CECCO::SDMEC< T > Class Template Reference

Symmetric Discrete Memoryless Erasure Channel (SDMEC) over any finite field 𝔽_q. 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
	Observed symbol error probability pe.
double	get_px () const noexcept
	Observed symbol erasure probability px.
double	get_capacity () const noexcept
	Shannon capacity in bits per symbol.
long double	get_Bhattacharyya_param () const
	Bhattacharyya parameter γ = 2·√(pe·(1 − pe)).
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 Discrete Memoryless Erasure Channel (SDMEC) over any finite field 𝔽_q.

Template Parameters

T	Finite field type for channel input/output symbols

q-ary symmetric channel with independent error and erasure processes. Each transmitted symbol is changed to a uniformly random different value with observed probability pe, marked erased (overwriting any error) with observed probability px, and otherwise passed through unchanged.

For px = 0 this reduces to the traditional symmetric channel (use CECCO::SDMC, or CECCO::BSC for q = 2). For pe = 0 it is the erasure channel (use CECCO::BEC for q = 2). Erasure support requires the CECCO_ERASURE_SUPPORT macro at compile time.

Capacity (bits/symbol): C = (1 − px) · [ log₂(q) + (1 − p̃)·log₂(1 − p̃) + p̃·log₂(p̃) − p̃·log₂(q − 1) ], where p̃ = pe / (1 − px) is the conditional error probability.

using F4 = Ext<Fp<2>, {1, 1, 1}>;
SDMEC<F4> channel(0.05, 0.1);                    // 5% errors, 10% erasures
Vector<F4> r = Vector<F4>(20).randomize() >> channel;
double C = channel.get_capacity();

See also

CECCO::SDMC, CECCO::BSC, CECCO::BEC, CECCO::BAC

Definition at line 222 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 284 of file blocks.hpp.

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Member Function Documentation

get_Bhattacharyya_param()

template<FieldType T>

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

inline

Bhattacharyya parameter γ = 2·√(pe·(1 − pe)).

Exceptions

std::logic_error

if px ≠ 0 (γ is undefined for channels with erasures)

Note

Defined only for binary channels (q = 2).

Definition at line 265 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 327 of file blocks.hpp.

get_pe()

template<FieldType T>

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

inlinenoexcept

Observed symbol error probability pe.

Definition at line 245 of file blocks.hpp.

get_px()

template<FieldType T>

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

inlinenoexcept

Observed symbol erasure probability px.

Definition at line 248 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 303 of file blocks.hpp.

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

• blocks.hpp