hamming-codec

Simple encode/decode utilties for single-bit error correcting Hamming codes

Table of Contents

1. Requirements
2. Installation
   • Python
   • C++
3. Python Usage
   • Command-line Usage
   • Importing the hamming_codec Python Module
4. C++ Usage
   • Including in your Project
   • Examples
5. Error-correction
6. References

Requirements

Tested on Python >=3.6 and requires C++ compilers supporting C++17 features.

Installation

Python Installation

Install using pip as follows:

$ python -m pip install hamming-codec

C++ Installation

If you wish to use the hamming-codec encoding/decoding from within C++, one needs to include the single header file src/cpp/hamming_codec.h in their project. There are a few ways to do this:

1. Copy the file hamming_codec.h into your project's include path.
2. Add hamming-codec as a sub-module (or equivalent) and use CMake to expose the HAMMING_CODEC_INCLUDE_DIRS variable by calling add_subdirectory(/path/to/hamming_codec) to your project's CMakeLists.txt file. See src/cpp/examples/CMakeLists.txt for an example.

Following either approach, you should be able to add #include "hamming_codec.h" to your source code.

Python Usage

From the Command-line

After following the Python installation, a commandline utility hamming will be available to you, which can be used for simple encoding and decoding of data words. Use hamming --help to show the full set of options and commands.

Encoding

You can use the hamming commandline utility to encode messages of specified length (in number of bits) as follows:

$ hamming encode 0x1234 16
0x2a3a1 21

Which shows that the 16-bit message 0x1234 is encoded as a 21-bit word 0x2a3a1.

Decoding

You can use the hamming commandline utility to decode messages of specified length (in number of bits) as follows:

$ hamming decode 0x2a3a1 21
0x1234 16

Which shows that the 21-bit encoded message 0x2a3a1 is decoded back into the 16-bit word 0x1234.

Importing as a Module

Once you have installed hamming-codec, you can import the hamming_codec module and perform encoding/decoding like so:

>>> import hamming_codec
>>> encoded_message = hamming_codec.encode(0x4235, 16)
>>> print(encoded_message)
010001010001110101100
>>> hex(int(encoded_message,2))
'0x8a3ac'
>>> decoded_message = hamming_codec.decode(int(encoded_message,2), len(encoded_message))
>>> print(decoded_message)
0100001000110101
>>> hex(int(decoded_message,2))
'0x4235'

C++ Usage

Including in your Project

Following the steps to add hamming-codec to your include path, you can encode/decode messages as follows:

#include "hamming_codec.h"
...
uint32_t n_bits = 16;
uint32_t input_message = 0x4235;
std::string encoded_message = hamming_codec::encode(input_message, n_bits);
std::cout << "Encoded message: 0x" << std::hex << std::stoul(encoded_message, 0, 2) << std::endl; // prints "Encoded message: 0x8a3ac"
std::string decoded_message = hamming_codec::decode(std::stoul(encoded_message, 0, 2), encoded_message.length());
std::cout << "Decoded message: 0x" << std::hex << std::stoul(decoded_message, 0, 2) << std::endl; // prints "Decoded message: 0x4235"

C++ Examples

After following the steps to build the C++ library, you can run the C++ examples. For example,

$ ./build/bin/example_encode 0x4235 16
0x8a3ac 21

Single-bit Error Correction

The Hamming encoding algorithm used within hamming-codec allows for single-bit error corrections. That is, during the decoding process, errors in which a single bit has been flipped in the encoded message can both be detected and corrected.

For example, if we flip a single bit in the encoded message from a previous section such that the 21-bit word 0x2a3a1 becomes 0x2a1a1, you will get the same decoded message as before:

$ hamming encode 0x1234 16
0x2a3a1 21
$ hamming decode 0x2a3a1 21
0x1234 16
$ hamming decode 0x2a1a1 21 # flipped a bit
0x1234 16 # ...but decodes the same as before!

References

Further information about the Hamming encoding algorithm employed within hamming-codec can be found in the following resources:

• 3Blue1Brown's "Hamming codes and error correction"
• Ben Eater's "What is error correction? Hamming codes in hardware"
• tutorialspoint's "Error Correcting Codes - Hamming codes"
• Wikipedia entry for "Hamming Code"
• Wikipedia entry for "Linear error-correcting codes"