You are an expert in writing code in many different languages. Your goal is to perform code completion for the following code, keeping in mind the rest of the code and the file meta data.
    Metadata details:
    filename: PC_polar_decoder.m
    path of file: ./repos/polar-3gpp-matlab/components
    
    the code of the file until where you have to start completion: function a_hat = PC_polar_decoder(e_tilde, info_bit_pattern, PC_bit_pattern, PC_circular_buffer_length, rate_matching_pattern, mode, L, min_sum)
% PCCA_POLAR_DECODER Parity Check and CRC-Aided (CA) polar decoder.
%   a_hat = PCCA_POLAR_DECODER(e_tilde, crc_polynomial_pattern, info_bit_pattern, PC_bit_pattern, PC_circular_buffer_length, rate_matching_pattern, mode, L, min_sum, P2) 
%   decodes the encoded LLR sequence e_tilde, in order to obtain the
%   recovered information bit sequence a_hat.
%
%   e_tilde should be a real row vector comprising E number of Logarithmic
%   Likelihood Ratios (LLRS), each having a value obtained as LLR =
%   ln(P(bit=0)/P(bit=1)).
%
%   info_bit_pattern should be a row vector comprising N number of logical 
%   elements, each having the value true or false. The number of elements 
%   in info_bit_pattern having the value true should be A+n_PC. 
%   These elements having the value true identify the positions of the 
%   information and PC bits within the input to the polar encoder kernal.
%
%   PC_bit_pattern should be a row vector comprising N number of logical 
%   elements, each having the value true or false. The number of elements 
%   in PC_bit_pattern having the value true should be n_PC. 
%   These elements having the value true identify the positions of the 
%   PC bits within the input to the polar encoder kernal.
%
%   PC_circular_buffer_length should be an integer scalar. It specifies the
%   length of the circular buffer used to generate the PC bits.
%
%   rate_matching_pattern should be a row vector comprising E number of
%   integers, each having a value in the range 1 to N. Each integer
%   identifies which one of the N outputs from the polar encoder kernal
%   provides the corresponding bit in the encoded bit sequence e.
%
%   mode should have the value 'repetition', 'puncturing' or 'shortening'.
%   This specifies how the rate matching has been achieved. 'repetition'
%   indicates that some outputs of the polar encoder kernal are repeated in 
%   the encoded bit sequence two or more times. 'puncturing' and 
%   'shortening' indicate that some outputs of the polar encoder kernal 
%   have been excluded from the encoded bit sequence. In the case of
%   'puncturing' these excluded bits could have values of 0 or 1. In the
%   case of 'shortening' these excluded bits are guaranteed to have values
%   of 0.
%
%   L should be a scalar integer. It specifies the list size to use during
%   Successive Cancellation List (SCL) decoding.
%
%   min_sum shoular be a scalar logical. If it is true, then the SCL
%   decoding process will be completed using the min-sum approximation.
%   Otherwise, the log-sum-product will be used. The log-sum-product gives
%   better error correction capability than the min-sum, but it has higher
%   complexity.
%
%   a_hat will be a binary row vector comprising A number of bits, 
%   each having the value 0 or 1.
%
%   See also PCCA_POLAR_ENCODER
%
% Copyright © 2017 Robert G. Maunder. This program is free software: you 
% can redistribute it and/or modify it under the terms of the GNU General 
% Public License as published by the Free Software Foundation, either 
% version 3 of the License, or (at your option) any later version. This 

    
function a_hat = PC_polar_decoder(e_tilde, info_bit_pattern, PC_bit_pattern, PC_circular_buffer_length, rate_matching_pattern, mode, L, min_sum)
% PCCA_POLAR_DECODER Parity Check and CRC-Aided (CA) polar decoder.
%   a_hat = PCCA_POLAR_DECODER(e_tilde, crc_polynomial_pattern, info_bit_pattern, PC_bit_pattern, PC_circular_buffer_length, rate_matching_pattern, mode, L, min_sum, P2) 
%   decodes the encoded LLR sequence e_tilde, in order to obtain the
%   recovered information bit sequence a_hat.
%
%   e_tilde should be a real row vector comprising E number of Logarithmic
%   Likelihood Ratios (LLRS), each having a value obtained as LLR =
%   ln(P(bit=0)/P(bit=1)).
%
%   info_bit_pattern should be a row vector comprising N number of logical 
%   elements, each having the value true or false. The number of elements 
%   in info_bit_pattern having the value true should be A+n_PC. 
%   These elements having the value true identify the positions of the 
%   information and PC bits within the input to the polar encoder kernal.
%
%   PC_bit_pattern should be a row vector comprising N number of logical 
%   elements, each having the value true or false. The number of elements 
%   in PC_bit_pattern having the value true should be n_PC. 
%   These elements having the value true identify the positions of the 
%   PC bits within the input to the polar encoder kernal.
%
%   PC_circular_buffer_length should be an integer scalar. It specifies the
%   length of the circular buffer used to generate the PC bits.
%
%   rate_matching_pattern should be a row vector comprising E number of
%   integers, each having a value in the range 1 to N. Each integer
%   identifies which one of the N outputs from the polar encoder kernal
%   provides the corresponding bit in the encoded bit sequence e.
%
%   mode should have the value 'repetition', 'puncturing' or 'shortening'.
%   This specifies how the rate matching has been achieved. 'repetition'
%   indicates that some outputs of the polar encoder kernal are repeated in 
%   the encoded bit sequence two or more times. 'puncturing' and 
%   'shortening' indicate that some outputs of the polar encoder kernal 
%   have been excluded from the encoded bit sequence. In the case of
%   'puncturing' these excluded bits could have values of 0 or 1. In the
%   case of 'shortening' these excluded bits are guaranteed to have values
%   of 0.
%
%   L should be a scalar integer. It specifies the list size to use during
%   Successive Cancellation List (SCL) decoding.
%
%   min_sum shoular be a scalar logical. If it is true, then the SCL
%   decoding process will be completed using the min-sum approximation.
%   Otherwise, the log-sum-product will be used. The log-sum-product gives
%   better error correction capability than the min-sum, but it has higher
%   complexity.
%
%   a_hat will be a binary row vector comprising A number of bits, 
%   each having the value 0 or 1.
%
%   See also PCCA_POLAR_ENCODER
%
% Copyright © 2017 Robert G. Maunder. This program is free software: you 
% can redistribute it and/or modify it under the terms of the GNU General 
% Public License as published by the Free Software Foundation, either 
% version 3 of the License, or (at your option) any later version. This 
% program is distributed in the hope that it will be useful, but WITHOUT 
% ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or 
% FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for 
% more details.

E = length(e_tilde);
N = length(info_bit_pattern);
A = sum(info_bit_pattern & ~PC_bit_pattern);

if log2(N) ~= round(log2(N))
    error('N should be a power of 2');
end