Linear Codes Modules¶

Classical Codes¶

class HammingCode(r, extended=False)¶

Bases: lpdec.codes.BinaryLinearBlockCode

A class for Hamming codes, both standard and extended.

For given $r \geq 2$ , creates the Hamming code of block length $2^r-1$ or the extended Hamming code of block length $2^r$ ; the information length of both types ist $2^r-r-1$ .

Parameters:	r (int) – determines the size of the code extended (bool) – set to `True` to create the extended Hamming code instead of the “normal” one.

class ReedMullerCode(m, r=None, infolength=None)¶

Bases: lpdec.codes.BinaryLinearBlockCode

Reed-Muller code using the “polar code like” construction with $F^{\otimes 2}$ as generator matrix.

Parameters:	r (int) – Order of the RM code. m (int) – 2-logarithm of the code’s length: the code’s length will be $2^m$ .

LDPC Codes¶

class ArrayLDPCCode(q, m)¶

Bases: lpdec.codes.BinaryLinearBlockCode

An array LDPC code is defined by an odd prime $q$ and a number $m \leq q$ .

For the formal definition see: J. L. Fan, “Array codes as low-density parity-check codes”, in Proc. 2nd Int. Symp. Turbo Codes & Rel. Topics, Brest, France, Sep. 2000, pp. 543–546.

Factor Graphs¶

The lpdec.codes.factorgraph module contains classes for defining a factor graph of a parity-check matrix.

class FactorGraph(varNodes, checkNodes, x=None)¶

Bases: object

Factor graph main class.

varNodes¶: List of variable nodes of the graph.

checkNodes¶: List of check nodes of the graph.

classmethod fromLinearCode(code)¶: Creates the factor graph according to the parity-check matrix of code.

class FactorNode(identifier)¶

Bases: object

Base class for nodes of a factor graph.

Parameters:	identifier – A free-form identifier for this node.

neighbors¶: List of neighboring nodes.

connect(other)¶: Connect other to this node by updating the neighbors lists of both nodes.

degree¶: The degree of this node, i.e. number of connected nodes.

class VariableNode(identifier)¶

Bases: lpdec.codes.factorgraph.FactorNode

FactorNode subclass for variables.

merge(other)¶: Merge other into this node. Afterwards, other will be isolated and all of its neighbors connected to self.

class CheckNode(identifier)¶

Bases: lpdec.codes.factorgraph.FactorNode

FactorNode subclass for checks.

Non-Binary Codes¶

This module contains classes and helper functions for non-binary codes. Currently, the contents are not well integrated with the rest of the lpdec package.

class NonbinaryLinearBlockCode(name=None, parityCheckMatrix=None, q=None)¶

Bases: lpdec.codes.LinearBlockCode

Base class for non-binary linear block codes over GF(q).

name is a string uniquely describing the code. When storing results into a database, there must not be two different codes with the same name. If the parity-check matrix is given by a file, the code’s name defaults to the name of that file.

The class can be instanciated directly by providing a parity check matrix; the argument parityCheckMatrix must be either the path of a file containig the matrix, or a two-dimensional list or a np.ndarray representation of the matrix. Subclasses using a different code representation should leave the default value of None.

binaryEmbedding(vector, q)¶: Return the binary embedding of a q-ary vector $\in GF(q)^n$ into $GF(2)^{( q-1) imes n}$ using the map

0 -> 0 ... 0 1 -> 1 ... 0 2 -> 0 1...0 .. q-1 -> 0 0.. 1