Abstract The goal of this thesis is to provide a unified concept of lossy-forwarding from the theoretical analysis to practical scheme design for the decode-and-forward-based multiple access relay channel (MARC) system. To improve the performance of MARC with the relay subject to resources or/and time constraints, the erroneous estimates output from simple detection schemes are used at the relay are forwarded and exploited. A correlation is then found between two sequences: one is the network-coded sequence sent from the relay, and the other is their corresponding exclusive-OR-ed information sequence. Several joint network-channel coding (JNCC) techniques are provided in which the correlation is utilized to update the log-likelihood ratio sequences during the iterative decoding process at the destination. As a result, the bit error rate (BER) and frame error rate (FER) are improved compared with those of MARC with select DF strategy (SDF-MARC). The MARC proposed above is referred to as erroneous estimates-exploiting MARC (e-MARC). To investigate the achieved FER performance of the e-MARC system, the outage probability for e-MARC with two source nodes is theoretically derived. We re-formulate the e-MARC system and identify its admissible rate region according to the Slepian-Wolf theorem with a helper. Then, the outage probability is obtained by a set of integral over the rate region with respect to the probability density functions of all the links' instantaneous signal-to-noise power ratios. It is found through simulations that, as one of the source nodes is far away from both the relay and destination, e-MARC is superior to SDF-MARC in terms of outage performance. Furthermore, a joint adaptive network-channel coding (JANCC) technique is then proposed to support e-MARC with more source nodes. A vector is constructed at the destination in JANCC to identify the indices of the incorrectly decoded source node(s), and re-transmitted to the relay for requesting additional redundancy. The relay performs network-coding only over the estimates specified by the vector upon receiving the request. Numerical results show that JANCC-aided e-MARC is superior to e-MARC in terms of FER and goodput efficiency. In addition, compared iterative decoding is performed at relay with SDF-MARC, the use of differential detection with JANCC-aided e-MARC significantly reduces the computational complexity and latency with only a small loss in the FER. / Tiivistelmä Tämän väitöskirjan tarkoituksena on tuottaa yhtenäinen kokonaisuus häviöllisestä lähetyksestä pura-ja-lähetä (DF) -pohjaisessa monikäyttörelejärjestelmässä (MARC) sekä teoreettisesta että käytännöllisestä näkökulmasta. Parantaakseen resurssi- tai aikarajoitetun MARC-järjestelmän suorituskykyä, vastaanotin hyödyntää riippuvuussuhdetta releen välittämien informaatiosekvenssien virheellisten estimaattien ja suoraan lähteestä tulevien informaatiosekvenssien välillä (e-MARC). Työssä ehdotetaan useita yhdistetyn verkko -ja kanavakoodauksen menetelmiä (JNCC), joissa log-uskottavuussuhdesekvenssit iteratiivisen purkamisprosessin aikana päivitetään hyödyntämällä sekvenssien riippuvuussuhdetta vastaanottimessa. Tämän tuloksena sekä bittivirhe- että kehysvirhesuhdetta saadaan parannettua verrattuna selektiiviseen pura-ja-lähetä menetelmää käyttävään MARC-strategiaan (SDF-MARC). Kehysvirheen suorituskyvyn tarkastelua varten työssä johdetaan teoreettinen epäkäytettävyyden todennäköisyys e-MARC-menetelmälle kahden lähettimen tapauksessa. Lisäksi e-MARC-menetelmälle määritetään tiedonsiirtonopeusalue Slepian-Wolf -teoreeman mukaisesti. Tämän jälkeen saadaan epäkäytettävyyden todennäköisyys kaikkien linkkien signaalikohinasuhteen todennäköisyystiheysfunktion integraalina tiedonsiirtonopeusalueen yli. Simulointitulokset osoittavat e-MARC-menetelmän paremman epäkäytettävyyden todennäköisyyden verrattuna SDF-MARC-menetelmään silloin kun yksi lähettimistä on kaukana sekä releestä että vastaanottimesta. Mahdollistaakseen useamman lähteen käytön e-MARC-menetelmässä, työssä ehdotetaan lisäksi adaptiivinen yhdistetyn verkko-ja kanavakoodauksen menetelmä (JANCC). Siinä vastaanotin määrittää väärin purettujen sekvenssien lähettimet ja ilmoittaa ne vektorimuodossa takaisin releelle pyytääkseen näiden lähettimien informaation uudelleenlähetystä. Tämän jälkeen rele suorittaa verkkokoodauksen vain tunnistusvektorin määrittämien informaatiosekvenssien estimaatteihin perustuen. Tulokset näyttävät, että JANCC-menetelmää käyttävä e-MARC saavuttaa paremman kehysvirheen ja hyödyllisen läpäisyn tehokkuuden verrattuna e-MARC-menetelmään.

Network coding has emerged as an attractive alternative to routing because of the through put improvement it provides by reducing the number of channel uses. In a wireless scenario, in addition, further improvement can be obtained through Physical layer Network Coding (PNC), a technique in which nodes are allowed to transmit simultaneously, instead of transmitting in orthogonal slots. In this thesis, the design and analysis of network coding schemes are considered, for wireless two-way relaying, multi-user Multiple Access Relay Channel (MARC) and wireline networks. In a wireless two-way relay channel with PNC, the simultaneous transmissions of user nodes result in Multiple Access Interference (MAI) at there lay node. The harmful effect of MAI is the presence of signal set dependent deep channel fade conditions, called singular fade states, under which the minimum distance of the effective constellation at the relay become zero. Adaptively changing the network coding map used at the relay according to channel conditions greatly reduces the impact of this MAI. In this work, we obtain these adaptive PNC maps, which are finite in number ,by completing partially filled Latin Squares and using graph vertex coloring. Having obtained the network coding maps, the set of all possible channel realizations is quantized into a finite number of regions, with a specific network coding map chosen in a particular region and such a quantization is obtained analytically for 2λ-PSK signal set. The performance of the adaptive PNC scheme for two-way relaying is analyzed and tight high SNR upper bounds are obtained for the average end-to-end symbol error probability, in terms of the average error probability of a point-to-point fading channel. The adaptive PNC scheme is generalized for two-way relaying with multiple antennas at the nodes. As an alternative to the adaptive PNC scheme for two-way relaying, a Distributed Space Time Coding (DSTC) scheme is proposed, which effectively re-moves the effect of singular fade states at the transmitting nodes itself without any Channel State Information at the Transmitter (CSIT), and without any need to change the PNC map as a function of channel fade conditions. It is shown that the singular fade states can be viewed equivalently as vector subspaces of C2, which are referred to as the singular fade subspaces. DSTC design criterion to minimize the number of singular fade subspaces and maximize the coding gain is formulated and explicit low decoding complexity DSTC designs are provided. For the K-user MARC, in which K source nodes want to transmit messages to a destination node D with the help of are lay node R, a new PNC scheme is proposed. Use of a many-to-one PNC map with conventional minimum squared Euclidean distance decoding at D, results in a loss of diversity order due to error propagation from the relay node. To counter this, we propose a novel low complexity decoder which offers the maximum diversity order of two. Next, we consider wire line networks and explore the connections between linear network coding, linear index coding and discrete polymatroids, which are the multi-set analogue of matroids. We define a discrete polymatroidal network and show that a fractional vector linear solution over a field Fq exists for a network if and only if the network is discrete polymatroidal with respect to a discrete polymatroid representable over Fq.An algorithm to construct networks starting from certain class of discrete polymatroids is provided. Every representation over Fq for the discrete polymatroid, results in a fractional vector linear solution over Fq for the constructed network. It is shown that a linear solution to an index coding problem exists if and only if there exists a representable discrete polymatroid satisfying certain conditions which are determined by the index coding problem considered. El Rouayheb et. al. showed that the problem of finding a multi-linear representation for a matroid can be reduced to finding a perfect linear index coding solution for an index coding problem obtained from that matroid. Multi-linear representation of a matroid can be viewed as a special case of representation of an appropriate discrete polymatroid. We generalize the result of El Rouayheb et. al. by showing that the problem of finding a representation for a discrete polymatroid can be reduced to finding a perfect linear index coding solution for an index coding problem obtained from that discrete polymatroid.