We consider a networkcoding problem where the destination wants to recover the sum of the signals (Gaussian random variables or random finite field elements) at all the source nodes, but the sum must be kept secret f...
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ISBN:
(纸本)9781665421607;9781665421591
We consider a networkcoding problem where the destination wants to recover the sum of the signals (Gaussian random variables or random finite field elements) at all the source nodes, but the sum must be kept secret from an eavesdropper that can wiretap on a subset of edges. This setting arises naturally in sensor networks, where the secrecy of the sum of the signals (e.g. weights, gradients) may be desired. While the case for finite field can be solved, the case for Gaussian random variables is surprisingly difficult. We give a simple conjecture on the necessary and sufficient condition under which such secret computation is possible for the Gaussian case, and prove the conjecture when the number of wiretapped edges is at most 2.
In arithmetic network coding (ANC), finite field operations are replaced by real or complex arithmetic operations. This has applications in physical layer networkcoding or in multi-resolution multicast, where users w...
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ISBN:
(纸本)9781467390538
In arithmetic network coding (ANC), finite field operations are replaced by real or complex arithmetic operations. This has applications in physical layer networkcoding or in multi-resolution multicast, where users with a higher download capacity experience a better quality of service. A major problem in random ANC is that the condition number of the network grows quickly with the network size, hence, noise can cause many errors in larger networks. An efficient solution for error correction in networkcoding is subspace coding. However, existing subspace coding solutions are based on finite field operations and cannot be used with ANC. Some of the difficulties of applying subspace coding to ANC are: (i) there are infinite subspaces to choose from;(ii) the effect of noise is on all links, where the noise strength increases hop by hop;and (iii) the decoding algorithms of ANC and subspace decoding are very different. In this work, we develop a subspace arithmetic network coding framework. We first model the network noise from which we then develop a decoding algorithm. Our simulation results show the success of our proposed method over conventional ANC.
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