On Scaling Rules for Energy of VLSI Polar Encoders and Decoders
Abstract
It is shown that all polar encoding schemes of rate R>12 of block length N implemented according to the Thompson VLSI model must take energy E(N3/2). 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>2/3 must take energy E(N3/2), 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 = (1-R/C)-1, have energy that scales as (5.325) E O(7.054()).