Arithenco and arithdeco not working with zeros

Why does arithenco/arithdeco not work with an input sequence including zeros and is there a way to work around this?

Example) Input message would be [2,1,2,1,2,0,0] and the decoded sequence is [3,2,3,2,3,1,2]. Whereas if I have an input message of [2,1,2,1,2,1,2], my decoded sequence is identical to the input as [2,1,2,1,2,1,2].

Below is my testing code. I believe you'll need the Signal Processing ToolBox for the arithenco/arithdeco functions.

clc;
clear all;
close all;

message = [2,1,2,1,2,0,1];

%% Encoder

table_size = height(message);
rows = table_size(1);
encodedY = [];

for row = 1:rows
    coeff_row = message(row,:);

    % Calculate unique values
    source = unique(coeff_row);
    for i=1:length(source)
        counts(i)=length(strfind(coeff_row,source(i)));   
    end

    seq=zeros(1,length(coeff_row));
    for i=1:length(coeff_row)
        seq(i)=strfind(source,coeff_row(i));
    end
    
    % Get arithmetic code for the block
    code = arithenco(seq, counts);
    
    % Store the block's code
    encodedY = [encodedY; {code}];
end

%% Decoder
decodedY = [];

for row = 1 : size(encodedY)
    temp = cell2mat(encodedY(row,:));
    dseq = arithdeco(temp,counts,length(seq));

    decodedY = [decodedY;dseq];
end

%%

Answer 1

[Abhimenyu]

Hi Bernard,

I understand that you want to decode the messages containing zeros using “arithenco” and “arithdeco” functions of MATLAB. You can modify the code to map the “decodedY” values back to the “source” as you have used “unique” function to map the “message” to “seq”. Here is the modified code:

clearvars; 
close all; 

message = [2,1,2,1,2,0,2]; 

%% Encoder 
table_size = height(message); 
rows = table_size(1); 
encodedY = []; 

for row = 1:rows 
    coeff_row = message(row,:); 
    % Calculate unique values 
    source = unique(coeff_row); 
    for i=1:length(source) 
        counts(i)=length(strfind(coeff_row,source(i)));    
    end 
    
    seq=zeros(1,length(coeff_row)); 

    for i=1:length(coeff_row) 
       seq(i)=strfind(source,coeff_row(i)); 
    end 

    % Get arithmetic code for the block 
    code = arithenco(seq, counts); 

    % Store the block's code 
    encodedY = [encodedY; {code}]; 
end 

%% Decoder 
decodedY = []; 

for row = 1 : size(encodedY) 
    temp = cell2mat(encodedY(row,:)); 
    dseq = arithdeco(temp,counts,length(seq)); 
    decodedY = [decodedY;dseq]; 
end 

%modified here 
decoded_message = zeros(size(decodedY)); 
for i = 1:length(decodedY) 
    decoded_message(i) = source(decodedY(i)); 
end 

disp("message") 

message

disp(message) 

     2     1     2     1     2     0     2

disp("decoded message") 

decoded message

disp(decoded_message) 

     2     1     2     1     2     0     2

%% 

This can properly encode and decode any message containing zeros.

I hope this helps!

Thank you,

Abhimenyu.