On generalized LDPC codes for ultra reliable communication

Ultra reliable low latency communication (URLLC) is an important feature in future mobile communication systems, as they will require high data rates, large system capacity and massive device connectivity [11]. To meet such stringent requirements, many error-correction codes (ECC)s are being investigated; turbo codes, low density parity check (LDPC) codes, polar codes and convolutional codes [70, 92, 38], among many others. In this work, we present generalized low density parity check (GLDPC) codes as a promising candidate for URLLC. Our proposal is based on a novel class of GLDPC code ensembles, for which new analysis tools are proposed. We analyze the trade-o_ between coding rate and asymptotic performance of a class of GLDPC codes constructed by including a certain fraction of generalized constraint (GC) nodes in the graph. To incorporate both bounded distance (BD) and maximum likelihood (ML) decoding at GC nodes into our analysis without resorting to multi-edge type of degree distribution (DD)s, we propose the probabilistic peeling decoding (P-PD) algorithm, which models the decoding step at every GC node as an instance of a Bernoulli random variable with a successful decoding probability that depends on both the GC block code as well as its decoding algorithm. The P-PD asymptotic performance over the BEC can be efficiently predicted using standard techniques for LDPC codes such as Density evolution (DE) or the differential equation method. We demonstrate that the simulated P-PD performance accurately predicts the actual performance of the GLPDC code under ML decoding at GC nodes. We illustrate our analysis for GLDPC code ensembles with regular and irregular DDs. This design methodology is applied to construct practical codes for URLLC. To this end, we incorporate to our analysis the use of quasi-cyclic (QC) structures, to mitigate the code error floor and facilitate the code very large scale integration (VLSI) implementation. Furthermore, for the additive white Gaussian noise (AWGN) channel, we analyze the complexity and performance of the message passing decoder with various update rules (including standard full-precision sum product and min-sum algorithms) and quantization schemes. The block error rate (BLER) performance of the proposed GLDPC codes, combined with a complementary outer code, is shown to outperform a variety of state-of-the-art codes, for URLLC, including LDPC codes, polar codes, turbo codes and convolutional codes, at similar complexity rates.Programa Oficial de Doctorado en Multimedia y ComunicacionesPresidente: Juan José Murillo Fuentes.- Secretario: Matilde Pilar Sánchez Fernández.- Vocal: Javier Valls Coquilla

VLSI Decoder Architecture for High Throughput, Variable Block-size and Multi-rate LDPC Codes

A low-density parity-check (LDPC) decoder architecture that supports variable block sizes and multiple code rates is presented. The proposed architecture is based on the structured quasi-cyclic (QC-LDPC) codes whose performance compares favorably with that of randomly constructed LDPC codes for short to moderate block sizes. The main contribution of this work is to address the variable block-size and multirate decoder hardware complexity that stems from the irregular LDPC codes. The overall decoder, which was synthesized, placed and routed on TSMC 0.13-micron CMOS technology with a core area of 4.5 square millimeters, supports variable code lengths from 360 to 4200 bits and multiple code rates between 1/4 and 9/10. The average throughput can achieve 1 Gbps at 2.2 dB SNR.NokiaNational Science Foundatio

Compute-and-Forward Relay Networks with Asynchronous, Mobile, and Delay-Sensitive Users

We consider a wireless network consisting of multiple source nodes, a set of relays and a destination node. Suppose the sources transmit their messages simultaneously to the relays and the destination aims to decode all the messages. At the physical layer, a conventional approach would be for the relay to decode the individual message one at a time while treating rest of the messages as interference. Compute-and-forward is a novel strategy which attempts to turn the situation around by treating the interference as a constructive phenomenon. In compute-and-forward, each relay attempts to directly compute a combination of the transmitted messages and then forwards it to the destination. Upon receiving the combinations of messages from the relays, the destination can recover all the messages by solving the received equations. When identical lattice codes are employed at the sources, error correction to integer combination of messages is a viable option by exploiting the algebraic structure of lattice codes. Therefore, compute-and-forward with lattice codes enables the relay to manage interference and perform error correction concurrently. It is shown that compute-and-forward exhibits substantial improvement in the achievable rate compared with other state-of-the-art schemes for medium to high signal-to-noise ratio regime. Despite several results that show the excellent performance of compute-and-forward, there are still important challenges to overcome before we can utilize compute-and- forward in practice. Some important challenges include the assumptions of \perfect timing synchronization "and \quasi-static fading", since these assumptions rarely hold in realistic wireless channels. So far, there are no conclusive answers to whether compute-and-forward can still provide substantial gains even when these assumptions are removed. When lattice codewords are misaligned and mixed up, decoding integer combination of messages is not straightforward since the linearity of lattice codes is generally not invariant to time shift. When channel exhibits time selectivity, it brings challenges to compute-and-forward since the linearity of lattice codes does not suit the time varying nature of the channel. Another challenge comes from the emerging technologies for future 5G communication, e.g., autonomous driving and virtual reality, where low-latency communication with high reliability is necessary. In this regard, powerful short channel codes with reasonable encoding/decoding complexity are indispensable. Although there are fruitful results on designing short channel codes for point-to-point communication, studies on short code design specifically for compute-and-forward are rarely found. The objective of this dissertation is threefold. First, we study compute-and-forward with timing-asynchronous users. Second, we consider the problem of compute-and- forward over block-fading channels. Finally, the problem of compute-and-forward for low-latency communication is studied. Throughout the dissertation, the research methods and proposed remedies will center around the design of lattice codes in order to facilitate the use of compute-and-forward in the presence of these challenges