Simulation preps for high speed.
This commit is contained in:
Silas Oettinghaus
@@ -1,44 +1,16 @@
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classdef ML_MLSE < handle
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% ALGORITHM DESCRIBED IN:
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% W. Lanneer and Y. Lefevre, “Machine Learning-Based Pre-Equalizers for
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% Maximum Likelihood Sequence Estimation in High-Speed PONs,”
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% in 2023 31st European Signal Processing Conference
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% Further ML Refs:
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% https://machinelearningmastery.com/cross-entropy-for-machine-learning/
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% https://docs.pytorch.org/docs/stable/generated/torch.nn.CrossEntropyLoss.html
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% The central idea is to overcome the (white-) noise assumption within the previously described
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% Viterbi algorithm, more precisely a closed-loop optimization is proposed that finds a suitable
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% filter-set to directly compute the branch metrics c_k (s,s^' ). These can directly be used to
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% carry out the conventional Viterbi algorithm. The system consists of S^L S=F linear FIR filters,
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% combined with one bias coefficient respectively. These filters take the received input samples to
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% compute the branch metrics estimates (c_k ) ̂(s,s^' ) according toThe central idea is to overcome
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% the (white-) noise assumption within the previously described Viterbi algorithm, more precisely
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% a closed-loop optimization is proposed that finds a suitable filter-set to directly compute the
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% branch metrics c_k (s,s^' ). These can directly be used to carry out the conventional Viterbi
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% algorithm. The system consists of S^L S=F linear FIR filters, combined with one bias coefficient
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% respectively. These filters take the received input samples to compute the branch metrics
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% estimates. Finally, the usual Viterbi is carried out...
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% Recommended Settings and some findings:
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% Requires many training epochs. According to ML people, 100,200 or
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% even up to 1000 epochs are normal for ML-convergence
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% The mu parameter _can_ be adaptive - using the cross entropy and when
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% analyzing the isolated training it looks very promisig. However, is
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% later use I found this is not as stable as a fixed learning rate.
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% mu = 0.1 worked good for me
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% Longer orders/ filter length are not always better. For me order=11
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% was good.
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% Delay factor (delta) is good when the order is also increased. With
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% order = 11, a delta of =4 shows good results
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% ---------------------------------------------------------------------
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% W. Lanneer and Y. Lefevre,
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% “Machine Learning-Based Pre-Equalizers for Maximum Likelihood
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% Sequence Estimation in High-Speed PONs,” EUSIPCO 2023
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% ---------------------------------------------------------------------
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% This implementation reproduces the closed-loop ML-based
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% pre-equalizer training for MLSE, supporting both training and
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% detection (decision-directed) modes.
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% ---------------------------------------------------------------------
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properties
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sps % usually 2
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sps
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order
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e
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e_tr
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@@ -48,27 +20,23 @@ classdef ML_MLSE < handle
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mu_tr
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epochs_tr
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dd_mode % 1 or 0 to set DD-mode on or off
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mu_dd %weight update in dd mode
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dd_mode
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mu_dd
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epochs_dd
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adaptive_mu
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constellation
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L %viterbi memory length
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L
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alpha
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DIR
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DIR_flip
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trellis_states
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traceback_depth
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delta
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% --- Added internal class variables used later ---
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% Internal variables
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S
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Nf
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delta
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nStates
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nFeasible
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combs
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@@ -79,38 +47,32 @@ classdef ML_MLSE < handle
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valid_from_idx
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w
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% --- New: fast state lookup ---
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% Fast lookup
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nSym
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key_table
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trans_index
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true_to_state_idx
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state_dict % containers.Map: key(sequence)->state index
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key_fmt = '%.8g_'; % key format for sequence strings
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nSym % |constellation|
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% Debug metrics
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ber = []
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ce = ones(1,1);
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ce = ones(1,1)
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end
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methods
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function obj = ML_MLSE(options)
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arguments(Input)
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options.sps = 2;
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options.order = 15;
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options.len_tr = 4096;
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options.mu_tr = 0;
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options.mu_tr = 0.001;
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options.epochs_tr = 5;
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options.dd_mode = 1;
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options.mu_dd = 1e-5;
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options.epochs_dd = 5;
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options.adaptive_mu = 1;
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options.delta = 0;
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options.traceback_depth = 1024;
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options.L = 1
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options.L = 1;
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end
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fn = fieldnames(options);
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@@ -122,13 +84,12 @@ classdef ML_MLSE < handle
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obj.error = 0;
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end
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% ==============================================================
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% PROCESS
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% ==============================================================
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function [X,X_viterbi] = process(obj, X, D)
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% actual processing of the signal (steps 1. - 3.)
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% 1 normalize RMS
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% Normalize input RMS
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X = X.normalize("mode","rms");
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% Use sorted constellation for deterministic mapping
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obj.constellation = sort(unique(D.signal),'ascend');
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obj.nSym = numel(obj.constellation);
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@@ -136,22 +97,17 @@ classdef ML_MLSE < handle
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warning('Signal length does not fit to reference!');
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end
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% ==============================================================
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% INITIALIZATION (only before final epoch and detection mode)
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% ==============================================================
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% --- Parameters
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obj.S = numel(obj.constellation); % alphabet size
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obj.Nf = obj.order*obj.sps; % filter length
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% obj.delta = 3;%ceil(obj.Nf/2); % delay parameter
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obj.S = obj.nSym;
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obj.Nf = obj.order * obj.sps;
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obj.nStates = obj.S^obj.L;
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obj.nFeasible = obj.nStates*obj.S;
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obj.nFeasible = obj.nStates * obj.S;
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% --- Trellis mapping
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obj.trellis_states = reshape(obj.constellation,1,[]);
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pre_comb_mat = repmat(obj.trellis_states, obj.L, 1);
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pre_comb_cell = mat2cell(pre_comb_mat, ones(1,obj.L), size(pre_comb_mat,2));
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obj.combs = fliplr(combvec(pre_comb_cell{:}).'); % rows: states, columns: [x_k, x_{k-1}, ...]
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obj.combs = fliplr(combvec(pre_comb_cell{:}).');
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obj.first_sym = obj.combs(:,1);
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obj.last_sym = obj.combs(:,end);
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obj.nStates = size(obj.combs,1);
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@@ -165,328 +121,235 @@ classdef ML_MLSE < handle
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end
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end
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end
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[obj.valid_to_idx, obj.valid_from_idx] = find(obj.valid);
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[obj.valid_to_idx,obj.valid_from_idx] = find(obj.valid);
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% --- Allocate vectors and weights
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% !! IF SHAPE FIT, then we already have smth there an we want
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% to start with the existing fitler-set
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% --- Initialize weights
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if isempty(obj.w) || any(size(obj.w) ~= [obj.Nf+1,obj.nFeasible])
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obj.w = zeros(obj.Nf+1,obj.nFeasible); % filter weights per transition + bias tap
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obj.w = randn(obj.Nf+1,obj.nFeasible);
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end
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% --- Precompute dictionary for fast state lookup (sequence -> state)
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keys = cell(obj.nStates,1);
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for i = 1:obj.nStates
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keys{i} = obj.seq_key(obj.combs(i,:)); % combs row is already [x_k, x_{k-1}, ...]
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% --- Fast lookup tables
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[~, sym_idx_mat] = ismember(obj.combs, obj.constellation);
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key_vals = 1 + sum((sym_idx_mat - 1) .* (obj.nSym .^ (0:obj.L-1)), 2);
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max_key = obj.nSym^obj.L;
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obj.key_table = zeros(max_key,1,'uint32');
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obj.key_table(key_vals) = 1:obj.nStates;
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obj.trans_index = sparse(obj.nStates,obj.nStates);
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for i = 1:length(obj.valid_from_idx)
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f = obj.valid_from_idx(i);
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t = obj.valid_to_idx(i);
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obj.trans_index(t,f) = i;
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end
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obj.state_dict = containers.Map(keys, 1:obj.nStates);
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% ==============================================================
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% TRAINING
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% TRAINING
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% ==============================================================
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% Training Mode
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n = obj.len_tr;
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training = 1;
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obj.equalize(X.signal, D.signal,obj.mu_tr,obj.epochs_tr,n,training);
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fprintf('\n--- Training mode ---\n');
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obj.equalize(X.signal, D.signal, obj.mu_tr, obj.epochs_tr, obj.len_tr, true);
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obj.e_tr = obj.e;
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% ==============================================================
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% DD-Mode / Fixed Mode
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% DECISION-DIRECTED / TESTING
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% ==============================================================
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% Decision Directed Mode
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n = X.length;
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training = 0;
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[y,y_vit]=obj.equalize(X.signal, D.signal,obj.mu_dd,obj.epochs_dd,n,training);
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fprintf('--- Decision-directed / detection mode ---\n');
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[y, y_vit] = obj.equalize(X.signal, D.signal, obj.mu_dd, obj.epochs_dd, X.length, false);
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X_viterbi = X;
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X.signal = y;
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X.fs = D.fs; %change sampling frequency of outgoing signal from fdac e.g. 2 sps to symbol spaced = fsym
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lbdesc = [num2str(obj.order),' tap FFE'];
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X = X.logbookentry(lbdesc); % append to logbook
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X_viterbi.signal = y_vit;
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X_viterbi.fs = D.fs; %change sampling frequency of outgoing signal from fdac e.g. 2 sps to symbol spaced = fsym
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lbdesc = [num2str(obj.order),'order FFE + PF + Viterbi'];
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X_viterbi = X_viterbi.logbookentry(lbdesc); % append to logbook
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end
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% ==============================================================
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% EQUALIZE
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% ==============================================================
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function [y,y_ref] = equalize(obj,x,d,mu,epochs,N,training)
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% ==============================================================
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% FFE + Whitening + ML-Based Branch Metric Estimation + Viterbi
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% ==============================================================
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debug = 1;
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showPlots = 1;
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% --- Input padding and preallocation
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y = zeros(N,1);
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% number of symbol steps in this block
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nSymbols = ceil(N/obj.sps);
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for epoch = 1:epochs
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% state metrics (log-domain costs): keep as column [nStates×1]
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pm = zeros(obj.nStates,1); % v_{k-1}(s′)
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c_hat = zeros(1,obj.nFeasible);
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v_tilde = zeros(1,obj.nFeasible);
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pred = zeros(nSymbols, obj.nStates, 'uint32');
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pm_sto = nan(obj.nStates, nSymbols,'like',pm);
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pm = zeros(obj.nStates,1);
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pred = zeros(nSymbols,obj.nStates,'uint32');
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pm_sto = nan(obj.nStates,nSymbols,'like',pm);
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CE_accum = 0;
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%%% START IDX
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if training
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max_start = length(x) - ( (ceil(N/obj.sps)-1)*obj.sps + 1 );
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max_start = max(1, max_start); % safety
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start_sample = randi([1, max_start], 1); %rnd training; not really good
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start_sample = 1;
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end_sample = start_sample + (ceil(N/obj.sps)-1)*obj.sps;
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else
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start_sample = 1;%obj.len_tr;
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end_sample = N;
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end
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start_symbol = 1 + floor((start_sample - 1)/obj.sps); % ABSOLUTE symbol index
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start_sample = 1;
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end_sample = N;
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start_symbol = 1 + floor((start_sample - 1)/obj.sps);
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% --- initialize true state
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if numel(d) >= obj.L && start_symbol >= obj.L
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init_seq = d(start_symbol-obj.L+1 : start_symbol); % [d_k-L+1 ... d_k]
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true_to_state_idx = obj.state_dict(obj.seq_key(flip(init_seq))); % [d_k ... d_k-L+1]
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init_seq = d(start_symbol-obj.L+1:start_symbol);
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key_init = obj.seq2key(init_seq);
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true_to_state_idx = obj.key_table(key_init);
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if true_to_state_idx==0, true_to_state_idx=1; end
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else
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% Not enough history – fall back to state 1
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true_to_state_idx = uint32(1);
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end
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symbol = 0;
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for sample = start_sample:obj.sps:end_sample
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symbol = symbol + 1;
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k = symbol;
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symbol = (sample - start_sample)/obj.sps + 1;
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sym_idx = start_symbol + (symbol - 1);
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% --- Build Δ-delayed observation window y_k
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i1 = sample - obj.Nf + 1 + obj.delta;
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i2 = sample + obj.delta;
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% --- Observation window (with delta)
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i1 = sample - obj.Nf + 1 + obj.delta;
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i2 = sample + obj.delta;
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buf = x(max(1,i1):min(length(x),i2));
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padL = max(0,1 - i1);
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padR = max(0,i2 - length(x));
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yk = [zeros(padL,1); buf(:); zeros(padR,1)]; % Nf×1
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yk = [yk;1];
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yk = [zeros(padL,1); buf(:); zeros(padR,1)];
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yk = [yk;1];
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% --- Predict branch metrics for all feasible transitions: c_hat
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c_hat = (yk.' * obj.w); % [1×nFeasible]
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c_hat = c_hat.'; % [nFeasible×1]
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% --- Extended path metrics: v_tilde = pm(from) + c_hat
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% normalize pm to avoid growth (invariant to additive const)
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% --- Branch metrics
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c_hat = (yk.' * obj.w).';
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pm = pm - min(pm);
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v_tilde = pm(obj.valid_from_idx) + c_hat; % [nFeasible×1]
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v_tilde = pm(obj.valid_from_idx) + c_hat;
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% ===== Gradient update (Algorithm 1) =====
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% --- allocate once
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if epoch==1 && symbol==1
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obj.true_to_state_idx = ones(ceil(N/obj.sps),1,'uint32');
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end
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if 1 %training
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% --- allocate storage once
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if epoch == 1 && symbol == 1
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obj.true_to_state_idx = ones(ceil(N/obj.sps),1,'uint32');
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end
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% --- previous "to" becomes "from"
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if symbol>1
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true_from_state_idx = obj.true_to_state_idx(symbol-1);
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else
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true_from_state_idx = 1;
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end
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% --- previous "to" becomes current "from"
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if symbol > 1
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true_from_state_idx = obj.true_to_state_idx(symbol-1);
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else
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true_from_state_idx = 1;
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end
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% --- compute or reuse "to" state
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if epoch == 1
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% only compute in first epoch
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if sym_idx >= obj.L
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key_to = obj.seq_key(flip(d(sym_idx-obj.L+1 : sym_idx)));
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if isKey(obj.state_dict, key_to)
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obj.true_to_state_idx(symbol) = obj.state_dict(key_to);
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else
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obj.true_to_state_idx(symbol) = true_from_state_idx;
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end
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else
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obj.true_to_state_idx(symbol) = true_from_state_idx;
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% --- compute or reuse "to" state
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if epoch==1
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if sym_idx>=obj.L
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key_to = obj.seq2key(d(sym_idx-obj.L+1:sym_idx));
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state_idx = obj.key_table(key_to);
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if state_idx==0
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state_idx = true_from_state_idx;
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end
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end
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% --- reuse cached state from second epoch onward
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true_to_state_idx = obj.true_to_state_idx(symbol);
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% --- ensure valid (from,to)
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dirac = zeros(obj.nFeasible,1);
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mask = obj.valid_from_idx==true_from_state_idx & ...
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obj.valid_to_idx ==true_to_state_idx;
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if any(mask)
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dirac(mask) = 1;
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obj.true_to_state_idx(symbol) = state_idx;
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else
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idx = find(obj.valid_from_idx==true_from_state_idx,1,'first');
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dirac(idx) = 1;
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obj.true_to_state_idx(symbol) = obj.valid_to_idx(idx);
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obj.true_to_state_idx(symbol) = true_from_state_idx;
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end
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end
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true_to_state_idx = obj.true_to_state_idx(symbol);
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% --- fast Dirac creation
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dirac = zeros(obj.nFeasible,1);
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trans_idx = obj.trans_index(true_to_state_idx,true_from_state_idx);
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if trans_idx~=0
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dirac(trans_idx)=1;
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end
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% softmax over -v_tilde (numerically safe shift)
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v_shift = -(v_tilde - min(v_tilde)); % shift to small positive numbers
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v_shift = min(v_shift, 100); % clamp exponent argument (≈ exp(50)=3e21)
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% ===================================================================
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% TRAINING MODE (weight update)
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% ===================================================================
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if training
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% --- Softmax and CE
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v_shift = -(v_tilde - min(v_tilde));
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v_shift = min(v_shift,100);
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expv = exp(v_shift);
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p = expv ./ (sum(expv) + eps);
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p = expv./(sum(expv)+eps);
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CE_symbol(symbol) = -log(p(dirac==1)+eps);
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% for logging only:
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CE_symbol(symbol) = -log(p(dirac==1) + eps);
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if sym_idx > obj.L
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CE_smooth(symbol) = 0.01*CE_symbol(symbol) + 0.99*CE_smooth(symbol-1);
|
||||
% --- CE smoothing and adaptive μ
|
||||
if sym_idx>obj.L
|
||||
CE_smooth(symbol)=0.01*CE_symbol(symbol)+0.99*CE_symbol(symbol-1);
|
||||
else
|
||||
if epoch > 1
|
||||
CE_smooth(symbol) = obj.ce(end); %use ce from last epoch or =1 for very first round?!
|
||||
else
|
||||
CE_smooth(symbol) = CE_symbol(symbol);
|
||||
end
|
||||
CE_smooth(symbol)=CE_symbol(symbol);
|
||||
end
|
||||
CE_accum=CE_accum+CE_symbol(symbol);
|
||||
|
||||
CE_accum = CE_symbol(symbol) + CE_accum;
|
||||
|
||||
|
||||
% gradient term (t - p)
|
||||
dmp = (dirac - p)'; % 1×nFeasible
|
||||
|
||||
% Per-feature gradient; implicit expansion gives (Nf+1)×nFeasible
|
||||
dL_Dw = (yk) .* dmp;
|
||||
|
||||
% Start updates only when the ABSOLUTE symbol index has ≥ L history
|
||||
if sym_idx >= obj.L
|
||||
% --- Gradient update
|
||||
dmp=(dirac-p)';
|
||||
dL_Dw=(yk).*dmp;
|
||||
if sym_idx>=obj.L
|
||||
if obj.adaptive_mu
|
||||
mu_eff = CE_smooth(sym_idx);
|
||||
mu_eff = max(min(mu_eff, 0.2), 1e-4);
|
||||
mu_eff=CE_smooth(symbol);
|
||||
mu_eff=max(min(mu_eff,0.2),1e-4);
|
||||
else
|
||||
mu_eff = mu;
|
||||
mu_eff=mu;
|
||||
end
|
||||
|
||||
obj.w = obj.w - mu_eff .* dL_Dw; % (Nf+1)×nFeasible
|
||||
obj.w=obj.w - mu_eff.*dL_Dw;
|
||||
end
|
||||
|
||||
% if debug && epoch > 2
|
||||
% figure(100);
|
||||
% subplot(4,1,1);
|
||||
% heatmap(p');
|
||||
% title('Probs')
|
||||
% subplot(4,1,2);
|
||||
% heatmap(dmp);
|
||||
% title('Update')
|
||||
% subplot(4,1,3);
|
||||
% heatmap(dL_Dw);
|
||||
% title('Update')
|
||||
% subplot(4,1,4);
|
||||
% heatmap(bj.w);
|
||||
% title('Update')
|
||||
%
|
||||
% end
|
||||
|
||||
end
|
||||
|
||||
|
||||
|
||||
% --- Compare-Select (matrix form, min of costs)
|
||||
v_tilde_mat = inf(obj.nStates, obj.nStates);
|
||||
v_tilde_mat(obj.valid) = v_tilde;
|
||||
[pm_next, pred(k,:)] = min(v_tilde_mat, [], 2);
|
||||
|
||||
% re-center to keep metrics bounded (decision-invariant)
|
||||
pm_next = pm_next - min(pm_next);
|
||||
|
||||
pm = pm_next;
|
||||
pm_sto(:,symbol) = pm;
|
||||
% ===================================================================
|
||||
% DECODING MODE (Viterbi only)
|
||||
% ===================================================================
|
||||
% Compare-Select (always executed)
|
||||
vmat=inf(obj.nStates,obj.nStates);
|
||||
vmat(obj.valid)=v_tilde;
|
||||
[pm_next,pred(symbol,:)]=min(vmat,[],2);
|
||||
pm_next=pm_next-min(pm_next);
|
||||
pm=pm_next;
|
||||
pm_sto(:,symbol)=pm;
|
||||
end
|
||||
|
||||
% --- Traceback (full; you can window with traceback_depth if desired)
|
||||
[~, s_end] = min(pm);
|
||||
viterbi_path = zeros(symbol,1,'uint32');
|
||||
viterbi_path(symbol) = s_end;
|
||||
for n = symbol:-1:2
|
||||
viterbi_path(n-1) = pred(n, viterbi_path(n));
|
||||
% --- Traceback
|
||||
[~,s_end]=min(pm);
|
||||
vpath=zeros(symbol,1,'uint32');
|
||||
vpath(symbol)=s_end;
|
||||
for n=symbol:-1:2
|
||||
vpath(n-1)=pred(n,vpath(n));
|
||||
end
|
||||
|
||||
y_ref = d(start_symbol:end);
|
||||
y = obj.first_sym(viterbi_path);
|
||||
|
||||
if debug && training
|
||||
sym_start = start_symbol;
|
||||
sym_end = start_symbol + symbol - 1;
|
||||
ref_slice = d(sym_start : sym_end);
|
||||
err = sum(y ~= ref_slice(1:numel(y)));
|
||||
y_ref=d(start_symbol:end);
|
||||
y=obj.first_sym(vpath);
|
||||
|
||||
% --- BER/CE reporting and plots
|
||||
if training
|
||||
err=sum(y~=y_ref(1:length(y)));
|
||||
ser=err/length(y);
|
||||
try
|
||||
ref_bits = PAMmapper(obj.S,0).demap(ref_slice);
|
||||
eq_bits = PAMmapper(obj.S,0).demap(y);
|
||||
[~, ~, ber, ~] = calc_ber(ref_bits, eq_bits, "skip_front", 10, "skip_end", 10, "returnErrorLocation", 1);
|
||||
fprintf('Epoch: %d - BER: %.1e \n',epoch, ber);
|
||||
obj.ber(epoch) = ber;
|
||||
ref_bits=PAMmapper(obj.S,0).demap(y_ref(1:length(y)));
|
||||
eq_bits=PAMmapper(obj.S,0).demap(y);
|
||||
[~,~,ber,~]=calc_ber(ref_bits,eq_bits,"skip_front",10,"skip_end",10,"returnErrorLocation",1);
|
||||
fprintf('Epoch %d - BER: %.2e\n',epoch,ber);
|
||||
obj.ber(epoch)=ber;
|
||||
catch
|
||||
ser = err./length(y);
|
||||
fprintf('Epoch: %d - SER: %.1e \n',epoch, ser);
|
||||
fprintf('Epoch %d - SER: %.2e\n',epoch,ser);
|
||||
obj.ber(epoch)=ser;
|
||||
end
|
||||
|
||||
obj.ce(epoch) = CE_accum./symbol;
|
||||
obj.ce(epoch)=CE_accum/symbol;
|
||||
|
||||
if showPlots
|
||||
if debug && mod(epoch,10)==1 && showPlots
|
||||
figure(10);clf
|
||||
subplot(3,2,1:2);
|
||||
heatmap(obj.w);
|
||||
title('Filter')
|
||||
|
||||
imagesc(obj.w);axis xy;colorbar;title('Filter W');
|
||||
subplot(3,2,3);
|
||||
v_tildemat = NaN(obj.nStates, obj.nStates);
|
||||
v_tildemat(obj.valid) = v_tilde; % log-domain scores
|
||||
heatmap(v_tildemat);
|
||||
title('Path Metrics (v_tilde)')
|
||||
|
||||
vtilde_mat=NaN(obj.nStates,obj.nStates);
|
||||
vtilde_mat(obj.valid)=v_tilde;
|
||||
imagesc(vtilde_mat);axis xy;colorbar;title('Path Metrics (v\_tilde)');
|
||||
subplot(3,2,4);
|
||||
scatter(1:symbol,pm_sto,1,'.')
|
||||
title('Path Metric Winners')
|
||||
|
||||
subplot(3,2,5);hold on
|
||||
plot(1:symbol,pm_sto);title('Path Metric Evolution');
|
||||
subplot(3,2,5);hold on;
|
||||
scatter(1:symbol,CE_symbol,1,'.');
|
||||
scatter(1:symbol,CE_smooth,1,'.')
|
||||
title('Cross Entropy')
|
||||
|
||||
subplot(3,2,6); hold on
|
||||
|
||||
% Left y-axis: Cross Entropy (linear)
|
||||
scatter(1:symbol,CE_smooth,1,'.');
|
||||
title('Cross Entropy');
|
||||
subplot(3,2,6);hold on;
|
||||
yyaxis left
|
||||
scatter(1:length(obj.ce), obj.ce, 10, 's', 'filled')
|
||||
ylabel('Cross Entropy')
|
||||
|
||||
% Right y-axis: BER (logarithmic)
|
||||
scatter(1:length(obj.ce),obj.ce,10,'s','filled');
|
||||
ylabel('Cross Entropy');
|
||||
yyaxis right
|
||||
scatter(1:length(obj.ber), obj.ber, 10, 'd', 'filled')
|
||||
set(gca, 'YScale', 'log')
|
||||
ylabel('BER (log scale)')
|
||||
|
||||
xlim([1, epochs])
|
||||
xlabel('Epoch')
|
||||
title('Cross Entropy // BER')
|
||||
grid on
|
||||
|
||||
drawnow
|
||||
scatter(1:length(obj.ber),obj.ber,10,'d','filled');
|
||||
set(gca,'YScale','log');
|
||||
ylabel('BER (log)');
|
||||
xlabel('Epoch');grid on;
|
||||
title('Convergence');
|
||||
drawnow;
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
methods (Access=private)
|
||||
function k = seq_key(obj, seq)
|
||||
% Build a stable key string for a sequence row vector in the *same order as combs rows* ([x_k, x_{k-1}, ...])
|
||||
% Use rounding via sprintf to avoid floating-point issues.
|
||||
% seq must be a row vector.
|
||||
k = sprintf(obj.key_fmt, seq);
|
||||
% ==============================================================
|
||||
% Helper: Sequence → key (always scalar)
|
||||
% ==============================================================
|
||||
function key = seq2key(obj, seq)
|
||||
[~, idx] = ismember(flip(seq), obj.constellation);
|
||||
pow = (obj.nSym .^ (0:obj.L-1)).';
|
||||
key = 1 + sum((idx(:) - 1) .* pow);
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
Reference in New Issue
Block a user