c_beta.m

Space-Time Processing for CDMA Mobile Communications.Written for research students and design engine

% ======================================================================
% C_BETA.m
% =========
% Description: This m-file implements the Backward State-Metric Calcula-
%              tor (BSMC) to be used in the MAP-decoder.
%
% Usage:  [Beta0,Beta1] = c_beta(Gamma0, Gamma1, Alpha0, Alpha1, ...
%                                  NSC, PSC)
% Inputs:
%          Gamma0: Branch Metrics (BM) for complete trellis for input
%                  bit 0.
%          Gamma1: Branch Metrics (BM) for complete trellis for input
%                  bit 1.
%          Alpha0: Forward State- Metrics (FSM) for complete trellis for
%                  input bit 0.
%          Alpha1: Forward State- Metrics (FSM) for complete trellis for
%                  input bit 1.
%             NSC: Next-States-Connected.
%             PSC: Previous-States-Connected
% Outputs:
%           Beta0: The Backward State-Metrics (BSM) for complete trellis
%                  for input bit 0.
%           Beta1: The Backward State-Metrics (BSM) for complete trellis
%                  for input bit 1.
%
%   Output data format: AlphaI(State Number, Trellis Depth), where I=0,1
%                       depending on input bit.
% ======================================================================
function [Beta0,Beta1] = c_beta(Gamma0, Gamma1, Alpha0, Alpha1, NSC, PSC)

% --------------
% Initialisation
% --------------
[Number_Of_States, Trellis_Depth] = size(Gamma0);

Beta0 = zeros(Number_Of_States, Trellis_Depth);
Beta1 = zeros(Number_Of_States, Trellis_Depth);

SCHEME_Init = 3;        % Reed's 'NEW' approach
% -------------------------------------
% Backward State-Metrics Initialisation
% -------------------------------------

% SCHEME 1: Assuming trellis termintaion
if SCHEME_Init == 1
% Reset of states (at TrellisDepth = End) to zero
   for S=1:Number_Of_States
      Beta0(S,Trellis_Depth) = 0.0;
      Beta1(S,Trellis_Depth) = 0.0;
   end
   % Now we initialise the two branches ending in State 1
      Beta0(PSC(1,1),Trellis_Depth) = 1.0;
      Beta1(PSC(1,2),Trellis_Depth) = 1.0;
end

% SCHEME 2: Using Reed's 'NOTAIL' approach
if SCHEME_Init == 2
   % Reset of states (at TrellisDepth = End) to final value(s) of ALPHA
   for S=1:Number_Of_States
      Beta0(S,Trellis_Depth) = Alpha0(S,Trellis_Depth);
      Beta1(S,Trellis_Depth) = Alpha1(S,Trellis_Depth);
   end
end

% SCHEME 3: Using Reed's 'NEW' approach
if SCHEME_Init == 3
   % Reset of states (at TrellisDepth = End) to final
   % value 1/(Number of States)
   for S=1:Number_Of_States
      Beta0(S,Trellis_Depth) = 1.0/Number_Of_States;
      Beta1(S,Trellis_Depth) = 1.0/Number_Of_States;
   end
end
NormaliseFactor = 1.0;

% ----------------------------------------------
% M A P: Backward State-Metric Calculator (BSMC)
% ----------------------------------------------

% Now for the remaing trellis, calculate the Backward State Metrics
for TD=Trellis_Depth-1:-1:1
        NewLargest = 0.0;

   for S=1:Number_Of_States
      % Do for input bit 0:
      % ------------------
      Beta0_Temp = Beta0(NSC(S,1),TD+1) * Gamma0(NSC(S,1),TD+1);
      Beta1_Temp = Beta1(NSC(S,1),TD+1) * Gamma1(NSC(S,1),TD+1);

      Beta0(S,TD) = (Beta0_Temp + Beta1_Temp) / NormaliseFactor;

      if Beta0(S,TD) > NewLargest
         NewLargest = Beta0(S,TD);
      end


      % Do for input bit 1:
      % ------------------
      Beta0_Temp = Beta0(NSC(S,2),TD+1) * Gamma0(NSC(S,2),TD+1);
      Beta1_Temp = Beta1(NSC(S,2),TD+1) * Gamma1(NSC(S,2),TD+1);

      Beta1(S,TD) = (Beta0_Temp + Beta1_Temp) / NormaliseFactor;

      if Beta1(S,TD) > NewLargest
         NewLargest = Beta1(S,TD);
      end
   end
   NormaliseFactor = NewLargest;

   if NormaliseFactor < 1.0
      NormaliseFactor = 1.0;
   end
end
% ======================================================================