BCJR implementation

WDM code added (Pol Cont., Opt MUX/DEMUX, Opt Atten, DP_Fiber) -> the codebase is not optimized to always work with dp signals!

test/pam_6_differential_code_understand.m

@@ -0,0 +1,79 @@
+M = 6;
+data = [1,2,3,4,5,6];
+
+M = 6;
+
+bitpattern = [];
+s = RandStream('twister','Seed',1);
+for i = 1:log2(M)
+    N = 2^(12-1); %length of prbs
+    bitpattern(:,i) = randi(s,[0 1], N, 1);
+end
+
+if M == 6
+    bitpattern = reshape(bitpattern',[],1);
+    bitpattern = bitpattern(1:end-mod(length(bitpattern),5));
+end
+
+bits = Informationsignal(bitpattern);
+
+symbols = PAMmapper(M,0).map(bits);
+symbols_tx_prec = Duobinary().precode(symbols);
+
+% all possible transitions (for now 36, including the "edges"
+% of the QAM 32 constellation)
+states = PAMmapper(6,0,"eth_style",0).levels;
+pam6transitions = combvec(states,states)'; % pam6transitions =
+% [-5    -5;
+% -3    -5;
+% -1    -5; ...
+pam6transitions_serial = reshape(pam6transitions',[],1);
+
+data = pam6transitions_serial;
+data = round(data);
+b = min(data);
+data = data - b;
+data = data ./ 2;
+% THIS WAS USED!
+bk = zeros(size(data));
+for k = 2:numel(data)
+    bk(k) = mod(data(k)-bk(k-1),M);
+end
+
+
+%% State Analysis
+x = bk;%symbols_tx_prec.signal;
+levels = sort(unique(x)).';              % or provide known 1x6 level values
+
+[~,ix] = min(abs(x - levels),[],2);
+x = levels(ix);                          % snapped/quantized
+
+%% TRANSITION COUNTS & PROBABILITIES
+K = numel(levels);
+% map to state indices 1..K
+[tf, idx] = ismember(x, levels);        
+idx = idx(:);
+from = idx(1:end-1);
+to   = idx(2:end);
+from = idx(1:2:end);
+to   = idx(2:2:end);
+
+% counts C(from,to)
+C = accumarray([from,to], 1, [K K], @sum, 0);
+% row-stochastic transition matrix P(to|from)
+rowSums = sum(C,2);
+P = C ./ max(rowSums,1);
+
+%% 1) HEATMAP (which transitions are more probable?)
+figure('Name','Transition Probabilities (to | from)');
+h = heatmap(levels, levels, P, 'Colormap', parula, 'ColorbarVisible','on');
+colormap(gca,[[1,1,1];flip(cbrewer2('Spectral',100))]);clim([0,ceil(max(P(:))*10)/10]);
+h.XLabel = 'From state (level)'; 
+h.YLabel = 'To state (level)';
+h.Title  = 'P(to | from)';
+
+%% 2) WEIGHTED TRANSITION GRAPH
+% Use dtmc if you have Econometrics Toolbox:
+mc = dtmc(P, 'StateNames', string(levels));
+figure('Name','Markov Graph (dtmc)');
+gp = graphplot(mc, 'ColorEdges',true, 'LabelEdges',true);