Many changes here and there. I lost track... :-(
Current work is on MLSE and SD Decoding etc. MLSE is currently not 100% working, the scalings are maybe off?!
This commit is contained in:
Silas Oettinghaus
@@ -1,5 +1,5 @@
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function [ach_inf_rate] = calc_air(test_signal,reference_signal,options)
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% Calculation of AIR acc. to J. Kozesnik, „Numerically Computing Achievable Rates of Memoryless Channels“, Francisco Javier Garcıa-Gomez, doi: 10.1007/978-94-009-9857-5.
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% „Numerically Computing Achievable Rates of Memoryless Channels“, Francisco Javier Garcıa-Gomez, doi: 10.1007/978-94-009-9857-5.
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% Implementation is not accessible, I mailed TUM to get the code...
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arguments(Input)
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@@ -26,7 +26,7 @@ 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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% CALC EVM
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% CALC AIR
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%%% new implementation of AIR
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constellation = unique(reference_signal);
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reference_idx = arrayfun(@(x) find(constellation == x, 1), reference_signal);
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94
Functions/Metrics/calc_gmi_bitwise.m
Normal file
94
Functions/Metrics/calc_gmi_bitwise.m
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@@ -0,0 +1,94 @@
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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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arguments(Input)
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test_signal;
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reference_signal;
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options.skip_front = 0;
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options.skip_end = 0;
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options.returnErrorLocation = 0;
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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)<length(test_signal),"You can not skip more bits than overall length of data! Set skip_front or skip_end to lower value or check data_in");
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if isa(reference_signal,'Signal')
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reference_signal = reference_signal.signal;
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end
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if isa(test_signal,'Signal')
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test_signal = test_signal.signal;
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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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% CALC AIR
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%%% new implementation of AIR
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% Precompute
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N = length(test_signal);
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M = numel(unique(reference_signal));
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nBits = log2(M);
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levels = PAMmapper(M,0).levels / PAMmapper(M,0).scaling;
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grayBits= PAMmapper(M,0).showBitMapping;
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priors = ones(1,M)/M;
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noise = test_signal-reference_signal;
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sigma2 = var(noise);
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% Allocate
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LLR = zeros(N, nBits);
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rxBits = 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); % M×1
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% Per‐bit LLR
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for b = 1:nBits
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idx0 = grayBits(:,b)==0;
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idx1 = grayBits(:,b)==1;
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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;
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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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% Compute GMI (bit‐wise MI averaged over all symbols)
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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); % in bits per symbol
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NGMI = GMI / nBits; % normalized per bit
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% Auxiliary nested helper for numerically stable log-sum-exp
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function s = logsumexp(a)
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% LOGSUMEXP Compute log(sum(exp(a))) in a numerically stable way
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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_bits = length(reference) - length(data);
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skip_end = delta_bits + skip_end;
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reference_ = reference(skipstart+1:end-skip_end,:);
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end
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end
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@@ -1,5 +1,5 @@
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function [GMI,NGMI] = calc_ngmi(test_signal,reference_signal,options)
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% Silas implementation of (N)GMI calculation according to: J. Cho, L. Schmalen, und P. J. Winzer,
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% Silas implementation of (N)GMI calculation according to: J. Cho, L. Schmalen, und P. J. Winzer,
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% „Normalized Generalized Mutual Information as a Forward Error Correction Threshold for Probabilistically Shaped QAM“,
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% in 2017 European Conference on Optical Communication (ECOC), Sep. 2017, doi: 10.1109/ECOC.2017.8345872.
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@@ -38,7 +38,7 @@ end
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assert(length(test_signal) == length(reference_signal),"Sequence length does not match");
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%%% implemented according to [1] J. Cho, L. Schmalen, und P. J. Winzer,
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%%% implemented according to [1] J. Cho, L. Schmalen, und P. J. Winzer,
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% „Normalized Generalized Mutual Information as a Forward Error Correction Threshold for Probabilistically Shaped QAM“,
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% in 2017 European Conference on Optical Communication (ECOC), Sep. 2017, S. 1–3. doi: 10.1109/ECOC.2017.8345872.
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@@ -62,7 +62,7 @@ end
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m = log2(M); %bits per symbol
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entries = sum(~isnan(received_sd),2)';
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P_X = entries./N;
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P_X = ones(1,M)/M;%entries./N;
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% Parameters
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symbols = constellation'; % PAM-4 symbols
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@@ -75,18 +75,20 @@ end
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% Entropy term
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H_X = -sum(P_X .* log2(P_X)); % Entropy of input distribution
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% GMI computation
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noise_impact_term = 0;
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for k = 1:N
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y_k = test_signal(k); % Current received sample
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[~, closest_symbol_idx] = min(abs(symbols - y_k)); % Closest symbol index
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closest_symbol = symbols(closest_symbol_idx); % Closest symbol
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tx_bits = PAMmapper(M,0,"eth_style",0).demap(reference_signal);
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for i = 1:m
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% GMI computation
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bit_llr_sum = 0;
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for k = 1:N %loop over signal
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y_k = test_signal(k); % Current received sample
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% [~, closest_symbol_idx] = min(abs(symbols - y_k)); % Closest symbol index
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for i = 1:m %loop over bit position
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% Extract i-th bit for each symbol
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bit_mask = gray_bits(:, i); % Binary column for i-th bit of all symbols
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matching_symbols = symbols(bit_mask == gray_bits(closest_symbol_idx, i));
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% matching_symbols = symbols(bit_mask == gray_bits(closest_symbol_idx, i)); %old, based on decision that mihht be wrong
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matching_symbols = symbols(bit_mask == tx_bits(k,i)); %new, based on tx bits
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% Numerator: Sum over x in x_{b_{k, i}}
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numerator = sum(q_Y_given_X(y_k, matching_symbols) .* P_X(ismember(symbols, matching_symbols)));
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@@ -95,15 +97,15 @@ end
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denominator = sum(q_Y_given_X(y_k, symbols) .* P_X);
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% Logarithmic contribution
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noise_impact_term = noise_impact_term + log2(numerator / denominator);
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bit_llr_sum = bit_llr_sum + log2(numerator / denominator);
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end
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end
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% Normalize the noise impact term by N
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noise_impact_term = noise_impact_term / N;
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bit_llr_sum = bit_llr_sum / N;
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% GMI
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GMI = H_X + noise_impact_term;
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GMI = H_X + bit_llr_sum;
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NGMI = GMI / m;
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end
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@@ -1,24 +1,32 @@
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function [snr_all, snr_per_level] = calc_snr(tx_signal, eq_noise)
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% CALC_SNR Calculates overall SNR and level-wise SNR for a PAM-M constellation.
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%
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% [snr_all, snr_per_level] = calc_snr(tx_signal, eq_noise)
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%
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% Inputs:
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% tx_signal - Vector of transmitted signal values.
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% eq_noise - Vector of corresponding noise samples.
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%
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% Outputs:
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% snr_all - Overall SNR computed using all signal values.
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% snr_per_level - A vector where each element is the SNR computed
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% for a unique amplitude level in tx_signal.
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%
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% The function first computes the overall SNR using the full signal vectors.
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% Then it uses the unique levels in tx_signal to calculate the SNR for
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% the symbols corresponding to each level separately.
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% CALC_SNR Calculates overall SNR and level-wise SNR for a PAM-M constellation.
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%
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% [snr_all, snr_per_level] = calc_snr(tx_signal, eq_noise)
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%
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% Inputs:
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% tx_signal - Vector of transmitted signal values.
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% eq_noise - Vector of corresponding noise samples.
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%
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% Outputs:
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% snr_all - Overall SNR computed using all signal values.
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% snr_per_level - A vector where each element is the SNR computed
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% for a unique amplitude level in tx_signal.
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%
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% The function first computes the overall SNR using the full signal vectors.
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% Then it uses the unique levels in tx_signal to calculate the SNR for
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% the symbols corresponding to each level separately.
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if isa(tx_signal,'Signal')
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tx_signal = tx_signal.signal;
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end
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if isa(eq_noise,'Signal')
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eq_noise = eq_noise.signal;
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end
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% Calculate overall SNR using the complete signals
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snr_all = snr(tx_signal, eq_noise);
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% Get the unique amplitude levels in the transmitted signal
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levels = unique(tx_signal);
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@@ -27,10 +35,10 @@ function [snr_all, snr_per_level] = calc_snr(tx_signal, eq_noise)
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for i = 1:length(levels)
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% Find indices where tx_signal equals the current level
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idx = (tx_signal == levels(i));
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% Compute the SNR for these indices
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snr_per_level(i) = snr(tx_signal(idx), eq_noise(idx));
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histogram(eq_noise(idx));
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end
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end
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