Energy complexity of polar codes

Sequences of VLSI circuits implemented according to the Thompson VLSI model that compute encoding and decoding functions, called coding schemes, are classified according to the rate at which their associated block error probability scales with block length N. It is shown that coding schemes for binary symmetric channels with probability of error that scales as O(f(N)) must have encoding and decoding energy that scales at least as Ω(N√(-ln f (N))). Polar coding schemes of rate greater than 1/2 are shown to have encoding and decoding energy that scales at least as Ω(N3/2). This lower bound is achievable up to polylogarithmic factors on a mesh-network.