10], [11] for serially concatenatedschemes, whichareconstitutedbyafamilyofconvolutional codeshavingdifferent rates, inorder todesigna near-capacitysystem.They were specically designed with the aid of Extrinsic InformationTransfer (EXIT) charts conceived for analysing the convergence prop-erties of iterative decoding aided concatenated coding schemes [12].The nancial support of the Vietnamese International Education Develop-ment(VIED)fundandtheEUundertheauspicesoftheOPTIMIXprojectaswellasoftheRC-UKundertheIndia-UKAdvancedTechnologyCentreis gratefully acknowledged.As a further advance, it was shown in [13] that a recursive Unity-RateCode(URC) havinganinniteimpulseresponseis capableof efciently spreading the available extrinsic information acrosstheentireiterativereceiver chain. ThisURCmaybeemployedasanintermediatecode, inorder toimprovetheattainabledecodingconvergence. TheURCmaybeviewedasaprecoder invokedforcreatinga seriallyconcatenatedinner code component havinganinnite impulse response in order to reach the (1,1) point in the EXITchart andhencetoachieveaninnitesimallylowBit Error Ratio(BER) [14], as detailed in [15]. For example, a near-capacity IrregularConvolutional Coded (IrCC)-URC-M-ary Phase-Shift Keying (IrCC-URC-MPSK)schememaybedesignedforthesakeofapproachingthe achievable channel capacity.Based on this background, the novel contribution of this paper isthat a realistic near-capacity channel coding scheme is designed forthe sake of supporting network-coding aided multi-user communica-tions.Weconsidertheeffectsofboththeshadowfadingandofthesmall-scale Rayleigh fading in our channel model. The performanceof the proposed system obtained by simulations is compared to thatestimated by PRBM. The specic design guidelines presented in thiscontributioncanalsobeextendedtoadiverserangeof network-coding aided multi-user systems employing arbitrary channel codingschemes.The rest of this paper is organised as follows. In Section II,outageprobabilities arederived, beforedetailingbothour systemmodel andthedetectorusedat theBS. InSectionIII, weproposedesign procedures for both our near-capacity IrCC-URC-MPSK andfornetworkcodingmodels. Ourperformanceresultsarepresentedand discussed in Section IV, before concluding the paper in SectionV.II. PRELIMINARIESA. Single Link Channel Outage ProbabilityWeconsiderasingletransmissionlinkassociatedwiththetrans-mittedandreceivedsignalsof xandy, respectively. Thereceivedsignal can be represented asy= hx +n, (1)where h = hshfis the complex-valued fading coefcient thatcomprises twocomponents, a slowfadingcoefcient (large-scaleshadowfadingorquasi-staticfading) hs, whichisconstant forallsymbols within a frame and a fast fading (small-scale Rayleighfading)coefcient hf, whichvariesonasymbol bysymbol basis,while nis the Additive White GaussianNoise (AWGN) processhaving a variance ofN0/2 per dimension.Werefer toCasthemaximumachievabletransmissionrateofreliable communication supported by this channel. Let us assume thatthe transmitter encodes data at a rate ofRbits/s/Hz. If the channelrealisationhhasacapacityofC|h