Concepts of tree coding and of rate-distortion theory are applied to the problem of the transmission of analog signals over digital channels. Coding schemes are developed which yield improvements of up to six dB in signal-to-noise ratio over conventional techniques for the reproduction of speech waveforms. / Thesis / Master of Engineering (MEngr)

Consider a generalized multiterminal source coding system, where 􏱡(l choose m) 􏱢 encoders, each m observing a distinct size-m subset of l (l ≥ 2) zero-mean unit-variance symmetrically correlated Gaussian sources with correlation coefficient ρ, compress their observation in such a way that a joint decoder can reconstruct the sources within a prescribed mean squared error distortion based on the compressed data. The optimal rate- distortion performance of this system was previously known only for the two extreme cases m = l (the centralized case) and m = 1 (the distributed case), and except when ρ = 0, the centralized system can achieve strictly lower compression rates than the distributed system under all non-trivial distortion constaints. Somewhat surprisingly, it is established in the present thesis that the optimal rate-distortion preformance of the afore-described generalized multiterminal source coding system with m ≥ 2 coincides with that of the centralized system for all distortions when ρ ≤ 0 and for distortions below an explicit positive threshold (depending on m) when ρ > 0. Moreover, when ρ > 0, the minimum achievable rate of generalized multiterminal source coding subject to an arbitrary positive distortion constraint d is shown to be within a finite gap (depending on m and d) from its centralized counterpart in the large l limit except for possibly the critical distortion d = 1 − ρ. / Thesis / Master of Applied Science (MASc)

In the context of error control in random linear network coding, it is useful to construct codes that comprise well-separated collections of subspaces of a vector space over a finite field. This thesis concerns the construction of non-constant-dimension projective space codes for adversarial error-correction in random linear network coding. The metric used is the so-called injection distance introduced by Silva and Kschischang, which perfectly reflects the adversarial nature of the channel. A Gilbert-Varshamov-type bound for such codes is derived and its asymptotic behaviour is analysed. It is shown that in the limit as the ambient space dimension approaches infinity, the Gilbert-Varshamov bound on the size of non-constant-dimension codes behaves similar to the Gilbert-Varshamov bound on the size of constant-dimension codes contained within the largest Grassmannians in the projective space. Using the code-construction framework of Etzion and Silberstein, new non-constant-dimension codes are constructed; these codes contain more codewords than comparable codes designed for the subspace metric. To our knowledge this work is the first to address the construction of non-constant-dimension codes designed for the injection metric.

In the context of error control in random linear network coding, it is useful to construct codes that comprise well-separated collections of subspaces of a vector space over a finite field. This thesis concerns the construction of non-constant-dimension projective space codes for adversarial error-correction in random linear network coding. The metric used is the so-called injection distance introduced by Silva and Kschischang, which perfectly reflects the adversarial nature of the channel. A Gilbert-Varshamov-type bound for such codes is derived and its asymptotic behaviour is analysed. It is shown that in the limit as the ambient space dimension approaches infinity, the Gilbert-Varshamov bound on the size of non-constant-dimension codes behaves similar to the Gilbert-Varshamov bound on the size of constant-dimension codes contained within the largest Grassmannians in the projective space. Using the code-construction framework of Etzion and Silberstein, new non-constant-dimension codes are constructed; these codes contain more codewords than comparable codes designed for the subspace metric. To our knowledge this work is the first to address the construction of non-constant-dimension codes designed for the injection metric.

Abstract In this thesis we study the spatial throughput of interference-limited wireless networks from different perspectives, considering that the spatial distribution of nodes follows a 2-dimensional homogeneous Poisson point process and transmitters employ Gaussian point-to-point codes. To carry out this analysis, we model the interrelations between network elements using concepts from stochastic geometry, communication theory and information theory. We derive closed-form equations to compute/approximate the performance metric that is chosen to evaluate the system for each given specific scenario. Our first contribution is an investigation about whether it is preferable to have a large number of short single-hop links or a small number of long hops in multi-hop wireless networks, using a newly proposed metric denominated aggregate multi-hop information efficiency. For single-hop systems, we revisit the transmission capacity framework to study medium access protocols that use asynchronous transmissions and allow for packet retransmissions, showing when a carrier sensing capability is more suitable than synchronous transmissions, and vice-versa. We also cast the effective link throughput and the network spatial throughput optimization problems to find the combination of medium access probability, coding rate and maximum number of retransmissions that maximize each metric under packet loss and queue stability constraints, evincing when they do (and do not) have the same solution. Furthermore we analyze the expected maximum achievable sum rates over a given area – or spatial capacity – based on the capacity regions of Gaussian point-to-point codes for two decoding rules, namely (i) treating interference as noise (IAN) and (ii) jointly detecting the strongest interfering signals treating the others as noise (OPT), proving the advantages of the second. We additionally demonstrate that, when the same decoding rule and network density are considered, the spatial-capacity-achieving scheme always outperforms the spatial throughput obtained with the best predetermined fixed rate strategy. With those results in hand, we discuss general guidelines on the construction of ad hoc adaptive algorithms that would improve the information flow throughout the interference network, respecting the nodes’ internal and external constraints. / Tiivistelmä Tässä työssä tutkitaan häiriörajoitteisten langattomien verkkojen tila-alueen suorituskykyä, olettaen verkkosolmujen sijoittuvan 2-ulotteisen Poissonin pisteprosessin mukaisesti, sekä olettaen lähettimien hyödyntävän Gaussisia pisteestä-pisteeseen -koodeja. Suorituskykyanalyysi pohjautuu stokastiseen geometriaan, tietoliikenneteoriaan sekä informaatioteoriaan. Suljetun muodon suorituskyky-yhtälöitä hyödyntäen arvioidaan suorityskykymetriikoita eri skenaarioissa. Työn aluksi esitetään uusi monihyppyverkkojen informaatiotehokkuuteen perustuva metriikka. Sen avulla voidaan tutkia onko tehokkaampaa käyttää useita lyhyen hypyn linkkejä vai pienempää määrää pidempien hyppyjen linkkejä. Yhden hypyn verkoissa tutkitaan mediaanpääsyprotokollia asynkronisissa verkoissa pakettien uudelleenlähetykseen perustuen ja verrataan tätä synkroniseen lähetykseen ilman vapaan kanavan tunnistusmekanismia. Työssä tutkitaan myös linkin efektiivisen suorituskyvyn ja verkon tila-alueen suorituskyvyn optimointia, jotta sopiva yhdistelmä mediaan pääsyn todennäköisyydelle, koodausnopeudelle ja uudelleenlähetysten maksimilukumäärälle löytyisi ja samalla maksimoisi jokaisen käytetyn metriikan ehdollistettuna paketin menetyksille ja jonon stabiilisuudelle. Lisäksi arvioidaan maksimaalista odotettavaa nettosiirtonopeutta tietyllä alueella, eli tila-alueen kapasiteettia, Gaussimaisen pisteestä-pisteeseen koodien kapasiteettialueisiin perustuen kahta eri dekoodaussääntöä hyödyntäen: (i) olettaen häiriön olevan kohinaa tai (ii) ilmaisemalla voimakkaimmat häiriösignaalit ja olettaen muiden olevan kohinaa. Jälkimmäinen osoittautui tehokkaammaksi menetelmäksi. Työssä osoitetaan myös, että samalla dekoodaussäännöllä ja verkon tiheydellä tila-alueen kapasiteetin saavuttava menetelmä on aina tehokkaampi kuin tavanomainen tila-alueen suorituskykyyn perustuva kiinteän siirtonopeuden menetelmä. Saavutettujen tulosten valossa työssä esitetään yleisiä suunnittelumenetelmiä mukautuville ad hoc -algoritmeille, joiden avulla voidaan parantaa tiedonsiirtoa häiriörajoitteisissa verkoissa, ehdollistettuna verkon solmujen sisäisille ja ulkoisille rajoitteille.