In the recent years, the exponential Internet traffic growth projections place enormous transmission rate demand on the underlying information infrastructure at every level, from the long haul submarine transmission to optical metro networks. In recent years, optical transmission at 100 Gb/s Ethernet date rate has been standardized by ITU-T and IEEE forums and 400Gb/s and 1Tb/s rates per DWDM channel systems has been under intensive investigation which are expected to be standardized within next couple of years.To facilitate the implementation of 400GbE and 1TbE technologies, the new advanced modulation scheme combined with advanced forward error correction code should be proposed. Instead of using traditional QAM, we prefer to use some other modulation techniques, which are more suitable for current coherent optical transmission systems and can also deal with the channel impairments. In this dissertation, we target at improving the channel capacity by designing the new modulation formats. For the first part of the dissertation, we first describe the optimal signal constellation design algorithm (OSCD), which is designed by placing constellation points onto a two dimensional space. Then, we expand the OSCD onto multidimensional space and design its corresponding mapping rule. At last, we also develop the OSCD algorithm for different channel scenario in order to make the constellation more tolerant to different channel impairments. We propose the LLR-OSCD for linear phase noise dominated channel and NL-OSCD for nonlinear phase noise dominated channel including both self-phase modulation (SPM) and cross-phase modulation (XPM) cases. For the second part of the dissertation, we target at probability shaping of the constellation sets (non-uniform signaling). In the conventional data transmission schemes, the probability of each point in a given constellation is transmitted equally likely and the number of constellation sets is set to 2!. If the points with low energy are transmitted with larger probability then the others with large energy, the non- uniform scheme can achieve higher energy efficiency. Meanwhile, this scheme may be more suitable for optical communication because the transmitted points with large probabilities, which have small energy, suffer less nonlinearity. Both the Monte Carlo simulations and experiment demonstration of both OSCD and non-uniform signaling schemes indicate that our proposed signal constellation significantly outperforms QAM, IPQ, and sphere-packing based signal constellations.

This thesis investigates channel-coded physical layer network coding, in which the relay directly transforms the noisy superimposed channel-coded packets received from the two end nodes, to the network-coded combination of the source packets. This is in contrast to the traditional multiple-access problem, in which the goal is to obtain each message explicitly at the relay. Here, the end nodes $A$ and $B$ choose their symbols, $S_A$ and $S_B$, from a small non-binary field, $\mathbb{F}$, and use non-binary PSK constellation mapper during the transmission phase. The relay then directly decodes the network-coded combination ${aS_A+bS_B}$ over $\mathbb{F}$ from the noisy superimposed channel-coded packets received from two end nodes. Trying to obtain $S_A$ and $S_B$ explicitly at the relay is overly ambitious when the relay only needs $aS_B+bS_B$. For the binary case, the only possible network-coded combination, ${S_A+S_B}$ over the binary field, does not offer the best performance in several channel conditions. The advantage of working over non-binary fields is that it offers the opportunity to decode according to multiple decoding coefficients $(a,b)$. As only one of the network-coded combinations needs to be successfully decoded, a key advantage is then a reduction in error probability by attempting to decode against all choices of decoding coefficients. In this thesis, we compare different constellation mappers and prove that not all of them have distinct performance in terms of frame error rate. Moreover, we derive a lower bound on the frame error rate performance of decoding the network-coded combinations at the relay. Simulation results show that if we adopt concatenated Reed-Solomon and convolutional coding or low density parity check codes at the two end nodes, our non-binary constellations can outperform the binary case significantly in the sense of minimizing the frame error rate and, in particular, the ternary constellation has the best frame error rate performance among all considered cases.

This thesis investigates channel-coded physical layer network coding, in which the relay directly transforms the noisy superimposed channel-coded packets received from the two end nodes, to the network-coded combination of the source packets. This is in contrast to the traditional multiple-access problem, in which the goal is to obtain each message explicitly at the relay. Here, the end nodes $A$ and $B$ choose their symbols, $S_A$ and $S_B$, from a small non-binary field, $\mathbb{F}$, and use non-binary PSK constellation mapper during the transmission phase. The relay then directly decodes the network-coded combination ${aS_A+bS_B}$ over $\mathbb{F}$ from the noisy superimposed channel-coded packets received from two end nodes. Trying to obtain $S_A$ and $S_B$ explicitly at the relay is overly ambitious when the relay only needs $aS_B+bS_B$. For the binary case, the only possible network-coded combination, ${S_A+S_B}$ over the binary field, does not offer the best performance in several channel conditions. The advantage of working over non-binary fields is that it offers the opportunity to decode according to multiple decoding coefficients $(a,b)$. As only one of the network-coded combinations needs to be successfully decoded, a key advantage is then a reduction in error probability by attempting to decode against all choices of decoding coefficients. In this thesis, we compare different constellation mappers and prove that not all of them have distinct performance in terms of frame error rate. Moreover, we derive a lower bound on the frame error rate performance of decoding the network-coded combinations at the relay. Simulation results show that if we adopt concatenated Reed-Solomon and convolutional coding or low density parity check codes at the two end nodes, our non-binary constellations can outperform the binary case significantly in the sense of minimizing the frame error rate and, in particular, the ternary constellation has the best frame error rate performance among all considered cases.

On sait depuis vingt ans maintenant qu'un ordinateur quantique permettrait de résoudre en temps polynomial plusieurs problèmes considérés comme difficiles dans le modèle classique de calcul, comme la factorisation ou le logarithme discret. Entre autres, un tel ordinateur mettrait à mal tous les systèmes de chiffrement à clé publique actuellement utilisés en pratique, mais sa réalisation se heurte, entre autres, aux phénomènes de décohérence qui viennent entacher l'état des qubits qui le constituent. Pour protéger ces qubits, on utilise des codes correcteurs quantiques, qui doivent non seulement être performants mais aussi munis d'un décodage très rapide, sous peine de voir s'accumuler les erreurs plus vite qu'on ne peut les corriger. Une solution très prometteuse est fournie par des équivalents quantiques des codes LDPC (Low Density Parity Check, à matrice de parité creuse). Ces codes classiques offrent beaucoup d'avantages : ils sont faciles à générer, rapides à décoder (grâce à un algorithme de décodage itératif) et performants. Mais leur version quantique se heurte (entre autres) à deux problèmes. On peut voir un code quantique comme une paire de codes classiques, dont les matrices de parité sont orthogonales entre elles. Le premier problème consiste alors à construire deux « bons » codes qui vérifient cette propriété. L'autre vient du décodage : chaque ligne de la matrice de parité d'un des codes fournit un mot de code de poids faible pour le second code. En réalité, dans un code quantique, les erreurs correspondantes sont bénignes et n'affectent pas le système, mais il est difficile d'en tenir compte avec l'algorithme de décodage itératif usuel. On étudie dans un premier temps une construction existante, basée sur un produit de deux codes classiques. Cette construction, qui possède de bonnes propriétés théoriques (dimension et distance minimale), s'est avérée décevante dans les performances pratiques, qui s'expliquent par la structure particulière du code produit. Nous proposons ensuite plusieurs variantes de cette construction, possédant potentiellement de bonnes propriétés de correction. Ensuite, on étudie des codes dits q-Aires~: ce type de construction, inspiré des codes classiques, consiste à agrandir un code LDPC existant en augmentant la taille de son alphabet. Cette construction, qui s'applique à n'importe quel code quantique 2-Régulier (c'est-À-Dire dont les matrices de parité possèdent exactement deux 1 par colonne), a donné de très bonnes performances dans le cas particulier du code torique. Ce code bien connu se décode usuellement très bien avec un algorithme spécifique, mais mal avec l'algorithme usuel de propagation de croyances. Enfin, un équivalent quantique des codes spatialement couplés est proposé. Cette idée vient également du monde classique, où elle améliore de façon spectaculaire les performances des codes LDPC : le décodage s'effectue en temps quasi-Linéaire et atteint, de manière prouvée, la capacité des canaux symétriques à entrées binaires. Si dans le cas quantique, la preuve éventuelle reste encore à faire, certaines constructions spatialement couplées ont abouti à d'excellentes performances, bien au-Delà de toutes les autres constructions de codes LDPC quantiques proposées jusqu'à présent. / Quantum information is a developping field of study with various applications (in cryptography, fast computing, ...). Its basic element, the qubit, is volatile : any measurement changes its value. This also applies to unvolontary measurements due to an imperfect insulation (as seen in any practical setting). Unless we can detect and correct these modifications, any quantum computation is bound to fail. These unwanted modifications remind us of errors that can happen in the transmission of a (classical) message. These errors can be accounted for with an error-Correcting code. For quantum errors, we need to set quantum error-Correcting codes. In order to prevent the clotting of errors that cannot be compensated, these quantum error-Correcting codes need to be both efficient and fast. Among classical error-Correcting codes, Low Density Parity Check (LDPC) codes provide many perks: They are easy to create, fast to decode (with an iterative decoding algorithme, known as belief propagation) and close to optimal. Their quantum equivalents should then be good candidates, even if they present two major drawbacks (among other less important ones). A quantum error correction code can be seen as a combination of two classical codes, with orthogonal parity-Check matrices. The first issue is the building of two efficient codes with this property. The other is in the decoding: each row of the parity-Check matrix from one code gives a low-Weight codeword of the other code. In fact, with quantum codes, corresponding errors do no affect the system, but are difficult to account for with the usual iterative decoding algorithm. In the first place, this thesis studies an existing construction, based on the product of two classical codes. This construction has good theoritical properties (dimension and minimal distance), but has shown disappointing practical results, which are explained by the resulting code's structure. Several variations, which could have good theoritical properties are also analyzed but produce no usable results at this time. We then move to the study of q-Ary codes. This construction, derived from classical codes, is the enlargement of an existing LDPC code through the augmentation of its alphabet. It applies to any 2-Regular quantum code (meaning with parity-Check matrices that have exactly two ones per column) and gives good performance with the well-Known toric code, which can be easily decoded with its own specific algorithm (but not that easily with the usual belief-Propagation algorithm). Finally this thesis explores a quantum equivalent of spatially coupled codes, an idea also derived from the classical field, where it greatly enhances the performance of LDPC codes. A result which has been proven. If, in its quantum form, a proof is still not derived, some spatially-Coupled constructions have lead to excellent performance, well beyond other recent constuctions.