CECCO::BAC Class Reference

Binary Asymmetric Channel (Z-channel) — 0 is preserved; 1 flips to 0 with probability p. More...

#include <blocks.hpp>

Inheritance diagram for CECCO::BAC:

Public Member Functions
	BAC (double p)
	Construct with flip probability p.
Fp< 2 >	operator() (const Fp< 2 > &in)
	Process one bit.
double	get_pe () const noexcept
	Flip probability p (probability that 1 → 0).
double	get_capacity () const noexcept
	Shannon capacity in bits per symbol.
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

Binary Asymmetric Channel (Z-channel) — 0 is preserved; 1 flips to 0 with probability p.

BAC bac(0.1);                            // 10% probability that 1 flips to 0
Vector<Fp<2>> c = {0, 1, 1, 0};
Vector<Fp<2>> r = c >> bac;
double C = bac.get_capacity();

See also

CECCO::BSC, CECCO::BEC

Definition at line 400 of file blocks.hpp.

Constructor & Destructor Documentation

BAC()

CECCO::BAC::BAC ( double p )

inline

Construct with flip probability p.

Parameters

p	Probability that 1 → 0, p ∈ [0, 1]

Exceptions

std::out_of_range

if p ∉ [0, 1] or 0 < p < 1e−9

Note

p = 0 is the perfect channel (capacity 1); p = 1 makes only 0 transmissible (capacity 0).

Definition at line 412 of file blocks.hpp.

Member Function Documentation

get_capacity()

double CECCO::BAC::get_capacity ( ) const

inlinenoexcept

Shannon capacity in bits per symbol.

Returns

C = log₂(1 + (1 − p)·p^{p/(1−p)}); edge cases p ∈ {0, 1} handled explicitly.

Definition at line 431 of file blocks.hpp.

get_pe()

double CECCO::BAC::get_pe ( ) const

inlinenoexcept

Flip probability p (probability that 1 → 0).

Definition at line 425 of file blocks.hpp.

operator()()

Fp< 2 > CECCO::BAC::operator() ( const Fp< 2 > & in )

inline

Process one bit.

Parameters

in

Input bit

Returns

Output: 0 is preserved; 1 flips to 0 with probability p

Definition at line 419 of file blocks.hpp.

---

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

• blocks.hpp