A Hybrid Vector Quantization Combining a Tree Structure and a Voronoi Diagram

Pseudocode 2

Input: an input vector x, a root node of tree structure root, and a set of Voronoi regions V

Output: an optimal codeword 𝑐̃

Greedy search algorithm:

(1)  Project x to 𝑆_𝑏, and denote the projected vector as 𝑥

(2)  Call 𝑉(𝑐^′_𝑖) = 𝑇𝑟𝑒𝑒𝑆𝑒𝑎𝑟𝑐ℎ(𝑥,𝑟𝑜𝑜𝑡) to find a Voronoi region

(3)  Call 𝑐̃ = 𝐺𝑟𝑒𝑒𝑑𝑦𝑅𝑖𝑝𝑝𝑙𝑒(𝑥,𝑉(𝑐^′_𝑖),Θ,∞) to find an optimal codeword with a

    predefined number of ripples, Θ, and set the minimal distance is as infinite

(4)  Return 𝑐̃

Function 𝑇𝑟𝑒𝑒𝑆𝑒𝑎𝑟𝑐ℎ(𝑥^′,𝑛𝑜𝑑𝑒)

(5)  If 𝑥^′−𝑛𝑜𝑑𝑒.𝑐𝑒𝑛𝑡𝑟𝑜𝑖𝑑_𝐿<𝑥^′−𝑛𝑜𝑑𝑒.𝑐𝑒𝑛𝑡𝑟𝑜𝑖𝑑_𝑅 then {

(6)   If 𝑛𝑜𝑑𝑒.𝑠𝑜𝑛_𝐿=𝜙 then

(7)     Return a Voronoi region 𝑛𝑜𝑑𝑒.𝐼𝑛𝑖𝑡𝑖𝑎𝑙𝐶𝑜𝑑𝑒𝑤𝑜𝑟𝑑_𝐿

(8)   Else

(9)     Call 𝑇𝑟𝑒𝑒𝑆𝑒𝑎𝑟𝑐ℎ(𝑥^′, 𝑛𝑜𝑑𝑒.𝑠𝑜𝑛_𝐿)

(10)  }

(11)  Else {

(12)   If 𝑛𝑜𝑑𝑒.𝑠𝑜𝑛_𝑅=𝜙 then

(13)     Return a Voronoi region 𝑛𝑜𝑑𝑒.𝐼𝑛𝑖𝑡𝑖𝑎𝑙𝐶𝑜𝑑𝑒𝑤𝑜𝑟𝑑_𝑅

(14)   Else

(15)     Call 𝑇𝑟𝑒𝑒𝑆𝑒𝑎𝑟𝑐ℎ(𝑥^′, 𝑛𝑜𝑑𝑒.𝑠𝑜𝑛_𝑅)

(16)  }

Function 𝐺𝑟𝑒𝑒𝑑𝑦𝑅𝑖𝑝𝑝𝑙𝑒(𝑥^′, 𝑉(𝑐^′), 𝜃, 𝜀)

(17)  If 𝜃 > 1 then {

(18)   Find a 𝑐𝑒𝑛𝑡𝑟𝑜𝑖𝑑_𝑖 such that 𝑥^′−𝑉(𝑐^′).𝑐𝑒𝑛𝑡𝑟𝑜𝑖𝑑_𝑖 is minimized

(19)   Let Ω be the neighbors in group 𝑐𝑒𝑛𝑡𝑟𝑜𝑖𝑑_𝑖 of Voronoi region 𝑉(𝑐^′)

(20)  Find a 𝜔∈Ω such that the distance, Δ, between 𝑥^′ and the codeword of 𝜔 is minimized

(21)   If 𝜀>Δ then {

(22)      𝑐̂=𝐺𝑟𝑒𝑒𝑑𝑦𝑅𝑖𝑝𝑝𝑙𝑒(𝑥^′, 𝜔, 𝜃−1, Δ)

(23)     Return 𝑐̂

(24)   }

(25)  }

(26)  Return 𝑐^′