On generalized ldpc codes for ultra reliable communications

• Autores: Yanfang Liu
• Directores de la Tesis: Pablo Martínez Olmos (dir. tes.), Tobias Koch (codir. tes.)
• Lectura: En la Universidad Carlos III de Madrid ( España ) en 2019
• Idioma: español
• Tribunal Calificador de la Tesis: Juan José Murillo Fuentes (presid.), Matilde Pilar Sánchez Fernández (secret.), Xavier Valls (voc.)
• Programa de doctorado: Programa de Doctorado en Multimedia y Comunicaciones por la Universidad Carlos III de Madrid y la Universidad Rey Juan Carlos
• Materias:
  • Matemáticas
    • Ciencia de los ordenadores
      • Código y sistemas de codificación
• Enlaces
  • Tesis en acceso abierto en: e-Archivo
• Resumen

  • URLLC is one of the key factors in the 5G of cellular mobile communications. To meet expectations for the demanding digital industry and latency-sensitive services, it requires high data rates, large system capacity and massive device connectivity. Many error-correction codes (ECCs) are being investigated to meet the stringent requirements of URLLC: turbo codes, LDPC codes, polar codes, and convolutional codes, among many others. Beyond any doubt, LDPC codes, Polar codes and their variants will be included in other new standards in the future. The state-of-the-art achievements of LDPC codes show capacity achieving performance.

    However, this requires large block length. For short block length, the error floor problem which refers to the problem that the BER performance curve does not decrease as the SNR increases, becomes relevant. Under iterative message passing decoding, the error floor of LDPC codes depends on a number of structural properties of the codes and tanner graphs, such as girth, minimum weight, weight distribution of pseudocodewords, and is higher than the one under MAP decoding. Thus, the design of error correcting codes with short block length and good performance under practical iterative decoding, as required for next-generation wireless communication systems, is still very challenging. Generalized low-density parity-check (GLDPC) codes are a promising class of codes for low latency communication. To design codes for URLLC, we propose a novel class of GLDPC code ensembles, for which new analysis tools are proposed.

    We analyze the trade-off 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. The rate of the GLDPC ensemble is bounded using classical results on linear block codes, namely Hamming bound and Varshamov bound. We study the impact of the decoding method used at GC nodes. 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 distributions (DDs), 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. Furthermore, for a class of GLDPC ensembles, 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 structures, to mitigate the code error floor and facilitate the code VLSI implementation. Furthermore for the AWGN channle, 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.