% End-to-end run: encode, apply noise, correct, decode.
% Returns struct with fields decoded_bit, true_bit, success, syndrome, e_true, e_hat.

function out = simulate_bitflip_once(p, alpha_beta, logical_bit)
% logical_bit in {0,1};
% alpha_beta optional (defaults to |0> or |1>)
if nargin < 3 || isempty(logical_bit), logical_bit = 0;
end

if nargin < 2 || isempty(alpha_beta)
    if logical_bit==0
        alpha_beta = [1;0];
    else
        alpha_beta = [0;1];
    end
end

psi_enc = encode_bitflip(alpha_beta);

% sample physical error, compute syndrome, correct, decode
e_true   = sample_error_pattern(p);
psi_noisy= apply_error_pattern(psi_enc, e_true);
s        = syndrome_bitflip(psi_noisy);
psi_corr = correct_bitflip(psi_noisy, s);
bhat     = decode_majority(psi_corr);

% inferred error label
ehat = infer_from_syndrome_bitflip(s);

out.decoded_bit = bhat;
out.true_bit    = logical_bit;
out.success     = (bhat == logical_bit);
out.syndrome    = s;
out.e_true      = e_true;
out.e_hat       = ehat;
end