Palacio Baus, Kenneth Samuel2019-02-062019-02-062018978-153864780-62157-8095http://dspace.ucuenca.edu.ec/handle/123456789/31929https://www.scopus.com/record/display.uri?eid=2-s2.0-85052438684&doi=10.1109%2fISIT.2018.8437657&origin=inward&txGid=54e86b55e00627408a2d18d0d4234f34A primitive relay channel (PRC) has one source (S) communicating a message to one destination (D) with the help of a relay (R). The link between R and D is considered to be noiseless, of finite capacity, and parallel to the link between S and (R,D). Prior work has established, for any fixed number of channel uses, the minimal R-D link rate needed so that the overall S-D message rate equals the zero-error single-input multiple output outer bound (Problem 1). The zero-error relaying scheme was expressed as a coloring of a carefully defined 'relaying compression graph'. It is shown here that this relaying compression graph for n channel uses is not obtained as a strong product from its n = 1 instance. Here we define a new graph, the 'primitive relaying graph' and a new 'special strong product' such that the n-channel use primitive relaying graph corresponds to the n-fold special strong product of the n = 1 graph. We show how the solution to Problem 1 can be obtained from this new primitive relaying graph directly. Further study of this primitive relaying graph has the potential to highlight the structure of optimal codes for zero-error relaying. © 2018 IEEE.A primitive relay channel (PRC) has one source (S) communicating a message to one destination (D) with the help of a relay (R). The link between R and D is considered to be noiseless, of finite capacity, and parallel to the link between S and (R,D). Prior work has established, for any fixed number of channel uses, the minimal R-D link rate needed so that the overall S-D message rate equals the zero-error single-input multiple output outer bound (Problem 1). The zero-error relaying scheme was expressed as a coloring of a carefully defined 'relaying compression graph'. It is shown here that this relaying compression graph for n channel uses is not obtained as a strong product from its n = 1 instance. Here we define a new graph, the 'primitive relaying graph' and a new 'special strong product' such that the n-channel use primitive relaying graph corresponds to the n-fold special strong product of the n = 1 graph. We show how the solution to Problem 1 can be obtained from this new primitive relaying graph directly. Further study of this primitive relaying graph has the potential to highlight the structure of optimal codes for zero-error relaying. © 2018 IEEE.es-ESZero-Error ProblemsZero-Error Relaying SchemePrimitive Relaying GraphRelaying Compression GraphARTÍCULO DE CONFERENCIA10.1109/ISIT.2018.8437657