2015/10/15 by Afşer, Hüseyin, Deliç, Hakan
#FOS: Computer and information sciences #Information Theory (cs.IT)
paper · doi:10.48550/arxiv.1510.04489
We introduce the design of a set of code sequences \ \mathscr Cn(m) : n≥ 1, m ≥ 1 \, with memory order m and code-length N=O(ϕn), where ϕ∈ (1,2] is the largest real root of the polynomial equation F(m,ρ)=ρm-ρm-1-1 and ϕ is decreasing in m. \ \mathscr Cn(m)\ is based on the channel polarization idea, where \ \mathscr Cn(1) \ coincides with the polar codes presented by Arıkan and can be encoded and decoded with complexity O(N log N). \ \mathscr Cn(m) \ achieves the symmetric capacity, I(W), of an arbitrary binary-input, discrete-output memoryless channel, W, for any fixed m and its encoding and decoding complexities decrease with growing m. We obtain an achievable bound on the probability of block-decoding error, Pe, of \ \mathscr Cn(m) \ and showed that Pe = O (2-Nβ ) is achievable for β< (ϕ-1)/(1+m(ϕ-1)).