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);