% Divsalar_K1000_N5000_Q5_Simulate.m
`% Simulate transmission and decoding of a regular RA code.
`% Copyright Brendan J Frey, January 14, 2018.
`% Software written and debugged from 8.00pm to 10.45pm on January
`14, 2018.
`% Parameters
`K=1000; % Number of information bits
`EbNo=[-.8:.1:.8]; % List of Gaussian noise levels (dB)
`B=10000; % Number of blocks per noise level
`I=100; % Number of iterations for decoding
`q=5; % Number of times to repeat information bits
`Pi=repmat([1:K],[q,1]); % Mapping from repeated bits to
`information bits
`Pi=Pi(:);
`rng(0); % Seed random number generator
`% Compute other parameters, allocate memory
`N=length(Pi); % Number of transmitted bits
`R=K/N; % Rate
`P=randperm(N); % Random permuter
`s=(2*R*10.^(EbNo/10)).^-.5; % Standard deviation of Gaussian
`noise
`Lf=zeros(1,N+1); % Forward messages (log-ratios)
`Lb=zeros(1,N); % Backward messages (log-ratios)
`Lx=zeros(1,K); % Combined messages at information bits (log-
`ratios)
`Lxd=zeros(1,N); % Messages sent from information bits down to
`accumulator
`Lxu=zeros(1,N); % Messages sent from accumulator up to
`information bits
`ber=zeros(1,length(EbNo)); % Bit error rate
`wer=zeros(1,length(EbNo)); % Word error rate
`fer=zeros(1,length(EbNo)); % Failure to decode rate
`fprintf('Number of information bits = %d\n',K);
`fprintf('Number of transmitted bits = %d\n',N);
`fprintf('Rate = %f\n',R);
`% Simulation
`for j=1:length(s) % Loop over noise levels
` for b=1:B % Loop over transmitted blocks
` y=randn(1,N)*s(j)+1; % Generate channel output assuming +
`1 sent
` Lc=-2*y/s(j)^2; % Channel log-likelihood ratio
` Lf(1)=-1e20; % Initialize forward state of Markov chain
`to 0
` Lb(N)=Lc(N); % Initialize backward message to channel llr
` Lxd(:)=0; % Initialize messages from information bits to
` for i=1:I % Apply I iterations of decoding
` for n=1:N % Forward pass
` Lf(n+1)=Lc(n)+f(Lf(n),Lxd(n));
`
`0
`
`(cid:20)
`
`Apple v. Caltech
`IPR2017-00219
`Apple 1268
`
`1
`
`
`% Simulate transmission and decoding of a regular RA code.
`% Copyright Brendan J Frey, January 14, 2018.
`% Software written and debugged from 8.00pm to 10.45pm on January
`14, 2018.
`% Parameters
`K=1000; % Number of information bits
`EbNo=[-.8:.1:.8]; % List of Gaussian noise levels (dB)
`B=10000; % Number of blocks per noise level
`I=100; % Number of iterations for decoding
`q=5; % Number of times to repeat information bits
`Pi=repmat([1:K],[q,1]); % Mapping from repeated bits to
`information bits
`Pi=Pi(:);
`rng(0); % Seed random number generator
`% Compute other parameters, allocate memory
`N=length(Pi); % Number of transmitted bits
`R=K/N; % Rate
`P=randperm(N); % Random permuter
`s=(2*R*10.^(EbNo/10)).^-.5; % Standard deviation of Gaussian
`noise
`Lf=zeros(1,N+1); % Forward messages (log-ratios)
`Lb=zeros(1,N); % Backward messages (log-ratios)
`Lx=zeros(1,K); % Combined messages at information bits (log-
`ratios)
`Lxd=zeros(1,N); % Messages sent from information bits down to
`accumulator
`Lxu=zeros(1,N); % Messages sent from accumulator up to
`information bits
`ber=zeros(1,length(EbNo)); % Bit error rate
`wer=zeros(1,length(EbNo)); % Word error rate
`fer=zeros(1,length(EbNo)); % Failure to decode rate
`fprintf('Number of information bits = %d\n',K);
`fprintf('Number of transmitted bits = %d\n',N);
`fprintf('Rate = %f\n',R);
`% Simulation
`for j=1:length(s) % Loop over noise levels
` for b=1:B % Loop over transmitted blocks
` y=randn(1,N)*s(j)+1; % Generate channel output assuming +
`1 sent
` Lc=-2*y/s(j)^2; % Channel log-likelihood ratio
` Lf(1)=-1e20; % Initialize forward state of Markov chain
`to 0
` Lb(N)=Lc(N); % Initialize backward message to channel llr
` Lxd(:)=0; % Initialize messages from information bits to
` for i=1:I % Apply I iterations of decoding
` for n=1:N % Forward pass
` Lf(n+1)=Lc(n)+f(Lf(n),Lxd(n));
`
`0
`
`(cid:20)
`
`Apple v. Caltech
`IPR2017-00219
`Apple 1268
`
`1
`
`
`
` end;
` for n=N:-1:2 % Backward pass
` Lb(n-1)=Lc(n-1)+f(Lb(n),Lxd(n));
` end;
` Lx(:)=0;
` for n=1:N % Fuse messages at information bits
` Lxu(n)=f(Lf(n),Lb(n));
` Lx(Pi(P(n)))=Lx(Pi(P(n)))+Lxu(n);
` end;
` for n=1:N % Messages sent down to accumulator
` Lxd(n)=Lx(Pi(P(n)))-Lxu(n);
` end;
` end;
` xhat=1-(Lx<0); % Threhshold information bit llrs
` ber(j)=ber(j)+sum(xhat); % Update BER
` wer(j)=wer(j)+(sum(xhat)>0); % Udate WER
` fer(j)=fer(j)+(mean(xhat)>.1); % Update DER
` end;
` ber(j)=ber(j)/K/B; % Compute BER
` wer(j)=wer(j)/B; % Compute WER
` fer(j)=fer(j)/B; % Compute FER
` fprintf(' Eb/No=%f, ber=%e, wer=%e, fer=%e\n', ...
` EbNo(j),ber(j),wer(j),fer(j));
`end;
`% Message passing for XOR function (check node, 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
`
`(cid:21)
`
`2
`
`
`
`% Divsalar_Plus_Frey_K1000_N5000_Q37_Simulate.m
`% Simulate transmission and decoding of Divsalar RA code modified
`using
`% Frey's irregular construction.
`% Copyright Brendan J Frey, January 21, 2018.
`% Software written and debugged from 4.00pm to 4.30pm on January
`21, 2018.
`% Based on Divsalar_K4096_N16384_Q4_Simulate.m.
`% Parameters
`k=[0,0,500,0,0,0,500]; % Number of information bits with each
`degree
`K=sum(k); % Number of information bits
`EbNo=[-.8:.1:.8]; % List of Gaussian noise levels (dB)
`B=10000; % Number of blocks per noise level
`I=100; % Number of iterations for decoding
`rng(0); % Seed random number generator
`% Compute other parameters
`Pi=[]; j=0; % Mapping from repeated bits to information bits
`for i=1:length(k) tmp=repmat([j+1:j+k(i)],[i,1]); Pi=[Pi;tmp(:)];
`j=j+k(i); end;
`N=length(Pi); % Number of transmitted bits
`P=randperm(N); % Random permuter mapping from transmitted to
`repeated bits
`R=K/N; % Rate
`s=(2*R*10.^(EbNo/10)).^-.5; % Standard deviation of Gaussian
`noise
`Lf=zeros(1,N+1); % Forward messages (log-ratios)
`Lb=zeros(1,N); % Backward messages (log-ratios)
`Lx=zeros(1,K); % Combined messages at information bits (log-
`ratios)
`Lxd=zeros(1,N); % Messages sent from information bits down to
`accumulator
`Lxu=zeros(1,N); % Messages sent from accumulator up to
`information bits
`ber=zeros(1,length(EbNo)); % Bit error rate
`wer=zeros(1,length(EbNo)); % Word error rate
`fer=zeros(1,length(EbNo)); % Failure to decode rate
`fprintf('Number of information bits = %d\n',K);
`fprintf('Number of transmitted bits = %d\n',N);
`fprintf('Rate = %f\n',R);
`% Simulation
`for j=1:length(s) % Loop over noise levels
` for b=1:B % Loop over transmitted blocks
` y=randn(1,N)*s(j)+1; % Generate channel output assuming +
`1 sent
` Lc=-2*y/s(j)^2; % Channel log-likelihood ratio
` Lf(1)=-1e20; % Initialize forward state of Markov chain
`to 0
` Lb(N)=Lc(N); % Initialize backward message to channel llr
`
`(cid:20)
`
`3
`
`
`
` Lxd(:)=0; % Initialize messages from information bits to
` for i=1:I % Apply I iterations of decoding
` for n=1:N % Forward pass
` Lf(n+1)=Lc(n)+f(Lf(n),Lxd(n));
` end;
` for n=N:-1:2 % Backward pass
` Lb(n-1)=Lc(n-1)+f(Lb(n),Lxd(n));
` end;
` Lx(:)=0;
` for n=1:N % % Fuse messages at information bits
` Lxu(n)=f(Lf(n),Lb(n));
` Lx(Pi(P(n)))=Lx(Pi(P(n)))+Lxu(n);
` end;
` for n=1:N % Messages sent down to accumulator
` Lxd(n)=Lx(Pi(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
` fer(j)=fer(j)+(mean(xhat)>.1); % Update DER
` end;
` ber(j)=ber(j)/K/B; % Compute BER
` wer(j)=wer(j)/B; % Compute WER
` fer(j)=fer(j)/B; % Compute FER
` fprintf(' Eb/No=%f, ber=%e, wer=%e, fer=%e\n', ...
` EbNo(j),ber(j),wer(j),fer(j));
`end;
`% Message passing for XOR function (check node, 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
`
`0
`
`(cid:21)
`
`4
`
`
`
`Divsalar compared to Divsalar + Frey, N=5000, K=1000, R=1I5
`
`
` 10'1
`
`_
`
`
`
`
`
`Worderrorrate
`
` - + Divsalar + Frey 0:3,?
`
`Divsalar 0:5
`
`:33:
`
`
`
`
`
`
`
`Biterrorrate
`
`
`
`
`
`5
`
`
`
`% Divsalar_K4096_N16384_Q4_Simulate.m
`% Simulate transmission and decoding of a regular RA code.
`Parameters taken
`% from Divsalar: K=4096, R=1/4, 20 iterations
`% Copyright Brendan J Frey, January 14, 2018.
`% Software written and debugged from 8.00pm to 10.45pm on January
`14, 2018.
`% Parameters
`K=4096;% Number of information bits
`EbNo=[.6,.7,.8,.85]; % List of Gaussian SNR's (dB)
`B=[10000,10000,1000000,1000000]; % Number of blocks per noise
`level
`I=20; % Number of iterations for decoding
`q=4; % Number of times to repeat information bits
`Pi=repmat([1:K],[q,1]); % Mapping from repeated bits to
`information bits
`Pi=Pi(:);
`rng(1); % Seed random number generator
`% Compute other parameters, allocate memory
`N=length(Pi); % Number of transmitted bits
`R=K/N; % Rate
`P=randperm(N); % Random permuter
`s=(2*R*10.^(EbNo/10)).^-.5; % Standard deviation of Gaussian
`noise
`Lf=zeros(1,N+1); % Forward messages (log-ratios)
`Lb=zeros(1,N); % Backward messages (log-ratios)
`Lx=zeros(1,K); % Combined messages at information bits (log-
`ratios)
`Lxd=zeros(1,N); % Messages sent from information bits down to
`accumulator
`Lxu=zeros(1,N); % Messages sent from accumulator up to
`information bits
`ber=zeros(1,length(EbNo)); % Bit error rate
`wer=zeros(1,length(EbNo)); % Word error rate
`fer=zeros(1,length(EbNo)); % Failure to decode rate
`fprintf('Number of information bits = %d\n',K);
`fprintf('Number of transmitted bits = %d\n',N);
`fprintf('Rate = %f\n',R);
`% Simulation
`for j=1:length(s) % Loop over noise levels
` for b=1:B(j) % Loop over transmitted blocks
` y=randn(1,N)*s(j)+1; % Generate channel output assuming +
`1 sent
` Lc=-2*y/s(j)^2; % Channel log-likelihood ratio
` Lf(1)=-1e20; % Initialize forward state of Markov chain
`to 0
` Lb(N)=Lc(N); % Initialize backward message to channel llr
` Lxd(:)=0; % Initialize messages from information bits to
`0
`
`(cid:20)
`
`6
`
`
`
` for i=1:I % Apply I iterations of decoding
` for n=1:N % Forward pass
` Lf(n+1)=Lc(n)+f(Lf(n),Lxd(n));
` end;
` for n=N:-1:2 % Backward pass
` Lb(n-1)=Lc(n-1)+f(Lb(n),Lxd(n));
` end;
` Lx(:)=0;
` for n=1:N % Fuse messages at information bits
` Lxu(n)=f(Lf(n),Lb(n));
` Lx(Pi(P(n)))=Lx(Pi(P(n)))+Lxu(n);
` end;
` for n=1:N % Messages sent down to accumulator
` Lxd(n)=Lx(Pi(P(n)))-Lxu(n);
` end;
` end;
` xhat=1-(Lx<0); % Threhshold information bit llrs
` ber(j)=ber(j)+sum(xhat); % Update BER
` wer(j)=wer(j)+(sum(xhat)>0); % Udate WER
` fer(j)=fer(j)+(mean(xhat)>.1); % Update DER
` end;
` ber(j)=ber(j)/K/B(j); % Compute BER
` wer(j)=wer(j)/B(j); % Compute WER
` fer(j)=fer(j)/B(j); % Compute FER
` fprintf(' Eb/No=%f, ber=%e, wer=%e, fer=%e\n', ...
` EbNo(j),ber(j),wer(j),fer(j));
`end;
`% Message passing for XOR function (check node, 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
`
`(cid:21)
`
`7
`
`
`
`
`Divsalar K=4096 N=16384 R=1f2 0:4 I=20
`
`
`
`Worderrorrate
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`0.7
`
`0.75
`
`0.
`
`8
`
`0.85
`
`beND (dB)
`
`8
`
`
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