& Ping_K30000_N60000_RW4_CW4_Simulate.m
`% Simulate transmission and decoding of a systematic regular Ping
`code.
`% Copyright Brendan J Frey, January 29, 2018.
`% Software written and debugged from 8.00pm to 9.04pm on January
`29, 2018.
`% Parameters
`K=30000; % Number of data bits
`N=60000; % Number of codeword bits
`T=4; % Column weight of Hd
`EbNo=[0.975,1.15,1.225]; % List of Gaussian noise levels (dB)
`B=[2000,10000,10000]; % Number of blocks per noise level
`I=20; % Number of iterations for decoding
`rng(0); % Seed random number generator
`% Report information, compute other parameters
`if mod(N-K,T)~=0 | mod(K*T,N-K)~=0 % Check N, K and T
` error('N, K and T not compatible');
`end;
`fprintf('Number of information bits = %d\n',K);
`fprintf('Number of transmitted bits = %d\n',N);
`R=K/N;
`fprintf('Rate = %f\n',R);
`L=K*T; % Length of convolutional encoder
`A=K*T/(N-K); % Puncturing rate of convolutional encoder
`s=(2*R*10.^(EbNo/10)).^-.5; % Standard deviation of Gaussian
`noise
`Lf=zeros(1,L+1); % Forward messages (log-ratios)
`Lb=zeros(1,L); % Backward messages (log-ratios)
`Lx=zeros(1,K); % Combined messages at information bits (log-
`ratios)
`Lxd=zeros(1,L); % Messages sent from information bits down to
`accumulator
`Lxu=zeros(1,L); % Messages sent from accumulator up to
`information bits
`% Mapping from convolutional code to data bits, using Ping
`P=zeros(1,L);
`for t=1:T % Loop over sub-blocks of Hd
` P((t-1)*K+1:t*K)=randperm(K); % Random permutation for sub-
`block
`end;
`% Simulation
`ber=zeros(1,length(EbNo)); % Bit error rate
`wer=zeros(1,length(EbNo)); % Word error rate
`der=zeros(1,length(EbNo)); % Decoding failure rate
`tic;
`for j=1:length(s) % Loop over noise levels
` for b=1:B(j) % Loop over transmitted blocks
`y=randn(1,L+K)*s(j)+1; % Generate channel output assuming
`Apple v. Caltech
`IPR2017-00701
`Apple 1168
`
`(cid:20)
`
`1
`
`
`% Simulate transmission and decoding of a systematic regular Ping
`code.
`% Copyright Brendan J Frey, January 29, 2018.
`% Software written and debugged from 8.00pm to 9.04pm on January
`29, 2018.
`% Parameters
`K=30000; % Number of data bits
`N=60000; % Number of codeword bits
`T=4; % Column weight of Hd
`EbNo=[0.975,1.15,1.225]; % List of Gaussian noise levels (dB)
`B=[2000,10000,10000]; % Number of blocks per noise level
`I=20; % Number of iterations for decoding
`rng(0); % Seed random number generator
`% Report information, compute other parameters
`if mod(N-K,T)~=0 | mod(K*T,N-K)~=0 % Check N, K and T
` error('N, K and T not compatible');
`end;
`fprintf('Number of information bits = %d\n',K);
`fprintf('Number of transmitted bits = %d\n',N);
`R=K/N;
`fprintf('Rate = %f\n',R);
`L=K*T; % Length of convolutional encoder
`A=K*T/(N-K); % Puncturing rate of convolutional encoder
`s=(2*R*10.^(EbNo/10)).^-.5; % Standard deviation of Gaussian
`noise
`Lf=zeros(1,L+1); % Forward messages (log-ratios)
`Lb=zeros(1,L); % Backward messages (log-ratios)
`Lx=zeros(1,K); % Combined messages at information bits (log-
`ratios)
`Lxd=zeros(1,L); % Messages sent from information bits down to
`accumulator
`Lxu=zeros(1,L); % Messages sent from accumulator up to
`information bits
`% Mapping from convolutional code to data bits, using Ping
`P=zeros(1,L);
`for t=1:T % Loop over sub-blocks of Hd
` P((t-1)*K+1:t*K)=randperm(K); % Random permutation for sub-
`block
`end;
`% Simulation
`ber=zeros(1,length(EbNo)); % Bit error rate
`wer=zeros(1,length(EbNo)); % Word error rate
`der=zeros(1,length(EbNo)); % Decoding failure rate
`tic;
`for j=1:length(s) % Loop over noise levels
` for b=1:B(j) % Loop over transmitted blocks
`y=randn(1,L+K)*s(j)+1; % Generate channel output assuming
`Apple v. Caltech
`IPR2017-00701
`Apple 1168
`
`(cid:20)
`
`1
`
`
`
`+1 sent
` Lc=-2*y/s(j)^2; % Channel log-likelihood ratio
` for l=2:A Lc(l:A:L)=0; end; % Puncture convolutional code
` Lf(1)=-1e20; % Initialize forward state of Markov chain
`to 0
` Lb(L)=Lc(L); % Initialize backward message to channel llr
` Lx=Lc(L+1:L+K); % Initialize information bit llr to
`channel llr
` Lxu(:)=0; % Initialize messages set up to information
`bits to 0
` for i=1:I % Apply I iterations of decoding
` for n=1:L % Messages sent down to accumulator
` Lxd(n)=Lx(P(n))-Lxu(n);
` end;
` for n=1:L % Forward pass
` Lf(n+1)=Lc(n)+f(Lf(n),Lxd(n));
` end;
` for n=L:-1:2 % Backward pass
` Lb(n-1)=Lc(n-1)+f(Lb(n),Lxd(n));
` end;
` Lx=Lc(L+1:L+K); % Initialize information bit llr to
`channel llr
` for n=1:L % Messages sent up to information bits
` Lxu(n)=f(Lf(n),Lb(n));
` Lx(P(n))=Lx(P(n))+Lxu(n);
` end;
` end;
` xhat=1-(Lx<0);
` ber(j)=ber(j)+sum(xhat); % Update BER
` wer(j)=wer(j)+(sum(xhat)>0); % Udate WER
` der(j)=der(j)+(mean(xhat)>.1); % Update DER
` end;
` ber(j)=ber(j)/K/B(j); % Compute BER
` wer(j)=wer(j)/B(j); % Compute WER
` der(j)=der(j)/B(j); % Compute FER
` fprintf(' Eb/No=%f, ber=%.2e, wer=%.2e, der=%.2e\n', ...
` EbNo(j),ber(j),wer(j),der(j));
`end;
`toc
`% Message passing for accumulator
`function c = f(a,b)
`if a>b c=a+log(1+exp(b-a));
`else c=b+log(1+exp(a-b));
`end;
`if a+b>0 c=c-(a+b+log(1+exp(-a-b)));
`else c=c-log(1+exp(a+b));
`end;
`end
`
`2
`
`(cid:21)
`
`
`
`& Ping_Plus_MacKay_K30000_N60000_RW458_CW39_Simulate.m
`% Simulate transmission and decoding of a systematic Ping code,
`made
`% irregular using a MacKay construction.
`% Copyright Brendan J Frey, January 29, 2018.
`% Software written and debugged from 9.15pm to 10.30pm on January
`30, 2018.
`% Parameters
`K=30000; % Number of data bits
`N=60000; % Number of codeword bits
`EbNo=[0.7,0.775,0.85,0.95]; % List of Gaussian noise levels (dB)
`B=[100,100,1000,40000]; % Number of blocks per noise level
`I=40; % Number of iterations for decoding
`rng(2); % Seed random number generator
`% Construct irregular Ping code using MacKay-like permutation
`matrices.
`% Row weight is 4,5, or 8. Column weight is 3 or 9
`% 1 4 1 indicates a K/6 x K/6 permutation matrix
`% 44 4 is a superposition of 4 K/6 x K/6 permutation
`matrices
`% 1- 2- 1-
`% |\ |\ |\ 1- is a K/3 x K/3 permutation matrix
`% 11 1- 20 |\
`% 1 |\ 20
`H=sparse(K,K); % Matrix that Ping calls Hd
`G=K/6; % Smallest sub-block size
`H=H+sparse(1:G,randperm(G),ones(1,G),K,K);
`for j=1:4 H=H+sparse(1:G,5*G+randperm(G),ones(1,G),K,K); end;
`for j=1:4 H=H+sparse(G+[1:G],4*G+randperm(G),ones(1,G),K,K); end;
`for j=1:4 H=H+sparse(G+[1:G],5*G+randperm(G),ones(1,G),K,K); end;
`H=H+sparse(2*G+[1:2*G],randperm(2*G),ones(1,2*G),K,K);
`for j=1:2 H=H+sparse(2*G+[1:2*G],2*G+randperm(2*G),ones(1,2
`*G),K,K); end;
`H=H+sparse(2*G+[1:2*G],4*G+randperm(2*G),ones(1,2*G),K,K);
`H=H+sparse(4*G+[1:G],randperm(G),ones(1,G),K,K);
`H=H+sparse(4*G+[1:G],G+randperm(G),ones(1,G),K,K);
`H=H+sparse(5*G+[1:G],G+randperm(G),ones(1,G),K,K);
`H=H+sparse(4*G+[1:2*G],2*G+randperm(2*G),ones(1,2*G),K,K);
`for j=1:2 H=H+sparse(4*G+[1:G],4*G+randperm(G),ones(1,G),K,K);
`end;
`for j=1:2 H=H+sparse(5*G+[1:G],4*G+randperm(G),ones(1,G),K,K);
`end;
`H(H(:)>1)=1;
`P=mod(find(H')-1,K)+1; % Mapping from convolutional code to data
`bits
`L=length(P); % Length of convolutional encoder
`A=zeros(1,L); A(cumsum(full(sum(H,2))))=1;% Puncturing pattern
`% Report information, compute other parameters
`fprintf('Number of information bits = %d\n',K);
`
`3
`
`(cid:20)
`
`
`
`fprintf('Number of transmitted bits = %d\n',N);
`R=K/N;
`fprintf('Rate = %f\n',R);
`s=(2*R*10.^(EbNo/10)).^-.5; % Standard deviation of Gaussian
`noise
`Lf=zeros(1,L+1); % Forward messages (log-ratios)
`Lb=zeros(1,L); % Backward messages (log-ratios)
`Lx=zeros(1,K); % Combined messages at information bits (log-
`ratios)
`Lxd=zeros(1,L); % Messages sent from information bits down to
`accumulator
`Lxu=zeros(1,L); % Messages sent from accumulator up to
`information bits
`% Simulation
`ber=zeros(1,length(EbNo)); % Bit error rate
`wer=zeros(1,length(EbNo)); % Word error rate
`der=zeros(1,length(EbNo)); % Decoding failure rate
`for j=1:length(s) % Loop over noise levels
` for b=1:B(j) % Loop over transmitted blocks
` y=randn(1,L+K)*s(j)+1; % Generate channel output assuming
`+1 sent
` Lc=-2*y/s(j)^2; % Channel log-likelihood ratio
` Lc(1:L)=Lc(1:L).*A; % Puncture convolutional code
` Lf(1)=-1e20; % Initialize forward state of Markov chain
`to 0
` Lb(L)=Lc(L); % Initialize backward message to channel llr
` Lx=Lc(L+1:L+K); % Initialize information bit llr to
`channel llr
` Lxu(:)=0; % Initialize messages set up to information
`bits to 0
` for i=1:I % Apply I iterations of decoding
` for n=1:L % Messages sent down to accumulator
` Lxd(n)=Lx(P(n))-Lxu(n);
` end;
` for n=1:L % Forward pass
` Lf(n+1)=Lc(n)+f(Lf(n),Lxd(n));
` end;
` for n=L:-1:2 % Backward pass
` Lb(n-1)=Lc(n-1)+f(Lb(n),Lxd(n));
` end;
` Lx=Lc(L+1:L+K); % Initialize information bit llr to
`channel llr
` for n=1:L % Messages sent up to information bits
` Lxu(n)=f(Lf(n),Lb(n));
` Lx(P(n))=Lx(P(n))+Lxu(n);
` end;
` end;
` xhat=1-(Lx<0);
` ber(j)=ber(j)+sum(xhat); % Update BER
` wer(j)=wer(j)+(sum(xhat)>0); % Udate WER
` der(j)=der(j)+(mean(xhat)>.1); % Update DER
`
`4
`
`(cid:21)
`
`
`
` end;
` ber(j)=ber(j)/K/B(j); % Compute BER
` wer(j)=wer(j)/B(j); % Compute WER
` der(j)=der(j)/B(j); % Compute FER
` fprintf(' Eb/No=%f, ber=%.2e, wer=%.2e, der=%.2e\n', ...
` EbNo(j),ber(j),wer(j),der(j));
`end;
`% Message passing for accumulator
`function c = f(a,b)
`if a>b c=a+log(1+exp(b-a));
`else c=b+log(1+exp(a-b));
`end;
`if a+b>0 c=c-(a+b+log(1+exp(-a-b)));
`else c=c-log(1+exp(a+b));
`end;
`end
`
`5
`
`(cid:22)
`
`
`
`% Ping_Plus_MacKay_K30000_N60000_RW5_CW459_Simulate.m
`% Simulate transmission and decoding of a systematic Ping code,
`made
`% irregular using a MacKay construction.
`% Copyright Brendan J Frey, January 29, 2018.
`% Software written and debugged from 9.15pm to 10.30pm on January
`30, 2018.
`% Simulation run Feb 1 to Feb 4, 2018.
`% Parameters
`K=30000; % Number of data bits
`N=60000; % Number of codeword bits
`EbNo=[0.775,0.85,0.95,1.025]-.2; % List of Gaussian noise levels
`(dB)
`B=[1000,1000,10000,80000]; % Number of blocks per noise level
`I=40; % Number of iterations for decoding
`rng(0); % Seed random number generator
`% Construct irregular Ping code using MacKay-like permutation
`matrices
`% Row weight is 5, column weight is 4, 5 or 9.
` 1 4 1 indicates a K/6 x K/6 permutation matrix
`% 14 4 is a superposition of 4 K/6 x K/6 permutation
`matrices
`% 2- 2- 1-
`% |\ |\ |\ 1- is a K/3 x K/3 permutation matrix
`% 11 2- 1 |\
`% 1 |\ 2
`H=sparse(K,K); % Matrix that Ping calls Hd
`G=K/6; % Smallest sub-block size
`H=H+sparse(1:G,randperm(G),ones(1,G),K,K);
`for j=1:4 H=H+sparse(1:G,5*G+randperm(G),ones(1,G),K,K); end;
`H=H+sparse(G+[1:G],4*G+randperm(G),ones(1,G),K,K);
`for j=1:4 H=H+sparse(G+[1:G],5*G+randperm(G),ones(1,G),K,K); end;
`for j=1:2 H=H+sparse(2*G+[1:2*G],randperm(2*G),ones(1,2*G),K,K);
`end;
`for j=1:2 H=H+sparse(2*G+[1:2*G],2*G+randperm(2*G),ones(1,2
`*G),K,K); end;
`H=H+sparse(2*G+[1:2*G],4*G+randperm(2*G),ones(1,2*G),K,K);
`H=H+sparse(4*G+[1:G],randperm(G),ones(1,G),K,K);
`H=H+sparse(4*G+[1:G],G+randperm(G),ones(1,G),K,K);
`H=H+sparse(5*G+[1:G],G+randperm(G),ones(1,G),K,K);
`for j=1:2 H=H+sparse(4*G+[1:2*G],2*G+randperm(2*G),ones(1,2
`*G),K,K); end;
`H=H+sparse(4*G+[1:G],4*G+randperm(G),ones(1,G),K,K);
`for j=1:2 H=H+sparse(5*G+[1:G],4*G+randperm(G),ones(1,G),K,K);
`end;
`H(H(:)>1)=1;
`P=mod(find(H')-1,K)+1; % Mapping from convolutional code to data
`bits
`L=length(P); % Length of convolutional encoder
`
`%%
`
`6
`
`(cid:20)
`
`
`
`A=zeros(1,L); A(cumsum(full(sum(H,2))))=1;% Puncturing pattern
`% Report information, compute other parameters
`fprintf('Number of information bits = %d\n',K);
`fprintf('Number of transmitted bits = %d\n',N);
`R=K/N;
`fprintf('Rate = %f\n',R);
`s=(2*R*10.^(EbNo/10)).^-.5; % Standard deviation of Gaussian
`noise
`Lf=zeros(1,L+1); % Forward messages (log-ratios)
`Lb=zeros(1,L); % Backward messages (log-ratios)
`Lx=zeros(1,K); % Combined messages at information bits (log-
`ratios)
`Lxd=zeros(1,L); % Messages sent from information bits down to
`accumulator
`Lxu=zeros(1,L); % Messages sent from accumulator up to
`information bits
`% Simulation
`ber=zeros(1,length(EbNo)); % Bit error rate
`wer=zeros(1,length(EbNo)); % Word error rate
`der=zeros(1,length(EbNo)); % Decoding failure rate
`tic;
`for j=1:length(s) % Loop over noise levels
` for b=1:B(j) % Loop over transmitted blocks
` y=randn(1,L+K)*s(j)+1; % Generate channel output assuming
`+1 sent
` Lc=-2*y/s(j)^2; % Channel log-likelihood ratio
` Lc(1:L)=Lc(1:L).*A; % Puncture convolutional code
` Lf(1)=-1e20; % Initialize forward state of Markov chain
`to 0
` Lb(L)=Lc(L); % Initialize backward message to channel llr
` Lx=Lc(L+1:L+K); % Initialize information bit llr to
`channel llr
` Lxu(:)=0; % Initialize messages set up to information
`bits to 0
` for i=1:I % Apply I iterations of decoding
` for n=1:L % Messages sent down to accumulator
` Lxd(n)=Lx(P(n))-Lxu(n);
` end;
` for n=1:L % Forward pass
` Lf(n+1)=Lc(n)+f(Lf(n),Lxd(n));
` end;
` for n=L:-1:2 % Backward pass
` Lb(n-1)=Lc(n-1)+f(Lb(n),Lxd(n));
` end;
` Lx=Lc(L+1:L+K); % Initialize information bit llr to
`channel llr
` for n=1:L % Messages sent up to information bits
` Lxu(n)=f(Lf(n),Lb(n));
` Lx(P(n))=Lx(P(n))+Lxu(n);
` end;
`
`7
`
`(cid:21)
`
`
`
` end;
` xhat=1-(Lx<0);
` ber(j)=ber(j)+sum(xhat); % Update BER
` wer(j)=wer(j)+(sum(xhat)>0); % Udate WER
` der(j)=der(j)+(mean(xhat)>.1); % Update DER
` end;
` ber(j)=ber(j)/K/B(j); % Compute BER
` wer(j)=wer(j)/B(j); % Compute WER
` der(j)=der(j)/B(j); % Compute FER
` fprintf(' Eb/No=%f, ber=%.2e, wer=%.2e, der=%.2e\n', ...
` EbNo(j),ber(j),wer(j),der(j));
`end;
`toc
`% Message passing for accumulator
`function c = f(a,b)
`if a>b c=a+log(1+exp(b-a));
`else c=b+log(1+exp(a-b));
`end;
`if a+b>0 c=c-(a+b+log(1+exp(-a-b)));
`else c=c-log(1+exp(a+b));
`end;
`end
`
`8
`
`(cid:22)
`
`
`
`
`t
`~~ Ping CW=4 RW=4
`4
`aaa ——_ Ping+MacKay CWe=4,5,9 RW=5
`
`[otaececeececectteeeteeetdpescteettteeecteectteesteeetteee{eesectiesttteetttestteeetteeetlges|ooteeetteeectees ne Ping+MacKay CW=3,9 RW=4,5,8 |
`10°
`
`
`
`
`
`
`a
`
`— S
`
`
`
`Biterrorrate o
`
`k
`
`10°
`
`10°
`
`10°"
`|
`|
`|
`|
`|
`
`0.7
`0.8
`0.9
`1
`1.4
`1.2
`E/N, (dB
`
`9
`
`
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