Alphabet size: vector network coding outperforms scalar network coding

• Grant number: 17/10018-5
• Support Opportunities: Scholarships abroad - Research Internship - Post-doctor
• Start date: November 05, 2017
• End date: November 04, 2018
• Field of knowledge: Engineering - Electrical Engineering - Telecommunications
• Principal Investigator: Marcelo Firer
• Grantee: Jerry Anderson Pinheiro
• Supervisor: Tuvi Etzion
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Institution abroad: Technion - Israel Institute of Technology, Israel
• Associated to the scholarship: 16/01551-9 - Metrics in coding theory, BP.PD

Abstract

Communications systems based in networks may be found in several contexts, some of them, such as the public Internet, the peer-to-peer networks and the wireless ad-hoc networks, have became central in our daily lives. Network coding was recently proposed as an alternative to the traditional approach (store-and-forward) in order to provide an improvement of the network throughput. When multicast networks are considered, it is well-known that scalar linear network coding is sufficient, i.e., there exist a linear solution to the network. Essentially, such solution is a pre-established script used to transmit in the network with maximum rate. Furthermore, random linear network coding can be used with a high level of reliability if some premisses are respected. However, to obtain such linear solutions, the cardinality of the finite field must be sufficiently large, but, in general, "large enough" can be translated as "computationally infeasible". Hence, it is desirable to obtain solutions over which the field is small. Several constructions were proposed with the aim to minimize the size of the field necessary to solve determined networks. Recently, in the work entitled "Vector Network Coding Based on Subspace Codes Outperforms Scalar Linear Network Coding", two constructions based on rank and subspace codes were proposed, these codes are immersed in structures endowed with the rank and the subspace metrics, respectively. For some modifications and generalizations of the well-known combination networks, it was shown that regarding the field size, vector network coding based on the proposed constructions outperform the best scalar solutions ever produced. Many research lines arise in this direction. In this project, the objective is to analyze the possibility to extend such constructions to others networks and, to produce, using different metrics, new constructions. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

PINHEIRO, JERRY ANDERSON; MACHADO, ROBERTO ASSIS; FIRER, MARCELO. Combinatorial metrics: MacWilliams-type identities, isometries and extension property. DESIGNS CODES AND CRYPTOGRAPHY, v. 87, n. 2-3, p. 14-pg., 2019-03-01. (17/14616-4, 17/10018-5, 13/25977-7)

PINHEIRO, JERRY ANDERSON; MACHADO, ROBERTO ASSIS; FIRER, MARCELO. Combinatorial metrics: MacWilliams-type identities, isometries and extension property. DESIGNS CODES AND CRYPTOGRAPHY, v. 87, n. 2-3, SI, p. 327-340, MAR 2019. (13/25977-7, 17/14616-4, 17/10018-5)