On Multiplicative Matrix Channels over Finite Chain Rings

Roberto W. Nóbrega, Chen Feng, Danilo Silva, Bartolomeu F. Uchôa-Filho


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.


Channel capacity; discrete memoryless channel; finite chain ring; multiplicative matrix channel; physical-layer network coding

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DOI: http://dx.doi.org/10.14209/jcis.2017.10


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