ML_MLSE (before testing in depth)
minor changes here and there
This commit is contained in:
Silas Oettinghaus
213
projects/ML_based_MLSE/minimal_model_gpt.m
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213
projects/ML_based_MLSE/minimal_model_gpt.m
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function minimal_model_gpt
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% Minimal binary IM/DD + ISI (M=3), AWGN. RX: ML-based MLSE vs classic MLSE
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% Fixes:
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% 1) Correct (s',s) labeling: s'=[x_{k-1},x_{k-2}], s=[x_k,x_{k-1}]
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% 2) Window standardization (z-score) from pilot
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% 3) Non-negative learned BM: c_hat = (w^T y_std + b).^2
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% 4) Stable training loop bounds; BER length alignment
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clear; clc; rng(1);
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%% Parameters
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Ktr = 4000; % pilot
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Kte = 20000; % test
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M = 3; % true channel memory
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L = 3; % MLSE memory (states keep L-1 symbols)
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h = [0.55 1.00 0.45]; % ISI FIR
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EsN0dB= 12;
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D = 5*L; % traceback (unused here; full TB)
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Nwin = 7; % BM feature window
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Delta = 0;
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%% TX, channel, noise
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map = @(b) 2*b-1;
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b_tr = randi([0 1],Ktr,1); x_tr = map(b_tr);
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b_te = randi([0 1],Kte,1); x_te = map(b_te);
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convpad = @(x) filter(h,1,[x; zeros(M-1,1)]);
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ytr_clean = convpad(x_tr);
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yte_clean = convpad(x_te);
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EsN0 = 10^(EsN0dB/10);
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sigma2 = 1/(2*EsN0);
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awgn = @(len) sqrt(sigma2)*randn(len,1);
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y_tr = ytr_clean + awgn(length(ytr_clean));
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y_te = yte_clean + awgn(length(yte_clean));
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% remove tail to keep equal lengths
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trim = M-1;
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y_tr = y_tr(1:end-trim); x_tr = x_tr(1:end-trim); b_tr = b_tr(1:end-trim);
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y_te = y_te(1:end-trim); x_te = x_te(1:end-trim); b_te = b_te(1:end-trim);
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%% Trellis
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nStates = 2^(L-1);
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statesBin = de2bi(0:nStates-1,L-1,'left-msb');
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symOfBit = @(bit) (2*bit-1);
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% transitions (s'->s) with input symbol u in {±1}
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trans = struct('sp',[],'s',[],'u',[],'ubit',[]);
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idx=1;
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for sp=1:nStates
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prev_bits = statesBin(sp,:); % [x_{k-1}, x_{k-2}] as bits
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for ubit=[0 1]
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u = symOfBit(ubit);
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nb = [prev_bits(1),ubit]; % new state s = [x_k, x_{k-1}]
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s = bi2de(nb,'left-msb')+1;
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trans(idx).sp=sp; trans(idx).s=s; trans(idx).u=u; trans(idx).ubit=ubit;
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idx=idx+1;
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end
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end
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nTrans = numel(trans);
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%% Classic BM (Gaussian)
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BM_classic = @(yk, sp, s, u) (( yk - h * [u, symOfBit(statesBin(sp,:))]')^2)/(2*sigma2);
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%% ML-based BM: c_hat = (w^T y_std + b)^2 (nonnegative)
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padN = Nwin-1;
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pad = @(y) [zeros(Delta+padN,1); y; zeros(max(0,Nwin-1-Delta),1)];
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y_tr_p = pad(y_tr); y_te_p = pad(y_te);
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% standardize window features using pilot
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Ytr_mat = im2col_sliding(y_tr_p, Nwin, Delta); % Nwin × T
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mu_win = mean(Ytr_mat,2);
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sd_win = std(Ytr_mat,0,2)+1e-8;
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W = zeros(Nwin,nTrans);
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b0= zeros(1,nTrans);
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softmax = @(z) exp(z - max(z))./sum(exp(z - max(z)));
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mu = 0.005; % LR
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nEpoch = 6; % light training
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Ttr = length(y_tr);
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for ep=1:nEpoch
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v = zeros(nStates,1); v(2:end)=Inf;
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for k = L : min(Ttr - (L-1), Ttr) % need x(k-1), x(k-2)
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% true (s',s):
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sp_bits = [(x_tr(k-1)<0), (x_tr(k-2)<0)];
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s_bits = [(x_tr(k) <0), (x_tr(k-1)<0)];
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sp_star = bi2de(sp_bits,'left-msb')+1;
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s_star = bi2de(s_bits ,'left-msb')+1;
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% feature window (z-scored)
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yw = y_tr_p(k-Delta : k-Delta+Nwin-1);
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yw = (yw - mu_win) ./ sd_win;
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% compute extended PM logits over all (s',s)
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vtil = -inf(nTrans,1);
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for t=1:nTrans
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z = W(:,t).'*yw + b0(t);
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c_hat = z*z; % (.)^2 nonnegative BM
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vtil(t) = -( v(trans(t).sp) + c_hat);
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end
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pext = softmax(vtil).';
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t_star = find([trans.sp]==sp_star & [trans.s]==s_star,1);
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% CE gradient wrt c_hat, chain rule through square
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delta = pext; delta(t_star)=delta(t_star)-1; delta = -delta; % sign for vtil=-(...)
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for t=1:nTrans
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z = W(:,t).'*yw + b0(t);
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dc_dz = 2*z; % d(z^2)/dz
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g = delta(t) * dc_dz; % ∂L/∂z
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W(:,t) = W(:,t) - mu * g * yw;
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b0(t) = b0(t) - mu * g;
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end
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% PM update for next step
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v_next = inf(nStates,1);
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for t=1:nTrans
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sp=trans(t).sp; s=trans(t).s;
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z = W(:,t).'*yw + b0(t);
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c_hat = z*z;
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cand = v(sp)+c_hat;
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if cand < v_next(s)
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v_next(s)=cand;
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end
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end
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v = v_next;
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end
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end
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%% Decode (full-length traceback)
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[xhat_ml, bhat_ml] = viterbi_decode(y_te, L, trans, @(k) feat_std(y_te_p,k,Nwin,Delta,mu_win,sd_win), ...
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@(yk,sp,s,u) learnedBM(W,b0,yk,sp,s,u), 0);
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[xhat_ex, bhat_ex] = viterbi_decode(y_te, L, trans, @(k) y_te(k), ...
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@(yk,sp,s,u) BM_classic(yk,sp,s,u), 0);
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%% BER (align by min length)
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Lmin = min([length(bhat_ml), length(bhat_ex), length(b_te)]);
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BER_ml = mean(bhat_ml(1:Lmin) ~= (b_te(1:Lmin)>0));
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BER_ex = mean(bhat_ex(1:Lmin) ~= (b_te(1:Lmin)>0));
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fprintf('BER (ML-based MLSE): %.3e\n', BER_ml);
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fprintf('BER (classic MLSE ): %.3e\n', BER_ex);
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end
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% ----------------- helpers -----------------
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function Y = im2col_sliding(y_pad, Nwin, Delta)
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T = length(y_pad) - (Nwin-1) - Delta;
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Y = zeros(Nwin,T);
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for k=1:T
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Y(:,k) = y_pad(k-Delta : k-Delta+Nwin-1);
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end
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end
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function yw = feat_std(y_pad,k,Nwin,Delta,mu_win,sd_win)
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yw = y_pad(k-Delta : k-Delta+Nwin-1);
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yw = (yw - mu_win) ./ sd_win;
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end
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function c = learnedBM(W,b0,yw,sp,s,~)
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% pick parameters of the (sp->s) transition
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persistent map;
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if isempty(map)
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% build once: index of W/b0 for each (sp,s)
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nStates = size(W,1)*0+1; %#ok<NASGU>
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end
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% linear scan is fine at this size:
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% (use first match of (sp,s))
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c = inf;
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for t=1:size(W,2)
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% suppose we stored (sp,s) order as in training; we cannot access here.
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% Instead, pass the exact column via a small mapper (build each call):
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end
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% Faster: precompute a table outside; here we reconstruct like in training
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% (rebuild tiny mapper)
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persistent key_sp key_s
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if isempty(key_sp)
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key_sp = evalin('caller','[trans.sp]');
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key_s = evalin('caller','[trans.s]');
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end
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t = find(key_sp==sp & key_s==s,1);
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z = W(:,t).'*yw + b0(t);
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c = z*z;
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end
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function [xhat, bhat] = viterbi_decode(y, L, trans, getFeat, BMfun, D_unused)
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nStates = 2^(L-1);
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T = length(y);
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v = inf(nStates,T); v(:,1)=Inf; v(1,1)=0;
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prev = zeros(nStates,T); in_u = zeros(nStates,T);
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for k=1:T
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if k==1, vprev=inf(nStates,1); vprev(1)=0; else, vprev=v(:,k-1); end
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vcur = inf(nStates,1); pre=zeros(nStates,1); inb=zeros(nStates,1);
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feat = getFeat(k); % either scalar y(k) or standardized window
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for t=1:numel(trans)
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sp=trans(t).sp; s=trans(t).s; u=trans(t).u;
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ck = BMfun(feat, sp, s, u);
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cand = vprev(sp)+ck;
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if cand < vcur(s)
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vcur(s)=cand; pre(s)=sp; inb(s)=u;
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end
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end
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v(:,k)=vcur; prev(:,k)=pre; in_u(:,k)=inb;
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end
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[~,st]=min(v(:,T));
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xhat=zeros(T,1);
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for k=T:-1:1
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xhat(k)=in_u(st,k);
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st=prev(st,k); if st==0, st=1; end
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end
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bhat = xhat>0;
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end
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