CECCO::SDMEC< T > Class Template Reference

Symmetric errors-and-erasures channel over a finite field. More...

#include <blocks.hpp>

Inheritance diagram for CECCO::SDMEC< T >:

Public Member Functions
	SDMEC (double pe, double px=0.0)
	Construct with error probability pe and erasure probability px.
T	operator() (const T &in)
	Process one symbol.
double	get_pe () const noexcept
	Symbol error probability pe (erroneous and not erased).
double	get_px () const noexcept
	Symbol erasure probability px.
double	get_capacity () const noexcept
	Shannon capacity in bits per symbol.
long double	get_Bhattacharyya_param () const noexcept
	Pairwise Bhattacharyya parameter.
Public Member Functions inherited from CECCO::details::BlockProcessor< T, ElementType, ElementType >
Vector< ElementType >	operator() (const Vector< ElementType > &in)
	Apply the block element-wise to each vector entry.
Vector< ElementType >	operator() (Vector< ElementType > &&in)
	Apply the block element-wise (rvalue input).
Matrix< ElementType >	operator() (const Matrix< ElementType > &in)
	Apply the block element-wise to each matrix entry.
Matrix< ElementType >	operator() (Matrix< ElementType > &&in)
	Apply the block element-wise (rvalue input).
ElementType	operator() (const U &)
	Catch-all for inputs whose element type differs from InputType.
Vector< ElementType >	operator() (const Vector< U > &)
Matrix< ElementType >	operator() (const Matrix< U > &)

Additional Inherited Members
Protected Member Functions inherited from CECCO::details::BlockProcessor< T, ElementType, ElementType >
const T &	derived () const noexcept
T &	derived () noexcept

Detailed Description

template<FieldType T>
class CECCO::SDMEC< T >

Symmetric errors-and-erasures channel over a finite field.

Template Parameters

T	Finite field of the transmitted symbols

Independently replaces a symbol by a uniformly selected different symbol with probability pe, then marks it erased with probability px; erasure takes precedence over error.

For px == 0 this is an CECCO::SDMC; over 𝔽₂, pe == 0 gives an CECCO::BEC. Erasures require CECCO_ERASURE_SUPPORT.

The capacity is C = (1 − px)[log₂(q) + (1 − p̃)log₂(1 − p̃) + p̃log₂(p̃) − p̃log₂(q − 1)], where p̃ = pe / (1 − px).

Definition at line 205 of file blocks.hpp.

Constructor & Destructor Documentation

SDMEC()

template<FieldType T>

CECCO::SDMEC< T >::SDMEC	(	double	pe,
		double	px = 0.0 )

Construct with error probability pe and erasure probability px.

Parameters

pe	Symbol error probability ∈ [0, 1]
px	Symbol erasure probability ∈ [0, 1 − pe]; default 0

Exceptions

std::out_of_range	if pe ∉ [0, 1] or px ∉ [0, 1 − pe]
std::invalid_argument	if px ≠ 0 and CECCO_ERASURE_SUPPORT is not defined

Definition at line 274 of file blocks.hpp.

Member Function Documentation

get_Bhattacharyya_param()

template<FieldType T>

long double CECCO::SDMEC< T >::get_Bhattacharyya_param ( ) const

inlinenoexcept

Pairwise Bhattacharyya parameter.

Uses γ = px + 2·√((1 − pe − px)·pe/(q − 1)) + (q − 2)·pe/(q − 1), with q = |T| and pe the probability of an erroneous, non-erased output.

Returns

Common pairwise Bhattacharyya parameter γ for distinct input symbols

Definition at line 249 of file blocks.hpp.

get_capacity()

template<FieldType T>
requires (FiniteFieldType<T>)

double CECCO::SDMEC< T >::get_capacity ( ) const

noexcept

Shannon capacity in bits per symbol.

Returns

C = (1 − px) · [log₂(q) + (1 − p̃)·log₂(1 − p̃) + p̃·log₂(p̃) − p̃·log₂(q − 1)], where p̃ = pe / (1 − px). Edge cases pe ∈ {0, 1} use lim_{x→0} x·log₂(x) = 0.

Definition at line 328 of file blocks.hpp.

get_pe()

template<FieldType T>

double CECCO::SDMEC< T >::get_pe ( ) const

inlinenoexcept

Symbol error probability pe (erroneous and not erased).

Definition at line 228 of file blocks.hpp.

get_px()

template<FieldType T>

double CECCO::SDMEC< T >::get_px ( ) const

inlinenoexcept

Symbol erasure probability px.

Definition at line 231 of file blocks.hpp.

operator()()

template<FieldType T>

T CECCO::SDMEC< T >::operator()

(

const T &

in

)

Process one symbol.

Parameters

in	Input symbol

Returns

Output symbol (possibly erased when CECCO_ERASURE_SUPPORT is defined)

Definition at line 298 of file blocks.hpp.

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The documentation for this class was generated from the following file:

• blocks.hpp