Skip to content
Efficient binary encoding for large alphabets
C C++ Python Makefile
Branch: master
Clone or download
Fetching latest commit…
Cannot retrieve the latest commit at this time.
Type Name Latest commit message Commit time
Failed to load latest commit information.
python Add Python implementation. Jun 6, 2019
tests Add Python implementation. Jun 6, 2019
LICENSE Initial commit Jun 1, 2019


Efficient binary encoding for large alphabets.

Build Status


  • Low fixed-size overhead.
  • Compression-friendly output.
  • Arbitrary alphabets.
  • Fast and simple algorithm.
  • Does not involve heavy-weight arithmetic.

Comparison chart

Encoding Alphabet Size Overhead
escapeless255 255 0.4%
escapeless254 254 0.8%
escapeless253 253 1.2%
yEnc 252 1.6%*, 0-100%
escapeless252 252 1.6%
escapeless251 251 2.0%
escapeless250 250 2.4%
B-News 224 2.5%
escapeless240 240 6.7%
escapeless230 230 11.4%
escapeless225 225 13.8%
Base122 122 14.3%
basE91 91 22%*, 14-23%
Base94 94 22.2%
Ascii85 85 25.0%
Z85 85 25.0%
Base64 64 33.3%
uuencode 64 33.3%
Base58 58 36.6%
Base36 / 64-bit 36 59.2%*, 0-62.5%
Base32 32 60.0%
Base36 / 32-bit 36 62.0%*, 0-75%
Base16 16 100.0%

(*) On uniform distribution of input octets.

Building and testing

$ git clone
$ cd c
$ make
$ make test

Basic idea

Given a source alphabet of size S and a target alphabet of size N < S, break the sequence of input characters into blocks so that the number of characters in each block does not exceed N − 1.

Since a block can contain at most N − 1 different characters and the target alphabet contains N characters, it is known that all those used characters can be mapped to the target alphabet and at least one extra character of the target alphabet will remain unmapped. For example:

 A B C D E F G H I J K L    12  Characters of the source alphabet (S)
 A   C D E     H I   K L     8  Characters of the target alphabet (N)
   x       x x     x         4  Characters missing in the target alphabet (takeouts)
   | | | |     | | |         7  Characters used in the block
 .         . .       . .     5  Characters not used in the block

Here, one possible mapping is:

 B −> A
 J −> K

with L left unmapped and all other characters of the target alphabet mapped to themselves.

What that unmapped character is for, is to make it possible to map unused takeouts, like F and G in the example, to a character of the target alphabet that does not represent any characters of the source alphabet for that block. Taking that into account, here's how a complete mapping would look:

 B −> A
 F -> L
 G -> L
 J −> K

Once the mapping is determined, we can output the encoded block with takeout characters in it replaced with members of the target alphabet. To let a decoder know the mapping, we also have to prepend each of the encoded blocks with a series of characters the takeouts are mapped to and assume that the decoder will be given the same set of takeout characters specified in the same order.

Overhead formula

For a source alphabet of size S, a target alphabet of size N and a block of N − 1 characters, the size of the encoded block is:

 encoded_block_size = takeouts_map_size + block_size =
                      (S − N) + (N - 1) =
                      S - 1

The overhead is thus:

 overhead = (encoded_block_size - block_size) / block_size =
            ((S - 1) - (N - 1)) / (N - 1) =
            (S - 1 - N + 1) / (N - 1) =
            (S - N) / (N - 1)

Encoding algorithm

  1. Break the input message into blocks so that no block contains more than N - 1 characters, where N is the size of the target alphabet. Process every block separately as specified below.

  2. Map every takeout character to a character of the target alphabet that is not used in the block and is not a takeout character. All takeouts not used in the block shall map to the same character.

  3. Replace takeout characters of the block using that map.

  4. Output the map followed by the rewritten block.

Decoding algorithm

  1. Read the takeouts map and the encoded block.

  2. Using the map, restore the takeouts in the block.

  3. Output decoded block.

You can’t perform that action at this time.