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-% vq_binary_switch.m
-% David Rowe Sep 2021
-%
-% Experiments in making VQs robust to bit errors, this is an Octave
-% implementation of [1].
-%
-% [1] Pseudo Gray Coding, Zeger & Gersho 1990
-
-1;
-
-% returns indexes of hamming distance 1 neighbours
-function index_neighbours = distance_one_neighbours(N,k)
- log2N = log2(N);
- index_neighbours = [];
- for b=0:log2N-1
- index_neighbour = bitxor(k-1,2.^b) + 1;
- index_neighbours = [index_neighbours index_neighbour];
- end
-end
-
-% equation (33) of [1], for hamming distance 1
-function c = cost_of_distance_one(vq, prob, k, verbose=0)
- [N K] = size(vq);
- log2N = log2(N);
- c = 0;
- for b=0:log2N-1
- index_neighbour = bitxor(k-1,2.^b) + 1;
- diff = vq(k,:) - vq(index_neighbour, :);
- dist = sum(diff*diff');
- c += prob(k)*dist;
- if verbose
- printf("k: %d b: %d index_neighbour: %d dist: %f prob: %f c: %f \n", k, b, index_neighbour, dist, prob(k), c);
- end
- end
-endfunction
-
-% equation (39) of [1]
-function d = distortion_of_current_mapping(vq, prob, verbose=0)
- [N K] = size(vq);
-
- d = 0;
- for k=1:N
- c = cost_of_distance_one(vq, prob, k);
- d += c;
- if verbose
- printf("k: %2d c: %f d: %f\n", k, c, d);
- end
- end
-endfunction
-
-function [vq distortion] = binary_switching(vq, prob, max_iteration, fast_en=1)
- [N K] = size(vq);
- iteration = 0;
- i = 1;
- finished = 0;
- switches = 0;
- distortion0 = distortion_of_current_mapping(vq, prob)
-
- while !finished
-
- % generate a list A(i) of which vectors have the largest cost of bit errors
- c = zeros(1,N);
- for k=1:N
- c(k) = cost_of_distance_one(vq, prob, k);
- end
- [tmp A] = sort(c,"descend");
-
- % Try switching each vector with A(i)
- best_delta = 0;
- for j=2:N
- % we can't switch with ourself
- if j != A(i)
- if fast_en
- delta = -cost_of_distance_one(vq, prob, A(i)) - cost_of_distance_one(vq, prob, j);
- n1 = [distance_one_neighbours(N,A(i)) distance_one_neighbours(N,j)];
- n1(n1 == A(i)) = [];
- n1(n1 == j) = [];
- for l=1:length(n1)
- delta -= cost_of_distance_one(vq, prob, n1(l));
- end
- else
- distortion1 = distortion_of_current_mapping(vq, prob);
- end
-
- % switch vq entries A(i) and j
- tmp = vq(A(i),:);
- vq(A(i),:) = vq(j,:);
- vq(j,:) = tmp;
-
- if fast_en
- delta += cost_of_distance_one(vq, prob, A(i)) + cost_of_distance_one(vq, prob, j);
- for l=1:length(n1)
- delta += cost_of_distance_one(vq, prob, n1(l));
- end
- else
- distortion2 = distortion_of_current_mapping(vq, prob);
- delta = distortion2 - distortion1;
- end
-
- if delta < 0
- if abs(delta) > best_delta
- best_delta = abs(delta);
- best_j = j;
- end
- end
-
- % unswitch
- tmp = vq(A(i),:);
- vq(A(i),:) = vq(j,:);
- vq(j,:) = tmp;
- end
- end % next j
-
- % printf("best_delta: %f best_j: %d\n", best_delta, best_j);
- if best_delta == 0
- % Hmm, no improvement, lets try the next vector in the sorted cost list
- if i == N
- finished = 1;
- else
- i++;
- end
- else
- % OK keep the switch that minimised the distortion
-
- tmp = vq(A(i),:);
- vq(A(i),:) = vq(best_j,:);
- vq(best_j,:) = tmp;
- switches++;
-
- % set up for next iteration
- iteration++;
- distortion = distortion_of_current_mapping(vq, prob);
- printf("it: %3d dist: %f %3.2f i: %3d sw: %3d\n", iteration, distortion,
- distortion/distortion0, i, switches);
- if iteration >= max_iteration, finished = 1, end
- i = 1;
- end
-
- end
-
-endfunction
-
-% return indexes of hamming distance one vectors
-function ind = neighbour_indexes(vq, k)
- [N K] = size(vq);
- log2N = log2(N);
- ind = [];
- for b=0:log2N-1
- index_neighbour = bitxor(k-1,2.^b) + 1;
- ind = [ind index_neighbour];
- end
-endfunction
-
-function test_binary_switch
- vq1 = [1 1; -1 1; -1 -1; 1 -1];
- %f=fopen("vq1.f32","wb"); fwrite(f, vq1, 'float32'); fclose(f);
- [vq2 distortion] = binary_switching(vq1, ones(1,4), 10);
- % algorithm should put hamming distance 1 neighbours in adjacent quadrants
- distance_to_closest_neighbours = 2;
- % there are two hamming distance 1 neighbours
- target_distortion = 2^2*distance_to_closest_neighbours*length(vq1);
- assert(target_distortion == distortion);
- printf("test_binary_switch OK!\n");
-endfunction
-
-function test_fast
- N=16; % Number of VQ codebook vectors
- K=2; % Vector length
- Ntrain=10000;
-
- training_data = randn(Ntrain,K);
- [idx vq1] = kmeans(training_data, N);
- f=fopen("vq1.f32","wb");
- for r=1:rows(vq1)
- fwrite(f,vq1(r,:),"float32");
- end
- fclose(f);
- [vq2 distortion] = binary_switching(vq1, [1 ones(1,N-1)], 1000, fast_en = 0);
- [vq3 distortion] = binary_switching(vq1, [1 ones(1,N-1)], 1000, fast_en = 1);
- assert(vq2 == vq3);
- printf("test_fast OK!\n");
-endfunction
-
-function demo
- N=16; % Number of VQ codebook vectors
- K=2; % Vector length
- Ntrain=10000;
- training_data = randn(Ntrain,K);
- [idx vq1] = kmeans(training_data, N);
- [vq2 distortion] = binary_switching(vq1, [1 ones(1,N-1)], 1000, 1);
-
- figure(1); clf; plot(training_data(:,1), training_data(:,2),'+');
- hold on;
- plot(vq1(:,1), vq1(:,2),'og','linewidth', 2);
- plot(vq2(:,1), vq2(:,2),'or','linewidth', 2);
-
- % plot hamming distance 1 neighbours
- k = 1;
- ind = neighbour_indexes(vq2, k);
- for i=1:length(ind)
- plot([vq2(k,1) vq2(ind(i),1)],[vq2(k,2) vq2(ind(i),2)],'r-','linewidth', 2);
- end
- hold off;
-endfunction
-
-pkg load statistics
-%test_binary_switch;
-test_fast;
-%demo
-
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