2 research outputs found

    On Scaling Rules for Energy of VLSI Polar Encoders and Decoders

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    It is shown that all polar encoding schemes of rate R>12R>\frac{1}{2} of block length NN implemented according to the Thompson VLSI model must take energy EΩ(N3/2)E\ge\Omega\left(N^{3/2}\right). This lower bound is achievable up to polylogarithmic factors using a mesh network topology defined by Thompson and the encoding algorithm defined by Arikan. A general class of circuits that compute successive cancellation decoding adapted from Arikan's butterfly network algorithm is defined. It is shown that such decoders implemented on a rectangle grid for codes of rate R>2/3R>2/3 must take energy EΩ(N3/2)E\ge\Omega(N^{3/2}), and this can also be reached up to polylogarithmic factors using a mesh network. Capacity approaching sequences of energy optimal polar encoders and decoders, as a function of reciprocal gap to capacity χ=(1R/C)1\chi = (1-R/C)^{-1}, have energy that scales as Ω(χ5.325)EO(χ7.05log4(χ))\Omega\left(\chi^{5.325}\right)\le E \le O\left(\chi^{7.05}\log^{4}\left(\chi\right)\right)

    Energy, Latency, and Reliability Tradeoffs in Coding Circuits

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    It is shown that fully-parallel encoding and decoding schemes with asymptotic block error probability that scales as O(f(n))O\left(f\left(n\right)\right) have Thompson energy that scales as Ω(lnf(n)n)\Omega\left(\sqrt{\ln f\left(n\right)}n\right). As well, it is shown that the number of clock cycles (denoted T(n)T\left(n\right)) required for any encoding or decoding scheme that reaches this bound must scale as T(n)lnf(n)T\left(n\right)\ge\sqrt{\ln f\left(n\right)}. Similar scaling results are extended to serialized computation. The Grover information-friction energy model is generalized to three dimensions and the optimal energy of encoding or decoding schemes with probability of block error PeP_\mathrm{e} is shown to be at least Ω(n(lnPe(n))13)\Omega\left(n\left(\ln P_{\mathrm{e}}\left(n\right)\right)^{\frac{1}{3}}\right).Comment: 13 pages, 2 figures, submitted for journal publication, submitted in part for presentation at 2016 International Symposium on Information Theor
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