halfway merged and pulled?!
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Silas Labor Zizou
158
Functions/Metrics/calc_gmi_bitwise.m
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158
Functions/Metrics/calc_gmi_bitwise.m
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function [GMI,NGMI] = calc_gmi_bitwise(test_signal,reference_signal,options)
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% https://cioffi-group.stanford.edu/doc/book/AppendixG.pdf
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% Supports PAM2/4/8 (per-symbol) and PAM6 (pairwise: 5 bits per 2 symbols)
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arguments(Input)
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test_signal
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reference_signal
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options.skip_front (1,1) double = 0
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options.skip_end (1,1) double = 0
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options.returnErrorLocation (1,1) double = 0 %#ok<NASGU>
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end
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options.skip_end = abs(options.skip_end);
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options.skip_front = abs(options.skip_front);
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assert((options.skip_end+options.skip_front) < numel(test_signal), ...
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"You can not skip more samples than overall length.");
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if isa(reference_signal,'Signal'); reference_signal = reference_signal.signal; end
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if isa(test_signal,'Signal'); test_signal = test_signal.signal; end
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% TRIM
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[test_signal,reference_signal] = trimseq(test_signal,reference_signal,options.skip_front,options.skip_end);
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% Common precompute
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N = length(test_signal);
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M = numel(unique(reference_signal));
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noise = test_signal - reference_signal;
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sigma2 = var(noise); % real AWGN variance
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% --- Constellation (levels observed)
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constellation = unique(reference_signal);
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M = numel(constellation);
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% --- Empirical P_X (uniform is fine too; keep your original behavior)
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N = numel(reference_signal);
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counts = arrayfun(@(c) sum(reference_signal==c), constellation);
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priors = counts / N;
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% ----- PAM6: 5 bits mapped to 2 consecutive symbols (36 transitions) -----
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if M == 6
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% Pair the stream (drop last if odd)
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numPairs = floor(N/2);
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if numPairs == 0, GMI = 0; NGMI = 0; return; end
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y1 = test_signal(1:2:2*numPairs);
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y2 = test_signal(2:2:2*numPairs);
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% Use the same level order as PAMmapper to be consistent with labeling
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levels = constellation;%PAMmapper(6,0,"eth_style",0).levels; % 1x6 (actual amplitudes used)
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% Build all 36 transitions (i,j)
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[S1,S2] = ndgrid(levels, levels); % 6x6
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trans_pairs = [S1(:), S2(:)]; % 36x2
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% 5-bit labels for each transition (ETH style).
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% NOTE: keep the normalization you use with your PAMmapper (often /sqrt(10)).
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bits72 = PAMmapper(6,0,"eth_style",0).demap( reshape(trans_pairs.',[],1) );
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pairBits = reshape(bits72.', 5, []).'; % 36 x 5
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% Transmitted 5-bit labels for each observed pair (from the reference)
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tx_bits_pair = PAMmapper(6,0,"eth_style",0).demap( reshape(reference_signal(1:2* numPairs).',[],1) );
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tx_bits_pair = reshape(tx_bits_pair.', 5, []).'; % numPairs x 5
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% Precompute symbol log-priors (uniform => constant; included for shaped inputs)
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logP = log(priors);
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% Precompute masks for bit=0 / bit=1 in the 6x6 grid
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mask1 = false(6,6,5);
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mask0 = false(6,6,5);
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for b = 1:5
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tmp = false(6,6);
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tmp(:) = pairBits(:,b)==1;
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mask1(:,:,b) = tmp;
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tmp = false(6,6);
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tmp(:) = pairBits(:,b)==0;
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mask0(:,:,b) = tmp;
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end
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% Exact LLRs via log-sum-exp over the 6x6 grid
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LLR = zeros(numPairs,5);
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cst = -0.5*log(2*pi*sigma2); % cancels in LLR but harmless
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for k = 1:numPairs
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li = cst - ((y1(k) - levels).^2)/(2*sigma2) + logP; % 1x6
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lj = cst - ((y2(k) - levels).^2)/(2*sigma2) + logP; % 1x6
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logW = li(:) + lj(:).'; % 6x6 (adds logP twice)
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for b = 1:5
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L1 = logsumexp(logW(mask1(:,:,b)));
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L0 = logsumexp(logW(mask0(:,:,b)));
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LLR(k,b) = L1 - L0; % natural-log LLR
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end
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end
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% Bit-wise MI using consistency relation
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MI_bits = zeros(1,5);
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for b = 1:5
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idx0 = (tx_bits_pair(:,b)==0);
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idx1 = ~idx0;
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r0 = LLR(idx0,b);
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r1 = LLR(idx1,b);
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I0 = mean( log2(1 + exp( r0)) ); % natural LLR inside exp()
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I1 = mean( log2(1 + exp(-r1)) );
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MI_bits(b) = 1 - 0.5*(I0 + I1);
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end
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% Per-symbol outputs (5 bits per 2 symbols)
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GMI = sum(MI_bits)/2;
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NGMI = GMI / 2.5;
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% ----- Generic PAM2/4/8…: per-symbol, Gray bits directly on symbols -----
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else
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nBits = log2(M);
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levels = PAMmapper(M,0).levels' / PAMmapper(M,0).scaling; % match PAMmapper ordering
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grayBits= PAMmapper(M,0).showBitMapping; % M x nBits
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% Allocate
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LLR = zeros(N, nBits);
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for n = 1:N
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y = test_signal(n);
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ll_table = -((y - levels).^2)/(2*sigma2) + log(priors); % 1xM (log-domain)
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for b = 1:nBits
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idx0 = grayBits(:,b)==0;
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idx1 = ~idx0;
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L0 = logsumexp(ll_table(idx0));
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L1 = logsumexp(ll_table(idx1));
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LLR(n,b) = L1 - L0; % natural-log LLR
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end
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end
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tx_bits = PAMmapper(M,0,"eth_style",0).demap(reference_signal);
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% Bit-wise MI
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MI_bits = zeros(1,nBits);
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for b = 1:nBits
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r0 = LLR(tx_bits(:,b)==0,b);
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r1 = LLR(tx_bits(:,b)==1,b);
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I0 = mean( log2(1 + exp( r0)) );
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I1 = mean( log2(1 + exp(-r1)) );
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MI_bits(b) = 1 - 0.5*(I0 + I1);
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end
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GMI = sum(MI_bits); % bits / symbol
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NGMI = GMI / nBits;
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end
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% ===== Helpers =====
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function s = logsumexp(a)
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if isempty(a), s = -inf; return; end
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m = max(a(:));
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s = m + log(sum(exp(a(:) - m)));
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end
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function [data_,reference_] = trimseq(data,reference,skipstart,skip_end)
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data_ = data(skipstart+1:end-skip_end,:);
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delta = numel(reference) - numel(data_);
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reference_ = reference(skipstart+1:end-(skip_end+delta),:);
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end
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end
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