itpp::LLR_calc_unit Class Reference

Log-likelihood algebra calculation unit. More...

#include <llr.h>

List of all members.

Public Member Functions

LLR_calc_unit ()

Constructor, using the default table resolution.

LLR_calc_unit (short int Dint1, short int Dint2, short int Dint3)

Constructor, using a specific table resolution.

void init_llr_tables (short int Dint1=12, short int Dint2=300, short int Dint3=7)

Set the quantization and table parameters.

QLLR to_qllr (double l) const

Convert a "real" LLR value to an LLR type.

QLLRvec to_qllr (const vec &l) const

Convert a vector of "real" LLR values to an LLR type.

QLLRmat to_qllr (const mat &l) const

Convert a matrix of "real" LLR values to an LLR type.

double to_double (QLLR l) const

Convert an LLR type to a "real" LLR.

vec to_double (const QLLRvec &l) const

Convert a vector of LLR types to a "real" LLR.

mat to_double (const QLLRmat &l) const

Convert a matrix of LLR types to a "real" LLR.

QLLR jaclog (QLLR a, QLLR b) const

Jacobian logarithm.

QLLR Boxplus (QLLR a, QLLR b) const

Hagenauer's "Boxplus" operator.

QLLR logexp (QLLR x) const

Logexp operator.

ivec get_Dint ()

Retrieve the table resolution values.

Friends

std::ostream & operator<< (std::ostream &os, const LLR_calc_unit &l)

Print some properties of the LLR calculation unit in plain text.

Related Functions

(Note that these are not member functions.)

typedef signed int QLLR

typedef Vec< QLLR > QLLRvec

typedef Mat< QLLR > QLLRmat

const QLLR QLLR_MAX = (std::numeric_limits<QLLR>::max() >> 4)

Detailed Description

Log-likelihood algebra calculation unit.

This class contains functions for algebra with log-likelihood ratios (LLRs). The (sole) purpose of this class is to provide numerically efficient functions for turbo and LDPC codes, which rely on certain nonlinear operations on LLRs.

An LLR for an information bit b is defined according to

$L = \log \frac{P(b=0)}{P(b=1)}$

and it is in general a real number.

LLR values are represented via the special type, "quantized LLR" (QLLR). The relation between the quantized representation and the real (floating-point) LLR value is

$\mbox{QLLR} = \mbox{round} \left(2^{\mbox{Dint1}}\cdot \mbox{LLR}\right)$

The user parameter Dint1 determines the granularity of the quantization, and it can be set arbitrarily. The functions to_double() and to_qllr() can be used to perform conversions between the two representations (QLLR to floating-point, and vice versa).

The class provides functions for the computation of the Jacobian logarithm and Hagenauer's "boxplus" operator. These functions are based on a table-lookup. The resolution of the table is determined by the parameters Dint2 and Dint3. See the class constructor for more detail. When an object of LLR_calc_unit is created, corresponding lookup-tables are also generated. The resolution of these tables can be adjusted by providing parameters to the constructor.

The variable table resolution allows one to study complexity versus accuracy (i.e., how different table resolutions would degrade performance) to some extent. Yet the main purpose of the QLLR representation is to provide a tool for writing efficient simulation code, rather than to provide for bit-level (fixed-point) simulations. For bit-level simulations, a true fixed point representation of LLRs would be preferred/required. With the default setting of the table parameters, using the QLLR type is practically as accurate (but much faster) as using "double" to represent LLRs. Decoder implementations may then provide functions using QLLR, fixed-point, or double (for compatibility reasons) representations of LLR values.

Note: the QLLR type does not check that the correct quantization level is used. I.e., in theory it would be possible to add two QLLR types with different quantization (Dint) parameters. This is intentionally implemented this way to achieve maximum runtime efficiency.

Constructor & Destructor Documentation

itpp::LLR_calc_unit::LLR_calc_unit	(	short int	Dint1,
		short int	Dint2,
		short int	Dint3
	)

Constructor, using a specific table resolution.

See init_llr_tables() for more details on the parameters.

References init_llr_tables().

Member Function Documentation

QLLR itpp::LLR_calc_unit::Boxplus	(	QLLR	a,
		QLLR	b
	)			const

Hagenauer's "Boxplus" operator.

This function computes:

$\mbox{sign}(a) * \mbox{sign}(b) * \mbox{min}(|a|,|b|) + f(|a+b|) - f(|a-b|)$

where

$f(x) = \log(1+\exp(-x))$

References it_info_debug, logexp(), and QLLR_MAX.

Referenced by itpp::LDPC_Code::bp_decode().

void itpp::LLR_calc_unit::init_llr_tables	(	short int	Dint1 = `12`,
		short int	Dint2 = `300`,
		short int	Dint3 = `7`
	)

Set the quantization and table parameters.

Parameters:

Dint1

Determines the relation between LLR represented as real number and as integer. The relation is

$\mbox{QLLR} = \mbox{round} \left(2^{\mbox{Dint1}}\cdot \mbox{LLR}\right)$

Dint2

Number of entries in the table. If this is zero, then logmap becomes logmax.

Dint3

Determines the table resolution. The spacing between each entry is

$2^{-(Dint1-Dint3)}$

The default parameter values are chosen to give a performance practically indistinguishable from that of using floating point calculations.

Example: (recommended settings with "exact" computation via high resolution lookup table)

    LLR_calc_unit lcalc(12, 300, 7);

Example: (recommended settings with logmax, i.e. no table lookup)

    LLR_calc_unit lcalc(12, 0, 7);

Referenced by LLR_calc_unit().

QLLR itpp::LLR_calc_unit::jaclog	(	QLLR	a,
		QLLR	b
	)			const `[inline]`

Jacobian logarithm.

This function computes

$\log(\exp(a)+\exp(b))$

References logexp(), and QLLR_MAX.

Referenced by itpp::Rec_Syst_Conv_Code::log_decode(), itpp::Rec_Syst_Conv_Code::log_decode_n2(), itpp::Modulator_ND::probabilities(), and itpp::Modulator_ND::update_LLR().

QLLR itpp::LLR_calc_unit::logexp ( QLLR x ) const [inline]

Logexp operator.

This function computes

$f(x) = \log(1+\exp(-x))$

References it_assert_debug.

Referenced by Boxplus(), and jaclog().

Friends And Related Function Documentation

typedef signed int QLLR [related]

The quantized log-likelihood ratio (QLLR) representation, scalar form. See LLR_calc_unit.

const QLLR QLLR_MAX = (std::numeric_limits<QLLR>::max() >> 4) [related]

The largest possible QLLR value

Referenced by Boxplus(), jaclog(), and to_qllr().

typedef Mat<QLLR> QLLRmat [related]

The quantized log-likelihood ratio (QLLR) representation, matrix form. See LLR_calc_unit.

typedef Vec<QLLR> QLLRvec [related]

The quantized log-likelihood ratio (QLLR) representation, vector form. See LLR_calc_unit.

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


Public Member Functions
	LLR_calc_unit ()
	Constructor, using the default table resolution.
	LLR_calc_unit (short int Dint1, short int Dint2, short int Dint3)
	Constructor, using a specific table resolution.
void	init_llr_tables (short int Dint1=12, short int Dint2=300, short int Dint3=7)
	Set the quantization and table parameters.
QLLR	to_qllr (double l) const
	Convert a "real" LLR value to an LLR type.
QLLRvec	to_qllr (const vec &l) const
	Convert a vector of "real" LLR values to an LLR type.
QLLRmat	to_qllr (const mat &l) const
	Convert a matrix of "real" LLR values to an LLR type.
double	to_double (QLLR l) const
	Convert an LLR type to a "real" LLR.
vec	to_double (const QLLRvec &l) const
	Convert a vector of LLR types to a "real" LLR.
mat	to_double (const QLLRmat &l) const
	Convert a matrix of LLR types to a "real" LLR.
QLLR	jaclog (QLLR a, QLLR b) const
	Jacobian logarithm.
QLLR	Boxplus (QLLR a, QLLR b) const
	Hagenauer's "Boxplus" operator.
QLLR	logexp (QLLR x) const
	Logexp operator.
ivec	get_Dint ()
	Retrieve the table resolution values.
Friends
std::ostream &	operator<< (std::ostream &os, const LLR_calc_unit &l)
	Print some properties of the LLR calculation unit in plain text.
Related Functions
(Note that these are not member functions.)
typedef signed int	QLLR
typedef Vec< QLLR >	QLLRvec
typedef Mat< QLLR >	QLLRmat
const QLLR	QLLR_MAX = (std::numeric_limits<QLLR>::max() >> 4)