Merge pull request #1 from krishna-praneet/bp-syndrome-decoding

Bp syndrome decoding

src/parity_generator.jl

@@ -1,21 +1,46 @@
 using Random
 
-function parity_check_matrix(n, rw, cw)
-  n_equations = (n  * cw) ÷ rw
+"""
+parity_check_matrix(n, wr, wc)
+
+Computes a regular LDPC matrix using Callager's algorithm
+
+Block is created initially and then the columns are randomly
+permuted to create additional parity check n_equations
+
+# Arguments
+* `n`: The length of the code
+* `wr`: Row weight (Number of bits a parity check equations acts upon). Must divide n
+* `wc`: Column weight (Number of parity check equations for a given bit)
+
+# Examples
+```julia
+julia> using LDPC
+julia> H = parity_check_matrix(1000, 10, 9)
+```
+"""
+function parity_check_matrix(n::Int, wr::Int, wc::Int)
 
-  block_size = n_equations ÷ rw
-  block = zeros(Int64, block_size, n)
+  # For a regular LDPC matrix
+  ## wr = wc * (n / n-k)
+  @assert n % wr == 0
 
+  n_equations = (n  * wc) ÷ wr
+  block_size = n_equations ÷ wc
+
+  block = zeros(Bool, block_size, n)
 
   for i in 1:block_size
-    for j in ((i-1)*cw + 1):((i)*cw)
+    for j in ((i-1)*wr + 1):((i)*wr)
       block[i,j] = 1
     end
   end
+
   H = block
 
-  for i in 1:rw - 1
+  for i in 1:wc - 1
     H = [H; block[:, shuffle(1:end)]] 
   end
+
   return H
 end

src/syndrome_it_decoder.jl

@@ -0,0 +1,40 @@
+function syndrome_it_decode(pcm::Matrix, syndrome, max_iters::Int)
+
+  # Get size of parity check matrix 
+  ## n is codeword length, m is number of parity check equations
+  m, n = size(pcm)
+
+  # Initialise error and success
+  error = zeros(Bool, n)
+  success = false
+
+  # Iterative decoding
+  for iter in 1:max_iters
+    curr_syn = (pcm * error) .% 2
+
+    # Check if the syndrome matches
+    if curr_syn == vec(syndrome)
+      success = true
+      break
+    end
+
+    # Initialise votes
+    votes = zeros(Int, n)
+    votes = vec(votes)
+
+    error_checks = .!(curr_syn .== syndrome)
+
+    for i in 1:m
+      if error_checks[i] == 1
+        votes += pcm[i, :]
+      else
+        votes -= pcm[i, :]
+      end
+    end
+
+    max_idx = argmax(votes)
+    error[max_idx] = 1 - error[max_idx]
+  end
+
+  return Bool.(error), success
+end

test/runtests.jl

@@ -3,30 +3,46 @@ using Test
 
 @testset "LDPC.jl" begin
 
+    ## Syndrome decoding tests
     error_rate = 0.1
 
-    parity_check_matrix = [1 0 1 0 1 0 1; 0 1 1 0 0 1 1; 0 0 0 1 1 1 1]
-    actual_message = [1 1 1 1 1 1 1]
-    received_message = [1 1 1 1 1 0 1]  # 2nd bit from right is an error
-    decoded_message, success = bp_decode(parity_check_matrix, received_message, error_rate)
-
-    actual_message = vec(actual_message)
-    @test decoded_message == actual_message
+    pcm = [1 0 1 0 1 0 1; 0 1 1 0 0 1 1; 0 0 0 1 1 1 1]
+    error = [0 0 0 0 0 1 0]
+    syn = (pcm * error') .% 2
+    decoded_error, success = syndrome_decode(pcm, syn, error_rate, 100)
+    decoded_error_it, success = syndrome_it_decode(pcm, syn, 100)
+    @test decoded_error == vec(error)
+    @test decoded_error_it == vec(error)
 
-    parity_check_matrix = [1 0 1 1 1 0 0; 1 1 0 1 0 1 0; 1 1 1 0 0 0 1]
-    actual_message = [1 0 0 0 1 1 1]
-    received_message = [1 0 0 1 1 1 1] # 4th bit from left is an error
-    decoded_message, success = bp_decode(parity_check_matrix, received_message, error_rate)
-
-    actual_message = vec(actual_message)
-    @test decoded_message == actual_message
+    pcm = [1 0 1 1 1 0 0; 1 1 0 1 0 1 0; 1 1 1 0 0 0 1]
+    error = [0 0 0 1 0 0 0]
+    syn = (pcm * error') .% 2
+    decoded_error, success = syndrome_decode(pcm, syn, error_rate, 100)
+    decoded_error_it, success = syndrome_it_decode(pcm, syn, 100)
+    @test decoded_error == vec(error)
+    @test decoded_error_it == vec(error)
 
-    parity_check_matrix = [1 1 1 1 0 0 0 0 0 0; 1 0 0 0 1 1 1 0 0 0; 0 1 0 0 1 0 0 1 1 0; 0 0 1 0 0 1 0 1 0 1; 0 0 0 1 0 0 1 0 1 1]
-    actual_message = [1 1 0 0 1 0 0 0 0 0]
-    received_message = [1 1 0 0 1 0 0 0 0 1] # last bit is an error
-    decoded_message, success = bp_decode(parity_check_matrix, received_message, error_rate)
+    pcm = [1 1 1 1 0 0 0 0 0 0; 1 0 0 0 1 1 1 0 0 0; 0 1 0 0 1 0 0 1 1 0; 0 0 1 0 0 1 0 1 0 1; 0 0 0 1 0 0 1 0 1 1]
+    error = [0 0 0 0 0 0 0 0 0 1] # last bit is an error
+    syn = (pcm * error') .% 2
+    decoded_error, success = syndrome_decode(pcm, syn, error_rate, 100)
+    decoded_error_it, success = syndrome_it_decode(pcm, syn, 100)
+    @test decoded_error == vec(error)
+    @test decoded_error_it == vec(error)
 
-    actual_message = vec(actual_message)
-    @test decoded_message == actual_message
+
+    ## Parity check matrix generation tests
+    wr = 10
+    wc = 9
+    n = 1000
+    H = parity_check_matrix(n, wr, wc)
+    rsums = sum(H, dims=2)
+    csums = sum(H, dims=1)
+
+    @test rsums[1] == wr
+    @test csums[1] == wc
+    @test all(rsums[1] .== rsums)
+    @test all(csums[1] .== csums)
+
 
 end