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codes.jl
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codes.jl
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# Copyright (c) 2022, 2023 Eric Sabo, Benjamin Ide
# All rights reserved.
#
# This source code is licensed under the BSD-style license found in the
# LICENSE file in the root directory of this source tree.
#############################
# constructors
#############################
"""
LDPCCode(H::fq_nmod_mat)
Return the LDPC code defined by the parity-check matrix `H`.
"""
function LDPCCode(H::CTMatrixTypes)
# TODO: remove empties
nnz, den = _density(H)
# den <= 0.01 || (@warn "LDPC codes typically expect a density of less than 1%.";)
cols, rows = _degree_distribution(H)
is_reg = true
c1 = cols[1]
for i in 2:length(cols)
c1 == cols[i] || (is_reg = false; break;)
end
if is_reg
r1 = rows[1]
for i in 2:length(rows)
r1 == rows[i] || (is_reg = false; break;)
end
end
c, r = maximum(cols), maximum(rows)
R, x = PolynomialRing(Nemo.QQ, :x)
col_poly = R(0)
for i in cols
col_poly += i * x^(i - 1)
end
col_poly = divexact(col_poly, nnz)
row_poly = R(0)
for i in rows
row_poly += i * x^(i - 1)
end
row_poly = divexact(row_poly, nnz)
C = LinearCode(H, true)
return LDPCCode(base_ring(H), C.n, C.k, C.d, C.l_bound, C.u_bound, H, nnz,
cols, rows, c, r, maximum([c, r]), den, is_reg, missing, col_poly,
row_poly, missing, [Vector{Int}() for _ in 1:C.n], [Vector{Int}() for _ in 1:C.n],
[Vector{Tuple{Int, Int}}() for _ in 1:C.n],
Dict{Int, Int}(), Dict{Int, Int}())
end
"""
LDPCCode(C::AbstractLinearCode)
Return the LDPC code given by the parity-check matrix of `C`.
"""
LDPCCode(C::AbstractLinearCode) = LDPCCode(parity_check_matrix(C))
"""
regular_LDPC_code(q::Int, n::Int, l::Int, r::Int [; seed=nothing])
Return a random regular LDPC code over `GF(q)` of length `n` with column degree `l`
and row degree `r`.
If a seed is given, i.e. `regulardLDPCCode(4, 1200, 3, 6, seed=123)`, the
results are reproducible.
"""
function regular_LDPC_code(q::Int, n::Int, l::Int, r::Int; seed::Union{Nothing, Int} = nothing)
Random.seed!(seed)
m = divexact(n * l, r)
F = if isprime(q)
GF(q)
else
factors = Nemo.factor(q)
length(factors) == 1 || throw(DomainError("There is no finite field of order $q"))
(p, t), = factors
GF(p, t, :α)
end
elems = collect(F)[2:end]
H = zero_matrix(F, m, n)
col_sums = zeros(Int, n)
for i in axes(H, 1)
ind = reduce(vcat, shuffle(filter(k -> col_sums[k] == s, 1:n)) for s in 0:l - 1)[1:r]
for j in ind
H[i, j] = rand(elems)
end
col_sums[ind] .+= 1
end
@assert all(count(.!iszero.(H[:, j])) == l for j in axes(H, 2))
@assert all(count(.!iszero.(H[i, :])) == r for i in axes(H, 1))
R, x = PolynomialRing(Nemo.QQ, :x)
C = LinearCode(H, true)
return LDPCCode(C.F, C.n, C.k, C.d, C.l_bound, C.u_bound, H, n * l, l * ones(Int, n),
r * ones(Int, m), l, r, max(l, r), r / n, true, missing, (1 // l) * x^l,
(1 // r) * x^r, missing, [Vector{Int}() for _ in 1:C.n], [Vector{Int}() for _ in 1:C.n],
[Vector{Tuple{Int, Int}}() for _ in 1:C.n], Dict{Int, Int}(), Dict{Int, Int}())
end
regular_LDPC_code(n::Int, l::Int, r::Int; seed::Union{Nothing, Int} = nothing) =
regular_LDPC_code(2, n, l, r, seed = seed)
#############################
# getter functions
#############################
"""
variable_degree_distribution(C::AbstractLDPCCode)
Return the variable node degree distribution of `C`.
"""
variable_degree_distribution(C::AbstractLDPCCode) = C.var_degs
"""
check_degree_distribution(C::AbstractLDPCCode)
Return the check node degree distribution of `C`.
"""
check_degree_distribution(C::AbstractLDPCCode) = C.check_degs
"""
degree_distributions(C::AbstractLDPCCode)
Return the variable and check node degree distributions of `C`.
"""
degree_distributions(C::AbstractLDPCCode) = C.var_degs, C.check_degs
"""
column_bound(C::AbstractLDPCCode)
Return the column bound `c` of the `(c, r)`-LDPC code `C`.
"""
column_bound(C::AbstractLDPCCode) = C.col_bound
"""
row_bound(C::AbstractLDPCCode)
Return the row bound `r` of the `(c, r)`-LDPC code `C`.
"""
row_bound(C::AbstractLDPCCode) = C.row_bound
"""
column_row_bounds(C::AbstractLDPCCode)
Return the column and row bounds `c, r` of the `(c, r)`-LDPC code `C`.
"""
column_row_bounds(C::AbstractLDPCCode) = C.col_bound, C.row_bound
"""
limited(C::AbstractLDPCCode)
Return the maximum of the row and column bounds for `C`.
"""
limited(C::AbstractLDPCCode) = C.limited
"""
density(C::AbstractLDPCCode)
Return the density of the parity-check matrix of `C`.
"""
density(C::AbstractLDPCCode) = C.density
"""
is_regular(C::AbstractLDPCCode)
Return `true` if the `C` is a regular LDPC code.
# Notes
- An LDPC is regular if all the column degrees and equal and all the row degrees are equal.
"""
is_regular(C::AbstractLDPCCode) = C.is_reg
"""
variable_degree_polynomial(C::AbstractLDPCCode)
Return the variable degree polynomial of `C`.
"""
variable_degree_polynomial(C::AbstractLDPCCode) = C.λ
"""
check_degree_polynomial(C::AbstractLDPCCode)
Return the check degree polynomial of `C`.
"""
check_degree_polynomial(C::AbstractLDPCCode) = C.ρ
#############################
# setter functions
#############################
#############################
# general functions
#############################
function _degree_distribution(H::Union{CTMatrixTypes,
MatElem{AbstractAlgebra.Generic.ResidueRingElem{fpPolyRingElem}}})
nr, nc = size(H)
cols = zeros(Int, 1, nc)
@inbounds @views @simd for i in 1:nc
# cols[i] = wt(H[:, i])
cols[i] = count(x -> !iszero(x), H[:, i])
end
rows = zeros(Int, 1, nr)
@inbounds @views @simd for i in 1:nr
# rows[i] = wt(H[i, :])
rows[i] = count(x -> !iszero(x), H[i, :])
end
return vec(cols), vec(rows)
end
function _density(H::CTMatrixTypes)
count = 0
nr, nc = size(H)
for c in 1:nc
for r in 1:nr
!iszero(H[r, c]) && (count += 1;)
end
end
return count, count / (nr * nc)
end
# TODO: make uniform with others
function show(io::IO, C::AbstractLDPCCode)
if ismissing(C.d)
if C.is_reg
println(io, "[$(C.n), $(C.k)]_$(order(C.F)) regular ($(C.col_bound), $(C.row_bound))-LDPC code with density $(C.density).")
else
println(io, "[$(C.n), $(C.k)]_$(order(C.F)) irregular $(C.limited)-limited LDPC code with density $(C.density).")
end
else
if C.is_reg
println(io, "[$(C.n), $(C.k), $(C.d)]_$(order(C.F)) regular ($(C.col_bound), $(C.row_bound))-LDPC code with density $(C.density).")
else
println(io, "[$(C.n), $(C.k), $(C.d)]_$(order(C.F)) irregular $(C.limited)-limited LDPC code with density $(C.density).")
end
end
if get(io, :compact, true)
println(io, "\nVariable degree polynomial:")
println(io, "\t", C.λ)
println(io, "Check degree polynomial:")
println(io, "\t", C.ρ)
if C.n <= 30
# was using Horig here, which is probably what I want
nr, nc = size(C.H)
println(io, "Parity-check matrix: $nr × $nc")
for i in 1:nr
print(io, "\t")
for j in 1:nc
if j != nc
print(io, "$(C.H[i, j]) ")
elseif j == nc && i != nr
println(io, "$(C.H[i, j])")
else
print(io, "$(C.H[i, j])")
end
end
end
# if !ismissing(C.weightenum)
# println(io, "\nComplete weight enumerator:")
# println(io, "\t", C.weightenum.polynomial)
# end
end
end
end
"""
degree_distributions_plot(C::AbstractLDPCCode)
Return a bar plot of the column and row degree distributions of `C`.
"""
function degree_distributions_plot(C::AbstractLDPCCode)
cols, rows = degree_distributions(C)
occurs_cols = [(i, count(==(i), cols)) for i in unique(cols)]
cols_x_data = [x for (x, _) in occurs_cols]
cols_y_data = [y for (_, y) in occurs_cols]
cols_title="Variable Nodes"
f1 = bar(cols_x_data, cols_y_data, bar_width=1, xticks=cols_x_data, yticks=cols_y_data,
legend=false, xlabel="Degree", ylabel="Occurrences", title=cols_title)
occurs_rows = [(i, count(==(i), rows)) for i in unique(rows)]
rows_x_data = [x for (x, _) in occurs_rows]
rows_y_data = [y for (_, y) in occurs_rows]
rows_title="Check Nodes"
f2 = bar(rows_x_data, rows_y_data, bar_width=1, xticks=rows_x_data, yticks=rows_y_data,
legend=false, xlabel="Degree", ylabel="Occurrences", title=rows_title)
f = Plots.plot(f1, f2, layout=(1, 2))
display(f)
return f
end
"""
girth(C::LDPCCode)
Return the girth of the Tanner graph of `C`.
An error is thrown if the maximum number of iterations is reached and
``-1`` is returned to represent infinite girth.
"""
function girth(C::LDPCCode, max_iter::Int=100)
check_adj_list, var_adj_list = _node_adjacencies(C.H)
girth_arr = zeros(Int, C.n)
Threads.@threads for vn in 1:C.n
iter = 0
not_found = true
to_check = [(0, [vn])]
while not_found
iter += 1
to_check_next = Vector{Tuple{Int, Vector{Int}}}()
for i in 1:length(to_check)
for (prev, v_arr) in (to_check[i], )
for v in v_arr
for cn in var_adj_list[v]
if cn != prev
if iter != 1 && vn ∈ check_adj_list[cn]
not_found = false
girth_arr[vn] = iter + 1
break
else
push!(to_check_next, (cn, [v2 for v2 in check_adj_list[cn] if v2 != v]))
end
end
end
!not_found && break
end
!not_found && break
end
!not_found && break
end
!not_found && break
iter += 1
iter > max_iter && error("Hit the maximum number of iterations")
isempty(to_check_next) && break
to_check = to_check_next
end
end
# println(girth_arr)
min = minimum(girth_arr)
iseven(min) || error("Computed girth to be an odd integer")
min == 0 ? (C.girth = -1;) : (C.girth = min;)
return C.girth
end
mutable struct _ACEVarNode
id::Int
parent_id::Int
lvl::Int
cum_ACE::Int
local_ACE::Int
end
mutable struct _ACECheckNode
id::Int
parent_id::Int
lvl::Int
cum_ACE::Int
end
# TODO: degree 1 nodes
# why did I make this note? is ACE defined for them differently?
"""
shortest_cycle_ACE(C::LDPCCode, v::Int)
shortest_cycle_ACE(C::LDPCCode, vs::Vector{Int})
shortest_cycle_ACE(C::LDPCCode)
Return a cycle of minimum length and minimum ACE in the Tanner graph of `C`
for the vertex `v` or vertices `vs`, in the order (ACEs, cycles). If no vertices
are given, all vertices are computed by default. The cycle `v1 -- c1 -- ... --
cn -- vn` is returned in the format `[(v1, c1), (c1, v2), ..., (cn, vn)]`.
"""
function shortest_cycle_ACE(C::LDPCCode, vs::Vector{Int})
isempty(vs) && throw(ArgumentError("Input variable node list cannot be empty"))
all(x->1 <= x <= C.n, vs) || throw(DomainError("Variable node indices must be between 1 and length(C)"))
# might not be efficient to have the or here
vs_to_do = [x for x in vs if isempty(C.ACEs_per_var_node[x]) || isempty(C.shortest_cycles[x])]
processed = false
if !isempty(vs_to_do)
processed = true
check_adj_list, var_adj_list = _node_adjacencies(C.H)
Threads.@threads for i in 1:length(vs_to_do)
# moving this inside allocates more but allows for multi-threading
check_nodes = [_ACECheckNode(j, -1, -1, -1) for j in 1:length(check_adj_list)]
var_nodes = [_ACEVarNode(j, -1, -1, -1, length(var_adj_list[j]) - 2) for j in 1:C.n]
ACEs = Vector{Int}()
cycle_lens = Vector{Int}()
cycles = Vector{Vector{Tuple{Int, Int}}}()
not_emptied = true
root = var_nodes[vs_to_do[i]]
root.lvl = 0
root.cum_ACE = root.local_ACE
queue = Deque{Union{_ACECheckNode, _ACEVarNode}}()
push!(queue, root)
while length(queue) > 0
curr = first(queue)
if isa(curr, _ACEVarNode)
for cn in var_adj_list[curr.id]
# can't pass messages back to the same node
if cn != curr.parent_id
cn_node = check_nodes[cn]
if cn_node.lvl != -1
# have seen before
push!(ACEs, curr.cum_ACE + cn_node.cum_ACE - root.local_ACE)
push!(cycle_lens, curr.lvl + cn_node.lvl + 1)
# trace the cycle from curr to root and cn_node to root
temp = Vector{Tuple{Int, Int}}()
node = cn_node
while node.lvl != 0
push!(temp, (node.parent_id, node.id))
if isodd(node.lvl)
node = var_nodes[node.parent_id]
else
node = check_nodes[node.parent_id]
end
end
reverse!(temp)
push!(temp, (cn_node.id, curr.id))
node = curr
while node.lvl != 0
push!(temp, (node.id, node.parent_id))
if isodd(node.lvl)
node = var_nodes[node.parent_id]
else
node = check_nodes[node.parent_id]
end
end
push!(cycles, temp)
# finish this level off but don't go deeper so remove children at lower level
if not_emptied
while length(queue) > 0
back = last(queue)
if back.lvl != curr.lvl
pop!(queue)
else
break
end
end
not_emptied = false
end
elseif not_emptied
cn_node.lvl = curr.lvl + 1
cn_node.parent_id = curr.id
cn_node.cum_ACE = curr.cum_ACE
push!(queue, cn_node)
end
end
end
else
for vn in check_adj_list[curr.id]
# can't pass messages back to the same node
if vn != curr.parent_id
vn_node = var_nodes[vn]
if vn_node.lvl != -1
# have seen before
push!(ACEs, curr.cum_ACE + vn_node.cum_ACE - root.local_ACE)
push!(cycle_lens, curr.lvl + vn_node.lvl + 1)
# trace the cycle from curr to root and cn_node to root
temp = Vector{Tuple{Int, Int}}()
node = vn_node
while node.lvl != 0
push!(temp, (node.parent_id, node.id))
if isodd(node.lvl)
node = var_nodes[node.parent_id]
else
node = check_nodes[node.parent_id]
end
end
reverse!(temp)
push!(temp, (vn_node.id, curr.id))
node = curr
while node.lvl != 0
push!(temp, (node.id, node.parent_id))
if isodd(node.lvl)
node = var_nodes[node.parent_id]
else
node = check_nodes[node.parent_id]
end
end
push!(cycles, temp)
# finish this level off but don't go deeper so remove children at lower level
if not_emptied
while length(queue) > 0
back = last(queue)
if back.lvl != curr.lvl
pop!(queue)
else
break
end
end
not_emptied = false
end
elseif not_emptied
vn_node.lvl = curr.lvl + 1
vn_node.parent_id = curr.id
vn_node.cum_ACE = curr.cum_ACE + vn_node.local_ACE
push!(queue, vn_node)
end
end
end
end
popfirst!(queue)
end
C.ACEs_per_var_node[vs_to_do[i]] = ACEs
C.cycle_lens[vs_to_do[i]] = cycle_lens
C.shortest_cycles[vs_to_do[i]] = cycles
end
end
vs_ACE = zeros(Int, length(vs))
cycles_vs = [Vector{Tuple{Int, Int}}() for _ in 1:length(vs)]
for i in 1:length(vs)
min, index = findmin(C.ACEs_per_var_node[vs[i]])
vs_ACE[i] = min
cycles_vs[i] = C.shortest_cycles[vs[i]][index]
end
if processed
if all(!isempty, C.cycle_lens)
girth = minimum([minimum(C.cycle_lens[i]) for i in 1:C.n])
if ismissing(C.girth)
C.girth = girth
else
if C.girth != girth
@warn "Known girth, $(C.girth), does not match just computed girth, $girth"
end
end
end
end
return vs_ACE, cycles_vs
end
shortest_cycle_ACE(C::LDPCCode, v::Int) = shortest_cycle_ACE(C, [v])[1]
shortest_cycle_ACE(C::LDPCCode) = shortest_cycle_ACE(C, collect(1:C.n))
"""
shortest_cycles(C::LDPCCode, v::Int)
shortest_cycles(C::LDPCCode, vs::Vector{Int})
shortest_cycles(C::LDPCCode)
Return all the cycles of shortest length in the Tanner graph of `C` for the vertex `v` or
vertices `vs`. If no vertices are given, all vertices are computed by default.
# Note
- The length of the shortest cycle is not necessarily the same for each vertex.
- To reduce computational complexity, the same cycle may appear under each vertex in the cycle.
"""
function shortest_cycles(C::LDPCCode, vs::Vector{Int})
# display(vs)
shortest_cycle_ACE(C, vs)
return C.shortest_cycles[vs]
# return [C.shortest_cycles[v] for v in vs]
# cycles_vs = [Vector{Tuple{Int, Int}}() for _ in 1:length(vs)]
# for (i, v) in enuemrate(vs)
# cycles_vs[i] = C.shortest_cycles[v]
# end
# isempty(vs) && throw(ArgumentError("Input variable node list cannot be empty"))
# all(x->1 <= x <= C.n, vs) || throw(DomainError("Variable node indices must be between 1 and length(C)"))
# check_adj_list, var_adj_list = _node_adjacencies(C.H)
# cycles_vs = [Vector{Vector{Tuple{Int, Int}}}() for _ in 1:length(vs)]
# Threads.@threads for i in 1:length(vs)
# # moving this inside allocates more but allows for multi-threading
# check_nodes = [_ACECheckNode(i, -1, -1, -1) for i in 1:length(check_adj_list)]
# var_nodes = [_ACEVarNode(i, -1, -1, -1, length(var_adj_list[i]) - 2) for i in 1:C.n]
# cycles = Vector{Vector{Tuple{Int, Int}}}()
# not_emptied = true
# root = var_nodes[vs[i]]
# root.lvl = 0
# queue = Deque{Union{_ACECheckNode, _ACEVarNode}}()
# push!(queue, root)
# while length(queue) > 0
# curr = first(queue)
# if isa(curr, _ACEVarNode)
# for cn in var_adj_list[curr.id]
# # can't pass messages back to the same node
# if cn != curr.parent_id
# cn_node = check_nodes[cn]
# if cn_node.lvl != -1
# # have seen before
# # trace the cycle from curr to root and cn_node to root
# temp = Vector{Tuple{Int, Int}}()
# node = cn_node
# while node.lvl != 0
# push!(temp, (node.parent_id, node.id))
# if isodd(node.lvl)
# node = var_nodes[node.parent_id]
# else
# node = check_nodes[node.parent_id]
# end
# end
# reverse!(temp)
# push!(temp, (cn_node.id, curr.id))
# node = curr
# while node.lvl != 0
# push!(temp, (node.id, node.parent_id))
# if isodd(node.lvl)
# node = var_nodes[node.parent_id]
# else
# node = check_nodes[node.parent_id]
# end
# end
# push!(cycles, temp)
# # finish this level off but don't go deeper so remove children at lower level
# if not_emptied
# while length(queue) > 0
# back = last(queue)
# if back.lvl != curr.lvl
# pop!(queue)
# else
# break
# end
# end
# not_emptied = false
# end
# elseif not_emptied
# cn_node.lvl = curr.lvl + 1
# cn_node.parent_id = curr.id
# push!(queue, cn_node)
# end
# end
# end
# else
# for vn in check_adj_list[curr.id]
# # can't pass messages back to the same node
# if vn != curr.parent_id
# vn_node = var_nodes[vn]
# if vn_node.lvl != -1
# # have seen before
# temp = Vector{Tuple{Int, Int}}()
# node = vn_node
# while node.lvl != 0
# push!(temp, (node.parent_id, node.id))
# if isodd(node.lvl)
# node = var_nodes[node.parent_id]
# else
# node = check_nodes[node.parent_id]
# end
# end
# reverse!(temp)
# push!(temp, (vn_node.id, curr.id))
# node = curr
# while node.lvl != 0
# push!(temp, (node.id, node.parent_id))
# if isodd(node.lvl)
# node = var_nodes[node.parent_id]
# else
# node = check_nodes[node.parent_id]
# end
# end
# push!(cycles, temp)
# # finish this level off but don't go deeper so remove children at lower level
# if not_emptied
# while length(queue) > 0
# back = last(queue)
# if back.lvl != curr.lvl
# pop!(queue)
# else
# break
# end
# end
# not_emptied = false
# end
# elseif not_emptied
# vn_node.lvl = curr.lvl + 1
# vn_node.parent_id = curr.id
# push!(queue, vn_node)
# end
# end
# end
# end
# popfirst!(queue)
# end
# C.shortest_cycles[vs_to_do[i]] = cycles
# cycles_vs[i] = cycles
# end
# return cycles_vs
end
shortest_cycles(C::LDPCCode, v::Int) = shortest_cycles(C, [v])[1]
shortest_cycles(C::LDPCCode) = shortest_cycles(C, collect(1:C.n))
# function shortest_cycles(C::LDPCCode)
# cycles = shortest_cycles(C, collect(1:C.n))
# girth = minimum([minimum([length(cycle) for cycle in cycles[i]]) for i in 1:C.n])
# if ismissing(C.girth)
# C.girth = girth
# else
# if C.girth != girth
# @warn "Known girth, $(C.girth), does not match just computed girth, $girth"
# end
# end
# C.shortest_cycles = filter.(x -> length(x) < 2 * girth - 2, C.shortest_cycles)
# return cycles
# end
function _progressive_node_adjacencies(H::CTMatrixTypes, vs::Vector{Int}, v_type::Symbol)
check_adj_list, var_adj_list = _node_adjacencies(H)
unique!(sort!(vs))
len = length(vs)
check_adj_lists = [deepcopy(check_adj_list) for _ in 1:len]
var_adj_lists = [deepcopy(var_adj_list) for _ in 1:len]
for i in 2:len
prev = vs[1:i - 1]
if v_type == :v
for (j, x) in enumerate(check_adj_lists[i])
check_adj_lists[i][j] = setdiff(x, prev)
end
else
for (j, x) in enumerate(var_adj_lists[i])
var_adj_lists[i][j] = setdiff(x, prev)
end
end
end
return check_adj_lists, var_adj_lists
end
function _count_cycles(C::LDPCCode)
check_adj_lists, var_adj_lists = _progressive_node_adjacencies(C.H, collect(1:C.n), :v)
lengths = [Vector{Int}() for _ in 1:C.n]
Threads.@threads for i in 1:C.n
check_nodes = [_ACECheckNode(i, -1, -1, -1) for i in 1:length(check_adj_lists[i])]
var_nodes = [_ACEVarNode(i, -1, -1, -1, length(var_adj_lists[i][i]) - 2) for i in 1:C.n]
cycle_lens = Vector{Int}()
root = var_nodes[i]
root.lvl = 0
queue = Queue{Union{_ACECheckNode,_ACEVarNode}}()
enqueue!(queue, root)
while length(queue) > 0
curr = first(queue)
if isa(curr, _ACEVarNode)
for cn in var_adj_lists[i][curr.id]
# can't pass messages back to the same node
if cn != curr.parent_id
cn_node = check_nodes[cn]
if cn_node.lvl != -1
# have seen before
push!(cycle_lens, curr.lvl + cn_node.lvl + 1)
else
cn_node.lvl = curr.lvl + 1
cn_node.parent_id = curr.id
enqueue!(queue, cn_node)
end
end
end
else
for vn in check_adj_lists[i][curr.id]
# can't pass messages back to the same node
if vn != curr.parent_id
vn_node = var_nodes[vn]
if vn_node.lvl != -1
# have seen before
push!(cycle_lens, curr.lvl + vn_node.lvl + 1)
else
vn_node.lvl = curr.lvl + 1
vn_node.parent_id = curr.id
enqueue!(queue, vn_node)
end
end
end
end
dequeue!(queue)
end
lengths[i] = cycle_lens
end
counts = Dict{Int, Int}()
lens = unique!(reduce(vcat, lengths))
for i in lens
for j in 1:C.n
if i ∈ keys(counts)
counts[i] += count(x -> x == i, lengths[j])
else
counts[i] = count(x -> x == i, lengths[j])
end
end
end
C.elementary_cycle_counts = counts
girth = minimum([isempty(lengths[i]) ? 9999999 : minimum(lengths[i]) for i in 1:C.n])
girth == 9999999 && (girth = -1)
if ismissing(C.girth)
C.girth = girth
else
if C.girth != girth
@warn "Known girth, $(C.girth), does not match just computed girth, $girth"
end
end
counts = Dict{Int, Int}()
for i in girth:2:2 * girth - 2
for j in 1:C.n
if i ∈ keys(counts)
counts[i] += count(x -> x == i, lengths[j])
else
counts[i] = count(x -> x == i, lengths[j])
end
end
end
C.short_cycle_counts = counts
return nothing
end
"""
count_short_cycles(C::LDPCCode)
Return a bar graph and a dictionary of (length, count) pairs for unique short
cycles in the Tanner graph of `C`. An empty graph and dictionary are returned
when there are no cycles.
# Note
- Short cycles are defined to be those with lengths between ``g`` and ``2g - 2``,
where ``g`` is the girth.
"""
function count_short_cycles(C::LDPCCode)
if isempty(C.short_cycle_counts) || isempty(C.elementary_cycle_counts)
_count_cycles(C)
end
len = length(C.short_cycle_counts)
x_data = [0 for _ in 1:len]
y_data = [0 for _ in 1:len]
index = 1
for (i, j) in C.short_cycle_counts
x_data[index] = i
y_data[index] = j
index += 1
end
fig = Plots.bar(x_data, y_data, bar_width=1, xticks=x_data, yticks=y_data,
legend=false, xlabel="Cycle Length", ylabel="Occurrences", title="Short Cycle Counts")
display(fig)
return fig, C.short_cycle_counts
end
"""
count_elementary_cycles(C::LDPCCode)
Return a bar graph and a dictionary of (length, count) pairs for unique elementary
cycles in the Tanner graph of `C`. An empty graph and dictionary are returned
when there are no cycles.
# Note
- Elementary cycles do not contain the same vertex twice and are unable to be
decomposed into a sequence of shorter cycles.
"""
function count_elementary_cycles(C::LDPCCode)
if isempty(C.short_cycle_counts) || isempty(C.elementary_cycle_counts)
_count_cycles(C)
end
len = length(C.elementary_cycle_counts)
x_data = [0 for _ in 1:len]
y_data = [0 for _ in 1:len]
index = 1
for (i, j) in C.elementary_cycle_counts
x_data[index] = i
y_data[index] = j
index += 1
end
fig = Plots.bar(x_data, y_data, bar_width=1, xticks=x_data, yticks=y_data,
legend=false, xlabel="Cycle Length", ylabel="Occurrences", title="Elementary Cycle Counts")
display(fig)
return fig, C.elementary_cycle_counts
end
"""
ACE_distribution(C::LDPCCode, v::Int)
ACE_distribution(C::LDPCCode, vs::Vector{Int})
ACE_distribution(C::LDPCCode)
Return the ACEs and cycle lengths for vertex `v` or vertices `vs` of the Tanner graph
of `C`. If no vertices are given, all vertices are computed by default.
"""
function ACE_distribution(C::LDPCCode, vs::Vector{Int})
# using the original DFS approach constructs a significantly larger tree than this truncated BFS approach
isempty(vs) && throw(ArgumentError("Input node list cannot be empty"))
all(x -> 1 <= x <= C.n, vs) || throw(DomainError("Variable node index must be between 1 and length(C)"))
vs_to_do = [x for x in vs if isempty(C.ACEs_per_var_node[x])]
processed = false
if !isempty(vs_to_do)
processed = true
check_adj_list, var_adj_list = _node_adjacencies(C.H)
Threads.@threads for i in 1:length(vs_to_do)
# moving this inside allocates more but allows for multi-threading
check_nodes = [_ACECheckNode(i, -1, -1, -1) for i in 1:length(check_adj_list)]
var_nodes = [_ACEVarNode(i, -1, -1, -1, length(var_adj_list[i]) - 2) for i in 1:C.n]
ACEs = Vector{Int}()
cycle_lens = Vector{Int}()
root = var_nodes[vs[i]]
root.lvl = 0
root.cum_ACE = root.local_ACE
queue = Queue{Union{_ACECheckNode, _ACEVarNode}}()
enqueue!(queue, root)
while length(queue) > 0
curr = first(queue)
if isa(curr, _ACEVarNode)
for cn in var_adj_list[curr.id]
# can't pass messages back to the same node
if cn != curr.parent_id
cn_node = check_nodes[cn]
if cn_node.lvl != -1
# have seen before
push!(ACEs, curr.cum_ACE + cn_node.cum_ACE - root.local_ACE)
push!(cycle_lens, curr.lvl + cn_node.lvl + 1)
else
cn_node.lvl = curr.lvl + 1
cn_node.parent_id = curr.id
cn_node.cum_ACE = curr.cum_ACE
enqueue!(queue, cn_node)
end
end
end
else
for vn in check_adj_list[curr.id]
# can't pass messages back to the same node
if vn != curr.parent_id
vn_node = var_nodes[vn]
if vn_node.lvl != -1
# have seen before
push!(ACEs, curr.cum_ACE + vn_node.cum_ACE - root.local_ACE)
push!(cycle_lens, curr.lvl + vn_node.lvl + 1)
else
vn_node.lvl = curr.lvl + 1
vn_node.parent_id = curr.id
vn_node.cum_ACE = curr.cum_ACE + vn_node.local_ACE
enqueue!(queue, vn_node)
end
end
end
end
dequeue!(queue)
end
C.ACEs_per_var_node[vs_to_do[i]] = ACEs
C.cycle_lens[vs_to_do[i]] = cycle_lens
end
end
vs_ACEs = [C.ACEs_per_var_node[i] for i in vs]
lengths = [C.cycle_lens[i] for i in vs]
if processed
if all(!isempty, C.cycle_lens)
girth = minimum([minimum(C.cycle_lens[i]) for i in 1:C.n])
if ismissing(C.girth)
C.girth = girth
else
if C.girth != girth
@warn "Known girth, $(C.girth), does not match just computed girth, $girth"
end
end
end
end
return vs_ACEs, lengths
end
function ACE_distribution(C::LDPCCode, v::Int)
vs_ACE, lengths = ACE_distribution(C, [v])
return vs_ACE[1], lengths[1]
end
# TODO: plots
ACE_distribution(C::LDPCCode) = ACE_distribution(C, collect(1:C.n))
"""
average_ACE_distribution(C::LDPCCode, v::Int)
average_ACE_distribution(C::LDPCCode, vs::Vector{Int})
average_ACE_distribution(C::LDPCCode)
Return the average ACE of the vertex `v` or vertices `vs` of the Tanner graph of `C`. If no
vertices are given, all vertices are computed (individually) by default.
"""
function average_ACE_distribution(C::LDPCCode, vs::Vector{Int})
vs_to_do = [x for x in vs if isempty(C.ACEs_per_var_node[x])]
isempty(vs_to_do) || ACE_distribution(C, vs_to_do)
return [mean(C.ACEs_per_var_node[v]) for v in vs]
end
average_ACE_distribution(C::LDPCCode, v::Int) = average_ACE_distribution(C, [v])[1]
average_ACE_distribution(C::LDPCCode) = average_ACE_distribution(C, collect(1:C.n))
"""
median_ACE_distribution(C::LDPCCode, v::Int)
median_ACE_distribution(C::LDPCCode, vs::Vector{Int})
median_ACE_distribution(C::LDPCCode)