On Multiplicative Matrix Channels over Finite Chain Rings

  • Roberto W. Nóbrega Federal Institute of Santa Catarina
  • Chen Feng University of British Columbia (Okanagan Campus)
  • Danilo Silva Federal University of Santa Catarina
  • Bartolomeu F. Uchôa-Filho Federal University of Santa Catarina
Keywords: Channel capacity, discrete memoryless channel, finite chain ring, multiplicative matrix channel, physical-layer network coding

Abstract

Motivated by physical-layer network coding, this paper considers communication in multiplicative matrix channels over finite chain rings. Such channels are defined by the law Y = AX, where X and Y are the input and output matrices, respectively, and A is called the transfer matrix. It is assumed a coherent scenario in which the instances of the transfer matrix are unknown to the transmitter, but available to the receiver. It is also assumed a memoryless channel, and that A and X are independent. Besides that, no restrictions on the statistics of A are imposed. As contributions, a closed-form expression for the channel capacity is obtained, and a coding scheme for the channel is proposed. It is then shown that the scheme can achieve the capacity with polynomial time complexity and can provide correcting guarantees under a worst-case channel model. The results in the paper extend the corresponding ones for finite fields.
Published
17-09-2017
How to Cite
Nóbrega, R., Feng, C., Silva, D., & Uchôa-Filho, B. (2017). On Multiplicative Matrix Channels over Finite Chain Rings. Journal of Communication and Information Systems, 32(1). https://doi.org/10.14209/jcis.2017.10
Section
Regular Papers