Implementation of Power decoding with Multiplicities
This is a publically available repository of an implementation which is connected with the following publication:
Power Decoding Reed--Solomon Codes Up to the Johnson Radius
by Johan S. R. Nielsen
Submitted for Advances in Mathematics of Communication
The code is written by me, Johan S. R. Nielsen
The code is documented in a self-contained fashion, but it should be understandable for someone with the article at hand.
The repository contains the following files
power_mults.sheet: Examples of how to call the decoder from Codinglib (see below) as well as computation of failure probability bound, and the examples on the (lack of) relation to list-decoding from the paper.
failure_rate_powermults.sage: Script taking specific code and decoder parameters and performs a specified number of decoding attempts with random errors. Outputs to standard out.
failure_rate_simulation.sage: Script for orchestrating the large-scale simulation whose results are given in the paper. The actual simulation is carried out in parallel on multiple machines using SSH and
failure_rate_powermults.sage. The results are saved in many files (it is assumed that all the machines share the same file system).
find_code_examples.sheet: Helper-functions for identifying code and decoder parameters that make for good examples under various constraints.
simulation_results.sage: Print the simulation results obtained using
interesting_results.sh: From the complete simulation results, extract only those received words where behaviour was surprising.
interesting_results/: Contains the received words with surprising decoding behaviour observed during the simulation documented in the paper.
The code is written in Sage, and will require this to run. The source file(s) mention the latest version of Sage for which I have verified they work. The code also requires installation of Codinglib, my library of functions and algorithms for algebraic coding theory. In fact, the bulk of the algorithm and work might well be done by Codinglib, and as such, the implementation here can be seen as calling examples of the library. Before running the code in the files of this repository, one needs to import Codinglib into the running Sage process:
from codinglib import *
The code here is structured into
.sheet-files. They are clear-text analogues
of the Sage Notebook's worksheets. Such a file is not meant to be imported as a
whole, but rather evaluated block by block in a Sage process. In a
the blocks are delimited by lines starting with
###, usually followed by a
one-line description of their contents. Possibly, the file is further
sub-structured by visibly larger whitespace. Usually, the first few blocks will
contain definitions, implementing the algorithms and helper functions. The
latter blocks then set up examples and objects for input in the algorithms.
The latter blocks of the sheet might also contain code for creating plots or running the simulations included in the paper.
If you are using Emacs, then working with
.sheet-files can be conveniently
accomplished using sage-mode, where the file
contains block-specific functionality.
This code is released under the GPL v3 or later to conform with Sage's licensing.
You are welcome to contact me for questions on the implementation or its usage, or, of course, a discussion of the paper.
Johan S. R. Nielsen