List Decoding Tensor Products and Interleaved Codes

We design the first efficient algorithms and prove new combinatorial bounds for list decoding tensor products of codes and interleaved codes. We show that for {\em every} code, the ratio of its list decoding radius to its minimum distance stays unchanged under the tensor product operation (rather than squaring, as one might expect). This gives the first efficient list decoders and new combinatorial bounds for some natural codes including multivariate polynomials where the degree in each variable is bounded. We show that for {\em every} code, its list decoding radius remains unchanged under $m$-wise interleaving for an integer $m$. This generalizes a recent result of Dinur et al \cite{DGKS}, who proved such a result for interleaved Hadamard codes (equivalently, linear transformations). Using the notion of generalized Hamming weights, we give better list size bounds for {\em both} tensoring and interleaving of binary linear codes. By analyzing the weight distribution of these codes, we reduce the task of bounding the list size to bounding the number of close-by low-rank codewords. For decoding linear transformations, using rank-reduction together with other ideas, we obtain list size bounds that are tight over small fields.Comment: 32 page

Gate-Level Simulation of Quantum Circuits

While thousands of experimental physicists and chemists are currently trying to build scalable quantum computers, it appears that simulation of quantum computation will be at least as critical as circuit simulation in classical VLSI design. However, since the work of Richard Feynman in the early 1980s little progress was made in practical quantum simulation. Most researchers focused on polynomial-time simulation of restricted types of quantum circuits that fall short of the full power of quantum computation. Simulating quantum computing devices and useful quantum algorithms on classical hardware now requires excessive computational resources, making many important simulation tasks infeasible. In this work we propose a new technique for gate-level simulation of quantum circuits which greatly reduces the difficulty and cost of such simulations. The proposed technique is implemented in a simulation tool called the Quantum Information Decision Diagram (QuIDD) and evaluated by simulating Grover's quantum search algorithm. The back-end of our package, QuIDD Pro, is based on Binary Decision Diagrams, well-known for their ability to efficiently represent many seemingly intractable combinatorial structures. This reliance on a well-established area of research allows us to take advantage of existing software for BDD manipulation and achieve unparalleled empirical results for quantum simulation

Pruned Bit-Reversal Permutations: Mathematical Characterization, Fast Algorithms and Architectures

A mathematical characterization of serially-pruned permutations (SPPs) employed in variable-length permuters and their associated fast pruning algorithms and architectures are proposed. Permuters are used in many signal processing systems for shuffling data and in communication systems as an adjunct to coding for error correction. Typically only a small set of discrete permuter lengths are supported. Serial pruning is a simple technique to alter the length of a permutation to support a wider range of lengths, but results in a serial processing bottleneck. In this paper, parallelizing SPPs is formulated in terms of recursively computing sums involving integer floor and related functions using integer operations, in a fashion analogous to evaluating Dedekind sums. A mathematical treatment for bit-reversal permutations (BRPs) is presented, and closed-form expressions for BRP statistics are derived. It is shown that BRP sequences have weak correlation properties. A new statistic called permutation inliers that characterizes the pruning gap of pruned interleavers is proposed. Using this statistic, a recursive algorithm that computes the minimum inliers count of a pruned BR interleaver (PBRI) in logarithmic time complexity is presented. This algorithm enables parallelizing a serial PBRI algorithm by any desired parallelism factor by computing the pruning gap in lookahead rather than a serial fashion, resulting in significant reduction in interleaving latency and memory overhead. Extensions to 2-D block and stream interleavers, as well as applications to pruned fast Fourier transforms and LTE turbo interleavers, are also presented. Moreover, hardware-efficient architectures for the proposed algorithms are developed. Simulation results demonstrate 3 to 4 orders of magnitude improvement in interleaving time compared to existing approaches.Comment: 31 page

A resource management scheme for multi-user GFDM with adaptive modulation in frequency selective fading channels

The topic is "Low-latency communication for machine-type communication in LTE-A" and need to be specified in more detail.This final project focus on designing and evaluating a resource management scheme for a multi-user generalized frequency division multiplexing (GFDM) system, when a frequency selective fading channel and adaptive modulation is used. GFDM with adaptive subcarrier, sub-symbol and power allocation are considered. Assuming that the transmitter has a perfect knowledge of the instantaneous channel gains for all users, I propose a multi-user GFDM subcarrier, sub-symbol and power allocation algorithm to minimize the total transmit power. This work analyzes the performance of using a specific set of parameters for aligning GFDM with long term evolution (LTE) grid. The results show that the performance of the proposed algorithm using GFDM is closer to the performance of using OFDM and outperforms multiuser GFDM systems with static frequency division multiple access (FDMA) techniques which employ fixed subcarrier allocation schemes. The advantage between GFDM and OFDM is that the latency of the system can be reduced by a factor of 15 if independent demodulation is considered.El objetivo de este proyecto final es el de diseñar y evaluar un esquema para administrar los recursos de un sistema multi-usuario donde se utiliza generalized frequency division multiplexing (GFDM), cuando el canal es de frequencia de desvanecimiento selectivo y se utiliza modulación adaptiva. Consideramos un sistema GFDM con subportadora, sub-símbolo i asignación de potencia adaptiva. Asumiendo que el transmisor conoce perfectamente el estado del canal para todos los usuarios, propongo un algoritmo que asigna los recursos de forma que la potencia total de transmisión es mínima. Este trabajo analiza la eficiencia de utilizar un grupo de parámetros concretos para alinear el sistema GFDM con el sistema de LTE. Los resultados muestran que el comportamiento del algoritmo en GFDM es muy similar al de OFDM, pero mucho mayor que cuando se compara con sistemas de asignación de recursos estáticos.L’objectiu d’aquest projecte final es dissenyar i avaluar un esquema per administrar els recursos per a un sistema multi-usuari fent servir generalized frequency division multiplexing (GFDM), quan el canal es de freqüència esvaniment selectiu i es fa servir modulació adaptativa. Considerem un sistema GFDM amb subportadora, sub-símbol i assignació de potencia adaptativa. Assumint que el transmissor coneix perfectament l’estat del canal per tots els usuaris, proposo un algoritme que assigna els recursos de forma que la potencia total de transmissió es la mínima. Aquest treball analitza l’eficiència de fer servir un grup de paràmetres concrets per tal d’alinear el sistema GFDM amb el sistema de LTE. Els resultats mostren que el comportament de l’algoritme en GFDM es molt similar al de OFDM i que millora bastant els resultats quan el comparem amb sistemes d’assignament de recursos estàtics