Valerio Bioglio

Laura Luzzi, Valerio Bioglio

We study the performance of polarizing codes over a degraded symmetric wiretap channel under a total variation distance (TVD) secrecy constraint. We show that the leakage can be bounded by the sum of the TVDs of the bit-channels corresponding to the confidential and frozen bits. In the asymptotic regime, this gives a new criterion to design wiretap codes with vanishing TVD leakage. In finite blocklength, it allows us to compute lower bounds for the secrecy rate of different families of polarizing wiretap codes over a binary erasure wiretap channel.

Attilio Fiandrotti, Valerio Bioglio, Marco Grangetto et al.

A key problem in random network coding (NC) lies in the complexity and energy consumption associated with the packet decoding processes, which hinder its application in mobile environments. Controlling and hence limiting such factors has always been an important but elusive research goal, since the packet degree distribution, which is the main factor driving the complexity, is altered in a non-deterministic way by the random recombinations at the network nodes. In this paper we tackle this problem proposing Band Codes (BC), a novel class of network codes specifically designed to preserve the packet degree distribution during packet encoding, ecombination and decoding. BC are random codes over GF(2) that exhibit low decoding complexity, feature limited and controlled degree distribution by construction, and hence allow to effectively apply NC even in energy-constrained scenarios. In particular, in this paper we motivate and describe our new design and provide a thorough analysis of its performance. We provide numerical simulations of the performance of BC in order to validate the analysis and assess the overhead of BC with respect to a onventional NC scheme. Moreover, peer-to-peer media streaming experiments with a random-push protocol show that BC reduce the decoding complexity by a factor of two, to a point where NC-based mobile streaming to mobile devices becomes practically feasible.