Log-likelihood algebra calculation unit. More...

#include <itpp/comm/llr.h>

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
ITPP_EXPORT 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)

ITPP_EXPORT std::ostream &	operator<< (std::ostream &os, const LLR_calc_unit &lcu)
	Print some properties of the LLR calculation unit in plain text.

Detailed Description

Log-likelihood algebra calculation unit.

This class contains functions for algebra with log-likelihood ratios (LLRs). The class is mainly useful for modules that rely on certain nonlinear operations on LLRs (e.g. boxplus for LDPC and turbo decoding and Jacobian logarithm for soft demodulation). The routines provided are numerically efficient and use only integer arithmetics. Additionally, they allow for arbitrary quantization of LLRs in order to study effects of limited precision (fixed point number representations). As a consequence, computations are approximate. With the standard settings, the numerical precision should be sufficient (and practically equivalent to floating point precision) for all practical applications. However, one can construct cases where small numerical artifacts due to quantization effects (e.g., soft demodulation with very high or very low SNR) can be observed.

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.

Definition at line 124 of file llr.h.

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.

Definition at line 41 of file llr.cpp.

References init_llr_tables().

Member Function Documentation

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