The structure of polarized channels via explicit parameters
| Autor: | Naveen Goela |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Channel dispersion
020206 networking & telecommunications 02 engineering and technology Polarization (waves) 01 natural sciences Information density Combinatorics 0103 physical sciences 0202 electrical engineering electronic engineering information engineering Polar Atomic physics Algebraic number 010306 general physics Mathematics Communication channel |
| Zdroj: | Allerton |
| Popis: | The polarization of the BSC(γ 1 ) with a BSC(γ 2 ) is characterized explicitly for γ 1 , γ 2 ∈ [0, 1/2]. The polarization yields a channel W− which is a BSC(λ), and a channel W+ which is composed of a BSC(ξ) with probability 1 − λ and a BSC(ϕ) with probability λ. The parameters λ, ξ and ϕ are functions of γ 1 and γ 2 . For a general binary-input, output-symmetric, discrete, memoryless (BMS) channel W, a simple method is identified for constructing polar codes based on the fact that each polarized channel is defined by a mutual information profile, and is comprised of sub-channel components, similar to results by [Pedarsani et al., 2011; Tal and Vardy, 2013]. Algebraic polar transforms may be applied recursively to each sub-channel component. As an example, polar codes are constructed for a hybrid BMS channel with an erasure probability ϵ, a bit-flip probability γ, and capacity C(ϵ, γ) = (1 − ϵ)(1 − h b (γ)) where h b (x) ≜ −x log 2 (x)−(1−x) log 2 (1−x). Based on the structure of polarization via explicit parameters, relations regarding the information density and channel dispersion V (W) are analyzed for polarized channels, including the super-martingale property of V (W). The analysis depends on second-order terms involving the function ψ(x) ≜ x log 2 2 x + (1 − x) log 2 2(1 − x). |
| Databáze: | OpenAIRE |
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