### A Pluto.jl notebook ###
# v0.17.2

# using Markdown
# using InteractiveUtils

# ╔═╡ d2056fd0-5419-11ec-2226-0b24c663de65
begin
	using Interpolations
end

# ╔═╡ 2c06b5c1-0345-444f-9664-338a60fedc83
#=╠═╡ notebook_exclusive
begin
	using BenchmarkTools
	using PlutoUtils
	using PlotlyBase
end
  ╠═╡ notebook_exclusive =#

# ╔═╡ 35450d8d-cda5-46ba-884e-636abf023ac1
abstract type CapacityComputationType end

# ╔═╡ a1158d4b-38cc-4c9b-a949-e94e98c2b5f6
"""
	DVBS2x <: CapacityComputationType
Structure used to dispatch on `speff2snr` and `snr2speff` to decide the method to use for the computation

See also: [`Shannon`](@ref), [`speff2snr`](@ref), [`snr2speff`](@ref)
"""
struct DVBS2x <: CapacityComputationType end

# ╔═╡ 94032874-a85b-4632-bc24-c8c0154b518a
"""
	Shannon <: CapacityComputationType
Structure used to dispatch on `speff2snr` and `snr2speff` to decide the method to use for the computation

See also: [`DVBS2x`](@ref), [`speff2snr`](@ref), [`snr2speff`](@ref)
"""
struct Shannon <: CapacityComputationType end

# ╔═╡ 4d74427d-21e3-4736-ab29-ef65c7ea0490
Base.broadcastable(c::CapacityComputationType) = Ref(c)

# ╔═╡ 5907b0b7-f81b-4cc3-a585-8f52fd191bae
# Thresholds 1:5 are for VLSNR, and 4:5 have a spreading factor of 2
# We put -.1 instead of 0 on the first point to avoid errors in case ones provide speff2snr with exactly 0
const dvbs2x_thresholds_linear = [0.102329299,0.147910839,0.245470892,0.323593657,0.424619564,0.5188000389,0.5821032178,0.6266138647,0.751622894,0.9332543008,1.051961874,1.258925412,1.396368361,1.671090614,2.041737945,2.529297996,2.937649652,2.971666032,3.25836701,3.548133892,3.953666201,4.518559444,4.83058802,5.508076964,6.45654229,6.886522963,6.966265141,7.888601176,8.452788452,9.354056741,10.49542429,11.61448614,12.67651866,12.88249552,14.48771854,14.96235656,16.48162392,18.74994508,20.18366364,23.1206479,25.00345362,30.26913428,35.2370871,38.63669771,45.18559444,49.88844875,52.96634439,64.5654229,72.27698036,76.55966069,90.57326009]

# ╔═╡ 37772abb-c600-4beb-a92e-7da3c3021370
# Spectral Efficiencies related to the DVBS2x MODCODs
const dvbs2x_modcod_speff =[0.095000,0.116111,0.184889,0.225975,0.333333,0.434841,0.490243,0.567805,0.656448,0.789412,0.889135,0.988858,1.088581,1.188304,1.322253,1.487473,1.587196,1.647211,1.713601,1.779991,1.972253,2.10485,2.193247,2.370043,2.458441,2.524739,2.635236,2.637201,2.745734,2.856231,2.966728,3.077225,3.165623,3.289502,3.300184,3.510192,3.620536,3.703295,3.841226,3.951571,4.206428,4.338659,4.603122,4.735354,4.933701,5.06569,5.241514,5.417338,5.593162,5.768987,5.900855]

# ╔═╡ 27cda06f-de16-47f6-be79-324963b155c9
const n_MODCODS_DVBS2x = length(dvbs2x_thresholds_linear)

# ╔═╡ f03f7ebb-dad0-4766-8615-afde6478f59d
# Find the minimum SNR needed for a MODCOD that has at least the specified spectral efficiency
const _dvbs2x_itp_speff = LinearInterpolation((dvbs2x_modcod_speff,),1:n_MODCODS_DVBS2x; extrapolation_bc = 1)

# ╔═╡ 4b14629a-b25f-4f3c-94bd-14e77c044695
"""
	speff2snr(DVBS2x(), η)
	speff2snr(Shannon(), η)
Computes the minimum SNR [linear] that is required to achieve the target spectral efficiency `η` [b/s/Hz].

The first argument specifies whether to use the DVBS2x thresholds or the Shannon formula for the computation

See also: [`DVBS2x`](@ref), [`Shannon`](@ref), [`snr2speff`](@ref)
"""
speff2snr(::DVBS2x, η) = η > dvbs2x_modcod_speff[end] ? NaN : dvbs2x_thresholds_linear[floor(Int,_dvbs2x_itp_speff(η))]

# ╔═╡ 1f389615-64d5-4084-b4a7-e7838a19ff9b
# Find the spectral efficiency that can be achieved with DVB-S2x modcods given a certain SNR 
const _dvbs2x_itp_snr = LinearInterpolation((dvbs2x_thresholds_linear, ), 1:n_MODCODS_DVBS2x; extrapolation_bc = n_MODCODS_DVBS2x)

# ╔═╡ 215ca230-77fd-4bbb-a4f7-8af1a0c9bcb3
"""
	snr2speff(DVBS2x(), linear_snr)
	snr2speff(Shannon(), linear_snr)
Computes the minimum the spectral efficiency `η` [b/s/Hz] that can be achieved given the input SNR [linear] `linear_snr`.

The first argument specifies whether to use the DVBS2x thresholds or the Shannon formula for the computation.

See also: [`DVBS2x`](@ref), [`Shannon`](@ref), [`speff2snr`](@ref)
"""
snr2speff(::DVBS2x, snr) = snr < dvbs2x_thresholds_linear[1] ? 0.0 : dvbs2x_modcod_speff[floor(Int,_dvbs2x_itp_snr(snr))]

# ╔═╡ 5203bbc5-4746-48cf-b209-ec618b223af4
snr2speff(::Shannon, snr_lin) = log2(1 + snr_lin)

# ╔═╡ 154d61e7-9014-4cc0-b817-3257fcfe1826
speff2snr(::Shannon, speff) = 2^(speff) - 1

# ╔═╡ 6c71d117-c2e5-4eb4-8abb-39109ffa30db
export DVBS2x, Shannon, snr2speff, speff2snr

# ╔═╡ 602c9baf-96e5-4e2d-9e84-3bf177d137e9
#=╠═╡ notebook_exclusive
a = rand(1000,1000)
  ╠═╡ notebook_exclusive =#

# ╔═╡ 039bfd43-c1e1-4086-b108-2079ce5e0453
#=╠═╡ notebook_exclusive
b = sort(vec(a))
  ╠═╡ notebook_exclusive =#

# ╔═╡ 1696f2e6-1753-41b4-b6c1-ab8038680c91
#=╠═╡ notebook_exclusive
@benchmark sort(vec($a))
  ╠═╡ notebook_exclusive =#

# ╔═╡ 03b7a36a-8a82-4834-baf1-a4114f6afca3
#=╠═╡ notebook_exclusive
@benchmark speff2snr.(Shannon(), $a)
  ╠═╡ notebook_exclusive =#

# ╔═╡ b959608b-2a49-4397-b974-9094480596ab
#=╠═╡ notebook_exclusive
@benchmark snr2speff.(Shannon(), $a)
  ╠═╡ notebook_exclusive =#

# ╔═╡ d0259918-920a-4b8e-b33d-a93da47425de
#=╠═╡ notebook_exclusive
@benchmark speff2snr.(DVBS2x(), $a)
  ╠═╡ notebook_exclusive =#

# ╔═╡ b6909885-61c0-4403-9639-c00ca7cd55e1
#=╠═╡ notebook_exclusive
@benchmark snr2speff.(DVBS2x(), $a)
  ╠═╡ notebook_exclusive =#

# ╔═╡ 080fdaa3-b9d7-4030-8bbc-88abcc5d37a3
#=╠═╡ notebook_exclusive
@benchmark snr2speff.(DVBS2x(), $b)
  ╠═╡ notebook_exclusive =#

# ╔═╡ 2f49954a-8e37-4d84-accc-f5537e734331
#=╠═╡ notebook_exclusive
snr = range(-20,20,1000)
  ╠═╡ notebook_exclusive =#

# ╔═╡ 1a6110f9-4086-43ee-8a12-26755ac0ee8a
#=╠═╡ notebook_exclusive
snr_lin = 10 .^ (snr./10)
  ╠═╡ notebook_exclusive =#

# ╔═╡ 87ca96a1-8f5a-4534-9e55-8f4bc4f0e437
#=╠═╡ notebook_exclusive
Plot(scatter(x = snr, y = snr2speff.(DVBS2x(), snr_lin)))
  ╠═╡ notebook_exclusive =#

# ╔═╡ 6c13719f-3b65-4550-88e9-6f1c5cd84394
#=╠═╡ notebook_exclusive
speff = range(0,7,1000)
  ╠═╡ notebook_exclusive =#

# ╔═╡ c68bc281-eb52-43db-b216-fa01350b932a
#=╠═╡ notebook_exclusive
snr_lin_min = speff2snr.(DVBS2x(), speff)
  ╠═╡ notebook_exclusive =#

# ╔═╡ 0dcb4a08-b8ed-4a4b-8be2-7ccda056846a
#=╠═╡ notebook_exclusive
Plot(scatter(;x=speff, y=10log10.(snr_lin_min)))
  ╠═╡ notebook_exclusive =#

# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
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[compat]
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"""

# ╔═╡ 00000000-0000-0000-0000-000000000002
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[[deps.PlutoUtils]]
deps = ["Chain", "Glob", "HypertextLiteral", "OrderedCollections", "PlutoDevMacros", "PlutoUI", "PrettyTables", "Reexport", "Requires", "StaticArrays", "UUIDs"]
git-tree-sha1 = "ab35c0427e1424d2365b0428b6296d02adb263b8"
uuid = "ed5d0301-4775-4676-b788-cf71e66ff8ed"
version = "0.5.3"

[[deps.PrettyTables]]
deps = ["Crayons", "Formatting", "Markdown", "Reexport", "Tables"]
git-tree-sha1 = "d940010be611ee9d67064fe559edbb305f8cc0eb"
uuid = "08abe8d2-0d0c-5749-adfa-8a2ac140af0d"
version = "1.2.3"

[[deps.Printf]]
deps = ["Unicode"]
uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7"

[[deps.Profile]]
deps = ["Printf"]
uuid = "9abbd945-dff8-562f-b5e8-e1ebf5ef1b79"

[[deps.REPL]]
deps = ["InteractiveUtils", "Markdown", "Sockets", "Unicode"]
uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"

[[deps.Random]]
deps = ["SHA", "Serialization"]
uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"

[[deps.Ratios]]
deps = ["Requires"]
git-tree-sha1 = "01d341f502250e81f6fec0afe662aa861392a3aa"
uuid = "c84ed2f1-dad5-54f0-aa8e-dbefe2724439"
version = "0.4.2"

[[deps.Reexport]]
git-tree-sha1 = "45e428421666073eab6f2da5c9d310d99bb12f9b"
uuid = "189a3867-3050-52da-a836-e630ba90ab69"
version = "1.2.2"

[[deps.Requires]]
deps = ["UUIDs"]
git-tree-sha1 = "4036a3bd08ac7e968e27c203d45f5fff15020621"
uuid = "ae029012-a4dd-5104-9daa-d747884805df"
version = "1.1.3"

[[deps.SHA]]
uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"

[[deps.Serialization]]
uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b"

[[deps.SharedArrays]]
deps = ["Distributed", "Mmap", "Random", "Serialization"]
uuid = "1a1011a3-84de-559e-8e89-a11a2f7dc383"

[[deps.Sockets]]
uuid = "6462fe0b-24de-5631-8697-dd941f90decc"

[[deps.SparseArrays]]
deps = ["LinearAlgebra", "Random"]
uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"

[[deps.StaticArrays]]
deps = ["LinearAlgebra", "Random", "Statistics"]
git-tree-sha1 = "3c76dde64d03699e074ac02eb2e8ba8254d428da"
uuid = "90137ffa-7385-5640-81b9-e52037218182"
version = "1.2.13"

[[deps.Statistics]]
deps = ["LinearAlgebra", "SparseArrays"]
uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"

[[deps.TOML]]
deps = ["Dates"]
uuid = "fa267f1f-6049-4f14-aa54-33bafae1ed76"

[[deps.TableTraits]]
deps = ["IteratorInterfaceExtensions"]
git-tree-sha1 = "c06b2f539df1c6efa794486abfb6ed2022561a39"
uuid = "3783bdb8-4a98-5b6b-af9a-565f29a5fe9c"
version = "1.0.1"

[[deps.Tables]]
deps = ["DataAPI", "DataValueInterfaces", "IteratorInterfaceExtensions", "LinearAlgebra", "TableTraits", "Test"]
git-tree-sha1 = "fed34d0e71b91734bf0a7e10eb1bb05296ddbcd0"
uuid = "bd369af6-aec1-5ad0-b16a-f7cc5008161c"
version = "1.6.0"

[[deps.Tar]]
deps = ["ArgTools", "SHA"]
uuid = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e"

[[deps.Test]]
deps = ["InteractiveUtils", "Logging", "Random", "Serialization"]
uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"

[[deps.UUIDs]]
deps = ["Random", "SHA"]
uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"

[[deps.UnPack]]
git-tree-sha1 = "387c1f73762231e86e0c9c5443ce3b4a0a9a0c2b"
uuid = "3a884ed6-31ef-47d7-9d2a-63182c4928ed"
version = "1.0.2"

[[deps.Unicode]]
uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"

[[deps.WoodburyMatrices]]
deps = ["LinearAlgebra", "SparseArrays"]
git-tree-sha1 = "de67fa59e33ad156a590055375a30b23c40299d3"
uuid = "efce3f68-66dc-5838-9240-27a6d6f5f9b6"
version = "0.5.5"

[[deps.Zlib_jll]]
deps = ["Libdl"]
uuid = "83775a58-1f1d-513f-b197-d71354ab007a"

[[deps.libblastrampoline_jll]]
deps = ["Artifacts", "Libdl", "OpenBLAS_jll"]
uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"

[[deps.nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"

[[deps.p7zip_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
"""

# ╔═╡ Cell order:
# ╠═d2056fd0-5419-11ec-2226-0b24c663de65
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# ╠═4b14629a-b25f-4f3c-94bd-14e77c044695
# ╠═1f389615-64d5-4084-b4a7-e7838a19ff9b
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# ╠═d0259918-920a-4b8e-b33d-a93da47425de
# ╠═b6909885-61c0-4403-9639-c00ca7cd55e1
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# ╠═2f49954a-8e37-4d84-accc-f5537e734331
# ╠═1a6110f9-4086-43ee-8a12-26755ac0ee8a
# ╠═87ca96a1-8f5a-4534-9e55-8f4bc4f0e437
# ╠═6c13719f-3b65-4550-88e9-6f1c5cd84394
# ╠═c68bc281-eb52-43db-b216-fa01350b932a
# ╠═0dcb4a08-b8ed-4a4b-8be2-7ccda056846a
# ╟─00000000-0000-0000-0000-000000000001
# ╟─00000000-0000-0000-0000-000000000002
