% Name: bounds_AWGN_conv_R12_K2_EbNo.m
% Date: November 21, 2007
% Description:
% Bounds for binary K=3 rate-1/2 convolutional codes with ML decoding with
% binary modulation over an AWGN channel.
%
% Copyright (c) 2007. Robert Morelos-Zaragoza. All rights reserved.

clear
rate=1/2;
df=3;
EbNo_init = 3; EbNo_inc = 0.5; EbNo_final = 14;
EbNov = []; Pb_VO = []; Pb_JZ = []; Pbp_VO = []; Pbp_JZ = [];

for EbNodB = EbNo_init:EbNo_inc:EbNo_final 
    EbNo = (10.^(EbNodB/10));
    x = exp(-rate*EbNo);
    % Omura-Viterbi bounds
    Pb = x^3/((1-2*x)^2);
    Pbp = x^2 + ( ((1-2*x^2)*(3*x^2+5*x^4) + 6*x^3*(x+x^3))/(1-2*x^2)^2 );
    Pb_VO = [Pb_VO Pb];
    Pbp_VO = [Pbp_VO Pbp];
    % Johannesson-Zigangirov bounds
    Pb = Q(sqrt(2*df*rate*EbNo))*exp(df*rate*EbNo)*x^3/((1-2*x)^2);
    Pbp = Q(sqrt(2*df*rate*EbNo))*exp(df*rate*EbNo)*( x^2 + ...
        ( ((1-2*x^2)*(3*x^2+5*x^4) + 6*x^3*(x+x^3))/(1-2*x^2)^2) );
    Pb_JZ = [Pb_JZ Pb];
    Pbp_JZ = [Pbp_JZ Pbp];
    EbNov = [EbNov EbNodB];
end

semilogy (EbNov,Pb_VO,'-ks');
hold on
semilogy (EbNov,Pbp_VO,':ks');
semilogy (EbNov,Pb_JZ,'-ko');
semilogy (EbNov,Pbp_JZ,':ko');
axis([3 14 1e-7 0.1])
legend('OV bound for C','OV bound for C_p', 'JZ bound for C', 'JZ bound for C_p')
xlabel('E_b/N_0 (dB)')
ylabel('P_b')
grid on
hold off