Soft bit metric generation

Soft bit metric generation computational complexity can be reduced by identifying and utilizing only the dominant terms in a reliability calculation such as a logarithmic likelihood ratio (LLR). The dominant terms are those terms for which the signs of the x and y components match those of channel outputs of the channel outputs. One technique for identifying the dominant terms is by determining the most likely transitions from two consecutive channel output samples Values for the dominant terms can be estimated by either the joint reliability of two consecutive samples of the in-phase component (x1,x2) or by the joint reliability of two consecutive samples of the quadrature components (y1,y2).

BACKGROUND OF THE INVENTION

Differential encoding techniques are used by some communications systems to mitigate the undesirable effects of phase noise and channel impairments. Examples include but are not limited to Quadrature Phase Shift Keying (QPSK), Differentially Encoded QPSK (DE-QPSK), 16 Quadrature Amplitude Modulation (QAM) and 64 QAM QPSK is a form of phase shift keying in which two bits are contemporaneously modulated by selecting one of four possible carrier phase shifts (0, π/2, π, and 3π/2). QAM is a modulation technique for conveying either two analog message signals or two digital bit streams by changing the amplitudes of two carrier waves using Amplitude Shift Keying (ASK) or Amplitude Modulation (AM). When these techniques are used, a differential decoding operation is implemented at the receiver to recover the transmitted information. In particular, a “soft decision” decoder uses soft bit metric information to decode data that has been encoded with an error correcting code. The soft bit metric information indicates the reliability of each input data point, and is used to generate a better estimate of the original data than a hard decision decoder would when the data is corrupted by noise. However, soft bit metric information may be computational costly to generate.

SUMMARY OF THE INVENTION

In accordance with one aspect a method comprises: from an expression of reliability of encoded bits associated with a higher order modulation scheme, the expression including a plurality of terms, selecting dominant terms from the plurality of terms; and calculating reliability of the encoded bits based on the selected dominant terms.

In accordance with another aspect an apparatus comprises: circuitry which selects dominant terms from an expression of reliability of encoded bits associated with a higher order modulation scheme; and circuitry which calculates reliability of the encoded bits based on the selected dominant terms.

In accordance with another aspect a computer program stored on a non-transitory computer-readable medium comprises: logic for selecting dominant terms from an expression of reliability of encoded bits associated with a higher order modulation scheme; and logic for calculating reliability of the encoded bits based on the selected dominant terms.

These and other features will be apparent from the detailed description and figures.

DETAILED DESCRIPTION

FIG. 1illustrates differential encoding. Symbols100represent DE-QPSK outputs from a differential encoder at rotational positions labeled as (I,Q). Transitions (0°, 90° CW, 90° CCW, 180°) between outputted symbol positions are indicative of input bits denoted as b, b2. For example, from (Ii-1, Qi-1)=(−1/√{square root over (2)},−1/√{square root over (2)}), if the input symbol (b1,b2) to the differential decoder at the next time instant is 00 then no rotation is applied as indicated by transition102, i.e., to where (Ii,Qi)=(−1/√{square root over (2)},−1/√{square root over (2)}). However, if the input symbol at the next time instant is 01 then 90-degree clockwise rotation is applied as indicated by transition104, i.e., to where (Ii,Qi)=(−1/√{square root over (2)},1/√{square root over (2)}). If the input symbol at the next time instant is 10 then 90-degree counter-clockwise rotation is applied as indicated by transition106, i.e., to where (Ii,Qi)=(1/√{square root over (2)},−1/√{square root over (2)}). If the input symbol at the next time instant is 11 then 180-degree counter-clockwise rotation is applied as indicated by transition108, i.e., to where (Ii,Qi)=(1/√{square root over (2)},1/√{square root over (2)}). The symbols a transmitted on a channel and a receiver observes received values Ctat times t=i−1 and t=i to recover the bits (b1, b2) transmitted at time i.

Soft Decision Encoding/Decoding is used to enhance the accuracy of the receiver, e.g., where the transmitted symbols are distorted by memory-less additive noise and previous and future values of Ctdo not provide extra information about the bits. A soft decision decoder operates in response to inputted “soft metrics” which represent the reliability of each encoded bit. If Ct-1and Ctdenote distorted DE-QPSK symbols at the channel output at time instants t−1 and t, respectively, these two symbols can be used to generate the soft metrics for two encoded bits denoted by b1,tand b2,t. The Logarithmic-Likelihood Ratio (LLR) is used for the purposes of this description, but it should be understood that soft metrics can take various other forms which might be utilized. The general equation for the LLR of b1,tis:

llr⁡(b2,t)=log⁡(P⁡(b2,t=1|Ct-1,⁢Ct)P⁡(b2,t=0|Ct-1,⁢Ct))(equation⁢⁢2)
Equation 1 can be expressed as

llr⁡(b1,t)=log⁡(ⅇ-x1-y1+x2-y2σ2/2+ⅇ-x1-y1+x2+y2σ2/2+ⅇ-x1+y1-x2-y2σ2/2⁢+ⅇ-x1+y1+x2-y2σ2/2⁢+ⅇx1-y1+x2+y2σ2/2+ⅇx1-y1-x2+y2σ2/2+ⅇx1+y1-x2-y2σ2/2+ⅇx1+y1-x2+y2σ2/2ⅇ-x1-y1-x2-y2σ2/2+ⅇ-x1-y1-x2+y2σ2/2+ⅇ-x1+y1-x2+y2σ2/2+ⅇ-x1+y1+x2+y2σ2/2+ⅇx1-y1+x2-y2σ2/2+ⅇx1-y1-x2-y2σ2/2+ⅇx1+y1+x2-y2σ2/2+ⅇx1+y1+x2+y2σ2/2)(equation⁢⁢4)
Also, llr(b2,t) can be written as

llr⁡(b2,t)=log⁡(ⅇx1+y1-x2-y2σ2/2+ⅇx1+y1+x2-y2σ2/2+ⅇ-x1+y1+x2-y2σ2/2+ⅇ-x1+y1+x2+y2σ2/2+ⅇ-x1-y1+x2+y2σ2/2+ⅇ-x1-y1-x2+y2σ2/2+ⅇx1-y1-x2+y2σ2/2+ⅇx1-y1-x2-y2σ2/2ⅇx1+y1+x2+y2σ2/2⁢+ⅇx1+y1-x2+y2σ2/2+ⅇ-x1+y1-x2+y2σ2⁢2+ⅇ-x1+y1-x2-y2σ2/2+ⅇ-x1-y1-x2-y2σ2/2+ⅇ-x1-y1+x2-y2σ2/2+ⅇx1-y1+x2-y2σ2/2+ⅇx1-y1+x2+y2σ2/2)(equation⁢⁢5)
Although values of equations 4 and 5 can be calculated, each equation includes sixteen terms, each one of which requires the evaluation of an exponential. Therefore, the computational complexity for these equations is relatively high.

In general, computational complexity can be reduced by identifying and utilizing only the dominant terms in a reliability calculation such as the logarithmic likelihood ratio (LLR). The dominant terms in equations 4 and 5 can be selected as, for example, those terms for which the signs of the x and y components match those of channel outputs of the channel outputs. On technique for identifying the dominant terms is by determining the most likely transitions from two consecutive channel output samples that are denoted by Ct-1=(x1,y1) and Ct=(x2,y2), where x and y denote in-phase and quadrature components of the symbol, respectively. [Moved to below] Techniques for reducing computational complexity for soft bit metric generation for differentially encoded higher order modulation schemes will now be described with regard to the example illustrated inFIG. 2.

In the example illustrated inFIG. 2dots300represent the transmitted DE-QPSK symbols denoted by (Ii-1, Qi-1). Dot302represents a corresponding noisy channel output received at time instant i−1. Similarly dot304denotes a corresponding noisy channel output at time instant i. The most likely transition306is (b1, b2)=11, i.e., transition from (Ii-1, Qi-1)=00 to (Ii, Qi)=11. Because x1has the smallest magnitude among all, the second most likely transition308is (b1, b2)=10, i.e., from (Ii-1, Qi-1)=10 to (Ii, Qi)=11, with Ii-1flipped sign.

In at least one embodiment a “G operation” is used to calculate the reliability of encoded bits (b1, b2) from noisy channel outputs Ct-1=(x1,y1) and Ct=(x2, y2). The G operation computes the joint reliability of two reliability values, which can be either in-phase components (x1, x2) or quadrature components (y1, y2). Given a and b as two reliability values, the G operation can be expressed as:
G(a,b)=min(|a|,|b|)−c(a,b),  (equation 6)
where c(a, b) is a correction term. In the illustrated example the G operation between (x1, x2) is assigned to b2as the reliability information because the flip of b2is the most likely event. Conversely, the G operation between (y1, y2) is assigned to b1as the reliability information.

Hard decision differential decoding can be used to indicate the most likely transition between each pair of received symbols, Ct-1=(x1, y1) and Ct=(x2, y2). In the illustrated example the hard decision differential decoder will return (1,1) since the most likely transition corresponds to (b1, b2)=(1,1).

The signs of the bit reliabilities that are generated using the G operation are determined by hard decision differential decoding. If hard decision decoder returns 1 (0), then positive (negative) signs are assigned to the reliabilities. If the G operation returns 3 for b1and 4 for b2then positive signs are assigned to these reliabilities, i.e., llr(b1)=3 and llr(b2)=4.

Referring toFIG. 3, in accordance with one aspect the correction term for the G operation is obtained from a look-up table based on scaling and the signal to noise ratio estimate, e.g., Table400(FIG. 4), where c(a,b) is expressed as a function of ∥a|−|b∥ as a further simplification. For example if the SNR estimate is 5.3 dB and ∥a|−|b∥=1, then c(1)=2 is outputted by table400as indicated by entry402.

FIG. 4illustrates an analysis of the most likely and second most likely transitions over cases A through P, assuming (x1, y1) is always in the third quadrant, and (x2, y2) is moving from 1stquadrant to 4thquadrant in each row. In row 1, x1has the smallest magnitude for cases A to D. In row 2, y1has the smallest magnitude for cases E to H. In row three, y2has the smallest magnitude in the first quadrant for case I, and cases J to L show rotation by 90, 180 and 270 degrees. In row 4, x2has the smallest magnitude in the first quadrant for case I, and cases N to P show rotation by 90, 180 and 270 degrees. Cases A through P combined cover all relative magnitude possibilities with (x1, y1) in the 3rdquadrant. Referring toFIG. 5, by analyzing cases A through P it can be determined that four of the cases, namely A, C, E and G, shall have the G operation between (x1, x2) assigned to b2and the G operation between (y1, y2) assigned to b1as indicated by Table500. In all other cases the G operation between (x1, x2) should be assigned to b1and the G operation between (y1, y2) should be assigned to b2. Although only the cases where (x1, y1) is in the third quadrant are described above, all other cases with (x1, y1) in other quadrants will also be analyzed.

FIG. 6is a block diagram of circuitry for soft bit metric generation. A Hard Decision differential decoder600indicates the most likely transition between each pair of received symbols, Ct-1=(x1, y1) and Ct=(x2, y2). The G operation is performed separately on x (x1, x2) and y (y1, y2) components for all cases in table500(FIG. 5) using G operation blocks602,604. G operation assignment to b1or b2is determined by the case index. Consequently, x and y components are applied to G operation blocks602,604separately. A “Case Logic” block606determines if the output of two G operations should be swapped by logic608,610based on the case index as described in table500(FIG. 5). The Case Logic block606computes output g from (x1, x2) and (y1, y2) as:
g=(d1⊕e1)⊕(f·((d1⊕e1)⊕(d2⊕e2))((d1⊕e1)⊕(d2⊕e2))(equation 7)
where

dn={1,xn≥00,otherwise(equation⁢⁢8)en={1,yn≥00,otherwise(equation⁢⁢9)f={1,min⁡(x1,y1)<min⁡(x2,y2)0,otherwise(equation⁢⁢10)
and where ⊕; denotes logical XOR and AND operations, respectively. A line drawn above the expression denotes logical NOT. The hard decision differential decoder600implements the following equations for the differential encoding scheme:
c1=(d1⊕d2)⊕((d1⊕e1)·(d2⊕e2))
c2=(e1⊕e2)⊕((d1⊕e1)·(e2⊕e2))
where llr(b1) and llr(b2) values are signed by C1and c2(Cn=1 indicates a positive number).

FIG. 7is a flow diagram of a method for soft bit metric generation. The method includes selecting the dominant terms in a reliability calculation such as the logarithmic likelihood ratio (LLR) as indicated by step700. One technique for identifying the dominant terms is by determining the most likely transitions from two consecutive channel output samples that are denoted by Ct-1(x1, y1) and Ct=(x2, y2), where x and y denote in-phase and quadrature components of the symbol, respectively. The dominant terms in equations 4 and 5 can be selected as, for example, those terms for which the signs of the x and y components match those of channel outputs of the channel outputs. Reliability of the encoded bits is then calculated based on the selected terms as indicated by step702. Values for the above-mentioned dominant terms can be estimated by either the joint reliability of two consecutive samples of the in-phase component (x1,x2) or by the joint reliability of two consecutive samples of the quadrature components (y1,y2).

It will be appreciated that the invention is not limited to QPSK or other features which have been used to provide context for the describe above. Further, aspects may be implemented using general purpose electronic hardware, purpose-designed electronic hardware, computer program code stored on a non-transitory computer-readable medium and operated upon by a general or purpose-designed processor, or any combinations thereof. Furthermore, while the invention is described through the above exemplary embodiments, it will be understood by those of ordinary skill in the art that modification to and variation of the illustrated embodiments may be made without departing from the inventive concepts herein disclosed. Moreover, while the preferred embodiments are described in connection with various illustrative structures, one skilled in the art will recognize that the system may be embodied using a variety of specific structures. Accordingly, the invention should not be viewed as limited except by the scope and spirit of the appended claims.