save

lab_1/lab_1.asv

@@ -4,8 +4,6 @@ p_gg = 0.99;
 p_bb = 0.1;
 p_bg = 1 - p_bb;
 
-pi_0 = p_bb / (2 - (p_gg + p_bb));
-
 % freely chosen bit error probability
 e_g = 10^-4;
 e_b = 10^-1;
@@ -14,49 +12,51 @@ e_b = 10^-1;
 bits_array_len = 10^6;
 bits = randi([0, 1], 1, bits_array_len);
 
-% choose beginning channel state, biased to false, 
-% assume pipe dirty at start of stream
-if rand() < pi_0
-    channel_state = true;
-else
-    channel_state = false;
-end
+% start with a clean error free pipe
+channel_state = true;
 
 % preallocated array/vector for the resulting bits
 result_stream = zeros(1, bits_array_len);
 
 bit_error_rate_counter = 0;
-gap_size_tracker = [];
-current_gap_size = 0;
+gap_begin = 1; % stores the last dirty bit idx, meaning the begin of a new gap
+gap_tracker = []; % holds a 3xn matrix of begin and end gap values and the gap size between them
+
+state_sequence = []; % collector array for the visited states
 
 for it = 1 : bits_array_len
     current_bit = bits(it);
 
-    r = rand();
+    % two different rands for channel and bit logic
+    % to prevent unwanted coupling of these two mechanics
+    channel_change_probability = rand();
+    bit_error_probability = rand();
 
     % error and channel
     if channel_state == true
+        state_sequence(end + 1) = 'Good';
         % channel selection from good state with probability p_gg
-        if r < p_gg
+        if channel_change_probability < p_gg
             channel_state = 1;
         else
             channel_state = 0;
         end
         
-        if r < e_g
+        % flip the bit with probability e_g
+        if bit_error_probability < e_g
             received_bit = 1 - current_bit;
         else 
             received_bit = current_bit;
         end
     else
-        % change channel to good with probability 
-        if r < p_bg
+        % change channel to good with probability of p_bg
+        if channel_change_probability < p_bg
             channel_state = 1;
         else
             channel_state = 0;
         end
 
-        if r < e_b
+        if bit_error_probability < e_b
             received_bit = 1 - current_bit;
         else 
             received_bit = current_bit;
@@ -68,15 +68,22 @@ for it = 1 : bits_array_len
     % BER and Gap
     if current_bit ~= received_bit
         bit_error_rate_counter = bit_error_rate_counter + 1;
-        gap_size_tracker(end + 1) = current_gap_size;
-        current_gap_size = 0;
-    end
         
-    current_gap_size = current_gap_size + 1;
+        gap_tracker(:, end + 1) = [gap_begin; it; it - gap_begin - 1];
+        gap_begin = it;
+    end
 end
 
+gap_tracker(:, 1) = []; % trim first gap, this is a fault entry by design
 bit_error_rate = bit_error_rate_counter / bits_array_len
 
-% limit gap size to 500 in histogram
+gap_sizes = gap_tracker(3, :);
+gap_sizes = gap_sizes(gap_sizes <= 500); % limit gap size to 500 for histogram
+
+histogram(gap_sizes, 'BinEdges', -0.5:1:500.5);
+xlabel('Gap size')
+ylabel('Frequency')
+title('Histogram of gap sizes between consecutive errors')
+
 % for pdf, 1 - 2 sites, describe what i did and what the results were and
 % are

lab_1/lab_1.m

@@ -19,8 +19,11 @@ channel_state = true;
 result_stream = zeros(1, bits_array_len);
 
 bit_error_rate_counter = 0;
-gap_size_tracker = [];
-current_gap_size = 0;
+gap_begin = 1; % stores the last dirty bit idx, meaning the begin of a new gap
+gap_tracker = []; % holds a 3xn matrix of begin and end gap values and the gap size between them
+
+state_sequence = []; % stores the state timeline
+state_visit_counter = 0;
 
 for it = 1 : bits_array_len
     current_bit = bits(it);
@@ -32,22 +35,29 @@ for it = 1 : bits_array_len
 
     % error and channel
     if channel_state == true
+        state_visit_counter = state_visit_counter + 1;
         % channel selection from good state with probability p_gg
         if channel_change_probability < p_gg
             channel_state = 1;
         else
             channel_state = 0;
+            state_sequence(end + 1) = state_visit_counter + 'x Good';
+            state_visit_counter = 0;
         end
         
+        % flip the bit with probability e_g
         if bit_error_probability < e_g
             received_bit = 1 - current_bit;
         else 
             received_bit = current_bit;
         end
     else
+        state_sequence(it) = 'Bad';
         % change channel to good with probability of p_bg
         if channel_change_probability < p_bg
             channel_state = 1;
+            state_sequence(end + 1) = state_visit_counter + 'x Bad';
+            state_visit_counter = 0;
         else
             channel_state = 0;
         end
@@ -64,15 +74,25 @@ for it = 1 : bits_array_len
     % BER and Gap
     if current_bit ~= received_bit
         bit_error_rate_counter = bit_error_rate_counter + 1;
-        gap_size_tracker(end + 1) = current_gap_size;
-        current_gap_size = 0;
-    end
         
-    current_gap_size = current_gap_size + 1;
+        gap_tracker(:, end + 1) = [gap_begin; it; it - gap_begin - 1];
+        gap_begin = it;
+    end
 end
 
-bit_error_rate = bit_error_rate_counter / bits_array_len
+gap_tracker(:, 1) = []; % trim first gap, this is a fault entry by design
+bit_error_rate = bit_error_rate_counter / bits_array_len;
+
+gap_sizes = gap_tracker(3, :);
+gap_sizes = gap_sizes(gap_sizes <= 500); % limit gap size to 500 for histogram
+
+histogram(gap_sizes, 'BinEdges', -0.5:1:500.5);
+xlabel('Gap size')
+ylabel('Frequency')
+title('Histogram of gap sizes between consecutive errors')
+
+disp(state_sequence)
+disp(bit_error_rate)
 
-% limit gap size to 500 in histogram
 % for pdf, 1 - 2 sites, describe what i did and what the results were and
 % are