Code covered by the BSD License

# Turbo Code

### Yogesh K Soniwal (view profile)

11 Dec 2012 (Updated )

Encoding: RSC, Decoding: BCJR

gamma_1(Apriori,N,Input_matrix,Parity_bit_matrix,R0,R1,SNR)
```%This function uses Apriori probabilities, Input matrix, Parity Bit Matrix,
%and received code bits (R0 and R1) and returns GAMMA probabilities at all
%stages. The formula used for calculating gamma at a particular stage and
%given input i (0 or 1) is following
%GAMMA(m',m)=P(X=i) * P(S(k+1)=m|S(k)=m',X=i) * P(R0(k) R1(k) | S(k+1)=m, S(k)=m', X=i))
%Due to the second term only 8 probabilities will survive corresponding to
%8 transitions of Trellis. GAMMA is constructed in following way:
%At each stage(fixed k), there are 2 columns, 1st for i/p 0 and 2nd for i/p
%1. The 4 entries for 1st columns are trasitions from 00 to 00, 10 to 01,
%01 to 10, 11 to 11 respectively and for 2nd column transitions from 00 to
%10, 10 to 11, 01 to 00, 11 to 01 respectively

function [g]=gamma_1(Apriori,N,Input_matrix,Parity_bit_matrix,R0,R1,SNR)

g=zeros(4,2*N);
for i=1:N
T1=((R0(i)-sqrt(SNR)*Input_matrix(1,1))^2)+((R1(i)-sqrt(SNR)*Parity_bit_matrix(1,1))^2);
T2=((R0(i)-sqrt(SNR)*Input_matrix(1,2))^2)+((R1(i)-sqrt(SNR)*Parity_bit_matrix(1,2))^2);
T3=((R0(i)-sqrt(SNR)*Input_matrix(2,1))^2)+((R1(i)-sqrt(SNR)*Parity_bit_matrix(2,1))^2);
T4=((R0(i)-sqrt(SNR)*Input_matrix(2,2))^2)+((R1(i)-sqrt(SNR)*Parity_bit_matrix(2,2))^2);
T5=((R0(i)-sqrt(SNR)*Input_matrix(3,1))^2)+((R1(i)-sqrt(SNR)*Parity_bit_matrix(3,1))^2);
T6=((R0(i)-sqrt(SNR)*Input_matrix(3,2))^2)+((R1(i)-sqrt(SNR)*Parity_bit_matrix(3,2))^2);
T7=((R0(i)-sqrt(SNR)*Input_matrix(4,1))^2)+((R1(i)-sqrt(SNR)*Parity_bit_matrix(4,1))^2);
T8=((R0(i)-sqrt(SNR)*Input_matrix(4,2))^2)+((R1(i)-sqrt(SNR)*Parity_bit_matrix(4,2))^2);

g(1,2*i-1)= Apriori(1,i)*(1/(2*pi))*exp(-0.5*T1);         %Current State=0(00), i/p=0
g(1,2*i)  = Apriori(2,i)*(1/(2*pi))*exp(-0.5*T2);         %Current State=0(00), i/p=1
g(2,2*i-1)= Apriori(1,i)*(1/(2*pi))*exp(-0.5*T3);         %Current State=2(10), i/p=0
g(2,2*i)  = Apriori(2,i)*(1/(2*pi))*exp(-0.5*T4);         %Current State=2(10), i/p=1
g(3,2*i-1)= Apriori(1,i)*(1/(2*pi))*exp(-0.5*T5);         %Current State=1(01), i/p=0
g(3,2*i)  = Apriori(2,i)*(1/(2*pi))*exp(-0.5*T6);         %Current State=1(01), i/p=1
g(4,2*i-1)= Apriori(1,i)*(1/(2*pi))*exp(-0.5*T7);         %Current State=3(11), i/p=0
g(4,2*i)  = Apriori(2,i)*(1/(2*pi))*exp(-0.5*T8);         %Current State=3(11), i/p=1
end

end```