WO2016057836A1 - Method and system for identifying optimal quadratic permutation polynomial turbo interleaver sets - Google Patents

Abstract

Systems and automated methods are provided for obtaining optimal Q.PP parameter sets. For a given block size N all possible Q.PP parameter sets may be generated to obtain a candidate set of f1,f2 pairs. The candidate set may then be initially tested for performance, and the poorer performing parameter pairs removed from consideration, resulting in a good candidate set. The good candidate set may then be subjected to more extensive testing, which may include decreasing SNR and lengthening the test bit sequences in various combinations to trigger errors, and thus allow ranking of the candidates by performance. Because some block sizes N are fixed by system design parameters, the inquiry may end there. In other embodiments, where there is an allowed range of possible block sizes for a system being designed ab initio, the above process may be an inner loop, for a given block size, where an outer loop runs through various possible block sizes N, where N may be subject to some condition. For example, in some embodiments block sizes are desired to be a multiple of some integer or even some power of 2, e.g., 8, and thus the outer loop runs through potential block sizes N that satisfy such conditions, for example, all N between 10,000 and 13,000 that are divisible by 8. Using an exemplary system, an optimal parameter set {f1,f2} = {217,1560} was found for a block size of N=12,168 bits, and an optimal parameter set {f1,f2} = {299, 510} for a block size of N=12,240 bits was found.

Description

PATENT APPLICATION UNDER THE PATENT CO-OPERAITON TREATY

FOR

METHOD AND SYSTEM FOR IDENTIFYING OPTIMAL QUADRATIC PERMUTATION POLYNOMIAL TURBO INTERLEAVER SETS

CROSS-REFERENCE TO RLEATED APPLICATIONS

This application claims the benefit of United States Provisional Patent Application No. 62/061,292, filed on October 8, 2014, which is hereby incorporated by reference in its entirety.

FIELD OF THE INVENTION

The present invention generally relates to Forward Error Correction ("FEC") based on a Quadratic Permutation Polynomial (Q.PP) turbo interleaver structure to facilitate high-speed turbo decoding of large code block sizes in, for example, a Satellite Digital Audio Radio Service ("SDARS") system.

BACKGROUND OF THE INVENTION

Modern communication systems have demanding throughput rates that are only expected to increase in future applications and uses. Historically, FEC systems have used trellis and Reed-Solomon coding, where high throughput can be achieved due to circuit simplicity. With the advent of modern iterative FEC techniques such as turbo codes (a common choice for low speed applications) and Low-Density Parity-Check (LDPC) codes (a common choice for high speed applications), high throughput rates are not nearly as easily achieved compared to non- iterative approaches. Throughputs above payload rates of lOMbits/sec have almost always been addressed exclusively by LDPC encoders/decoders. This is due to the ease of parallel implementation of the LDPC decoder. However, this has not been the case for turbo codes due to the nature of the interleaver used within a turbo encoder. Well performing codes have used interleavers that do not lend themselves to a parallel implementation. As a result, they have had lower throughput rates. Today, this turbo coding limitation has largely been solved by using Q.PP turbo interleaver technology, which allows for high speed decoding while taking advantage of the small turbo decoder footprint. Indeed, the Q.PP interleaver has been adopted by the 3GPP2 standards body as the turbo interleaver of choice for all LTE turbo

implementations.

Q.PP interleavers are easy to implement. They are based on permuting the input information bits by the following quadratic equation: y = Mod fl * x + fl * x², N)

Where:

x = input vector ranging from 0 to the information code block size (N) -1; N = the block size of the information bits prior to parity encoding;

/l, /2 = the Q.PP permutation parameter set; and

Mod = modulo function over subspace N.

The requirement to form a valid interleaver set is that the choice of values for {fl,f2} must uniquely map an input vector (x, from 0 to N-l) to an output vector (y) in the same subspace, i.e., from 0 to N-l. That is, for every input bit location, there exists a unique output bit location, spanning the entire input block size. Arbitrary values of fl, f2 will not achieve this requirement. As a result, algorithms based on number theory must be used to derive suitable parameter sets.

To find a suitable value of the f2 portion of the parameter set, one begins with the block size. All of the unique prime numbers of the information block size must be calculated, and then the resulting product of these unique primes must be found. For example, for an information block size of 12,168, the prime factors are 2, 2, 2, 3, 3, 13 and 13. The unique prime numbers are thus 2, 3, and 13, whose product is 78. Any multiple of 78 is thus a suitable value to use for the f2 parameter value.

Given a value for each f2, to find a corresponding suitable value of fl, a simple search algorithm can be used. From number theory, it can be proved that fl must be an odd integer greater than or equal to three. Number theory also shows that the value of fl needs to be no larger than ½ the information block size N, since values beyond that will yield similar results to smaller values due to the modulus function. In other words, for a given block size N, one calculates the product of its unique primes, and takes any multiple of that as f2; for a given f2, fl is an odd integer that is greater than 3 and less than or equal to N/2. For a large block size N, on the order of 10K+, there are thus thousands of possible fl candidates, and on the order of 100 or so possible f2 candidates. To find an appropriate pair, for each f2, a candidate output vector Y can be calculated for a given fl, which is then tested to see if it maps the input vector X to unique output addresses. If so, a successful pair of fl, f2 parameters will have been found for the given block size N. In general, there are typically thousands of suitable pairs that meet the above criterion, particularly for larger block sizes. This begs the question: which fl, f2 Q.PP parameter set pair yields the best performing Q.PP turbo interleaver?

Evaluating suitable fl, f2 pairs can be performed in a number of ways. Conventionally, the best approach is to analyze the resulting Q.PP interleaver structure and calculate its minimum distance (given the encoder's systematic recursive encoding polynomial). However, this method presents an extremely high computational demand for even moderate block sizes, and is essentially unsuitable for large block sizes, such as, for example, those in excess of 10,000 information bits. Moreover, the computational load is exactly the same for any proposed Q.PP pair. Testing a significant number of candidate {fl,f2} pairs is thus computationally significant, and often intractable.

What is needed in the art is a way to intelligently quickly rule out bad Q.PP sets, thereby speeding up the selection process for the best survivor pair. The present invention satisfies this need.

BRIEF DESCRIPTION OF THE DRAWINGS:

Fig. 1 depicts an exemplary bit error rate ("BER") curve for a rate 1/3 turbo interleaver, illustrating both good and bad exemplary Q.PP sets, according to an exemplary embodiment of the present invention.

SUMMARY OF THE INVENTION:

Automated methods are provided for obtaining optimal Q.PP parameter sets. For a given block size N all possible Q.PP parameter sets may be generated to obtain a candidate set of fl,f2 pairs. The candidate set may then be initially tested for performance, and the poorer performing parameter pairs removed from consideration, resulting in a good candidate set. The good candidate set may then be subjected to more extensive testing, which may include decreasing SNR and lengthening the test bit sequences in various combinations to trigger errors, and thus allow ranking of the candidates by performance. Because some bock sizes N are fixed by system design parameters, the inquiry may end there. In other exemplary embodiments, where there is an allowed range of possible block sizes for a system being designed ab initio, the above process may be an inner loop, for a given block size, where an outer loop runs through various possible block sizes N, where N may be subject to some condition. For example, in some embodiments block sizes are desired to be a multiple of some integer or even some power of 2, e.g. 8, and thus the outer loop runs through potential block sizes N that satisfy such conditions, such as, for example, all N between 10,000 and 13,000 that are divisible by 8. In other embodiments, other constraints upon block size N may, for example, be imposed, and the outer loop run through all possible N that meet the constraint.

Using an exemplary system, an optimal parameter set {fl,f2} = {217,1560} was found for a block size of N=12,168 bits, and an optimal parameter set {fl,f2} = {299, 510} for a block size of N=12,240 bits was found.

DETAILED DESCRIPTION OF THE INVENTION:

Conventionally, Q.PP parameter pairs may be calculated by searching for the pair that gives the maximum minimum distance between two valid code words. If there are multiple parameter pairs that achieve that maximum minimum distance, then the Q.PP parameter pair that gives the minimum number of multiplicities of that distance is used, where a multiplicity of a given code is how many code words hit that minimum distance. Researchers have published papers on the optimum minimum distance, where, for small block sizes parameter sets have been found that achieve such maximum minimum distance and, when there was a tie, a minimum number of multiplicities. However, the problem lies in trying to run standard discovery techniques for block sizes on the order of 10,000 bits and greater, where they take inordinately long, if they converge to an answer at all. In trials by the present inventors using standard software, the computation time increases quadratically with block size. Thus, while such conventional methods may work for, say a thousand bits, when up to 12,000 bits was attempted, such standard parameter discovery software was found to be useless. Thus, systems and automated methods are presented herein that quickly rule out bad Q.PP parameter sets early on, allowing a testing protocol to focus on the "good" candidates, so as to find those of them that are optimal. According to an exemplary embodiment of the present invention, which can be implemented via an algorithm executing on one or more suitable data processing devices, computing systems and/or the like, such methods may be developed around the shape of the Bit Error Rate ("BER") curve of the turbo encoder's mother code.

Fig. 1 depicts an exemplary BER curve for a rate 1/3 Q.PP turbo encoder, using each of a good and a not-so-good Q.PP interleaver parameter set for comparison. Obviously, the "good" Q.PP parameter set was used to generate the lower, solid line, curve, and the "not-so-good" Q.PP parameter set was used to generate the upper, dotted line curve.

Normally, curves for different Q.PP parameter sets are not as disparate as shown and hence are not so easily identifiable as being "good" or "bad." Recognizing that a good curve should have near error free performance at some Eb/No ratio (for a rate 1/3 turbo code it is around 0.4 dB) permits poorly performing code sets to be quickly ruled out. It is noted that Eb/No refers to the energy per bit to noise power spectral density ratio, and is an important parameter in digital communications or data transmission. It is a normalized signa!-to-noise ratio (SNR) measure, and is also known as the "SNR per bit." it is especially useful when comparing the BER performance of different digital modulation schemes without taking bandwidth into account. Eb/No is equal to the SNR divided by the "gross" link spectral efficiency in (bit/s)/Hz, where the bits in this context are transmitted data bits, inclusive of error correction information and other protocol overhead. When forward error correction (FEC) is being discussed, Eb/No is routinely used to refer to the energy per information bit (i.e. the energy per bit net of FEC overhead bits). The noise spectral density No, usually expressed in units of Watts per Hertz, can also be seen as having dimensions of energy, or units of joules, or joules per cycle. Eb/No is therefore a non-dimensional ratio.

As noted above, some bad Q.PP parameter sets will be vastly bad (as shown by the upper dotted line curve in Fig. 1), while others may not differ as greatly. Because the vertical axis has better bit error rates at the bottom, a poorly performing curve will generally be "on top" of a good curve, as shown in Fig. 1, where the dashed line poorer curve lies above the solid line good curve. In exemplary embodiments of the present invention, the idea is to not waste time computing the performance of a bad set, which will quickly reveal itself at known thresholds. For example, at a test point of 0.4 Eb/No, the bad set will almost immediately reveal itself with bit errors in the decoded turbo block.

According to an exemplary embodiment of the present invention, an error performance threshold may be set for a given Eb/No and a search then performed to identify bad codes that would statistically result in a block error. Each set can, for example, be used in a turbo decoder simulation under white Gaussian noise conditions, only examining the mother code's performance (no puncturing). The inventive algorithm can simulate the entire set of Q.PP parameters under evaluation at a given SNR, for example, Eb/No. A threshold allowance of K block errors can be permitted (because it is not guaranteed that any code can be error free at any Eb/No) at the given Eb/No setting. The set that requires the longest amount of time to reach the block error threshold is determined to be the best set. If multiple sets do not exceed the block error count for the given Eb/No, then the algorithm may move to a lower Eb/No value (i.e., move to the left in the BER curve of Fig. 1), and the remaining survivor parameter sets may then be re-evaluated. Alternatively, a longer time can be used to run the code at the higher Eb/No value until errors do occur. Still alternatively, combinations of (i) lowering the Eb/No value and (ii) extending the time in which the test is run may be successively and recursively used. As can be gleaned from the curve of Fig. 1, as the algorithm continues to lower the Eb/No value, all sets will eventually exceed the allowable block error threshold. The set that holds out the longest through this evaluation process can be determined to be the best Q.PP set.

Thus, for example, a first test may be run for a given block size N at a Eb/No ratio of 0.4, with a maximum BER of 10^"6. From the results of this first test, all "bad" Q.PP parameter sets that have a BER greater than such a threshold can be dropped. This obtains a subset of the originally identified Q.PP parameter pairs, each of which passes at a Eb/No ratio of 0.4, which can then, for example, be tested at a lower Eb/No ratio, such as, for example, 0.3, and running the decoding process until they all reach a BER of 10^"4. If some still survive, for example, then the Eb/No ratio may be further decremented, say by 0.1, for example, and the BER raised by some appropriate increment, or alternatively left where it is until all the remaining candidates reach it. This "whittling down" process may be continued until a "best" Q.PP parameter pair is found from the remaining candidates.

Alternatively, the subset of the originally identified Q.PP parameter pairs, each of which passed at a Eb/No ratio of 0.4, can then, for example, be tested at that same Eb/No ratio, where the decoding process is run until the last Q.PP parameter pair reaches a BER of 10^"7. If multiple Q.PP parameter pairs still survive, for example they never incur errors above the lowered BER of 10^"7, then either (i) the Eb/No ratio may be further decremented, say by 0.1, for example, and the BER further raised by some appropriate increment, or (ii) just the Eb/No ratio is further decremented and the BER left where it is until all but one of the remaining candidate pairs reaches it.

It is noted that any combination of SNR and minimal errors in various stages may be used as tests to whittle down an initial set of "good" Q.PP parameter sets to find a "best" Q.PP parameter set.

Due to the large number of possible sets that meet the Q.PP criterion, the inventive algorithm can be implemented across multiple computers, where each computer evaluates a subset of all possible sets in parallel with the other computers. The "winners" of each computer run can then compete against each other to determine the best overall Q.PP set in a final test or set of tests. Depending upon the number of possible Q.PP pairs for a given block size, the intermediate test stages may also be divided into subsets and themselves parallel processed in a distributed processing approach.

Exploiting the nature of the BER curve in the manner described above can be very effective in finding the best Q.PP set, at least in a statistical sense. It should be noted that unlike the minimum distance method (which is definitive), the inventive method can only yield a statistically high confidence level for finding good Q.PP sets.

Accordingly, the present invention is salutary in that it provides a way to quickly dispense with poor Q.PP sets at an initial stage - making the identification of good sets manageable even for very large block sizes. By way of example, for an information block size of N=12,168 bits, an algorithm according to a preferred embodiment of the present invention identifies the pair fl=217 and f2=1560 as yielding an excellent rate 1/3 turbo code with very low error floors (this block size and parameter set is not part of the LTE standard). In another example that is detailed in exemplary code below, for N=12,240 an optimal parameter pair of fl=299 and f2=510 was identified (this block size and parameter set is also not part of the LTE standard).

As is somewhat counterintuitive, often the best Q.PP parameter set is not obtained using a given fixed code block size. Rather, there is some variance in Q.PP turbo code performance with block size, even using the optimal Q.PP parameter set at each such block size. Thus, in exemplary embodiments where block size is constrained, but variable within some range, the testing protocol provided above for a defined block size may be implemented at each of multiple possible block sizes within the range of allowed block sizes. The greater the range of block sizes, of course, the more computation that must be performed. Thus, while the procedure described above for a fixed block size Nk may be considered to operate in an inner loop, an additional outer loop can increment through the range of all possible block sizes Nl to Nm. The "ultimate winner" will be a Q.PP parameter set for a given block size Nk within the defined range, or an {fl,f2} for a block size Nk. The outer loop processing may also be in parallel with a set of computers or data processors, and the entire process automated, by feeding an exemplary program (i) a range of block sizes, (ii) a threshold of performance by which to initially reject Q.PP parameter pair candidates (e.g., a BER at a specified Eb/No) in a first pass of the inner loop, and (iii) a performance threshold, either the same or different, by which to select an optimal pair form the "winners" of each first pass test at each block size. From the optimal Q.PP parameter pairs at each block size within the range, a final competition can be held to determine the best performing Q.PP interleaver with an associated optimal block size within the range.

It is noted that sometimes an external constraint is imposed upon the block size due to legacy data structures, or other framing and coding considerations, in exemplary embodiments of the present invention an optimal block size can be chosen that is closest to, but less than, the required block size, and then each block zero padded to make up the difference. For example, in some embodiments block sizes are desired to be a multiple of some integer or even some power of 2, e.g., 8, and thus the outer loop runs through potential block sizes N that satisfy such conditions, for example, all N between 10,000 and 13,000 that are divisible by 8. Exemplary Parameter Generation Code and Sample Output

Exemplary Matlab code is provided below that may be used to generate Q.PP interleavers according to exemplary embodiments of the present invention. The exemplary code contains a defined value of N=12,440, but this may be changed to any desired value, for example. The exemplary Matlab code is followed by an exemplary output set of possible {fl,f2} pairs which it generated, which may then be tested in one or more of the ways described above to whittle down to the best performing parameter sets, which can then be more rigorously tested to find the best performing parameter set.

As can be seen in the second line, the exemplary script uses a block size N=12,240. As noted above, the code is otherwise agnostic to block size N, and thus may be used for *any* block size, or any range of them. N is simply a variable that a user may set as she chooses, and an outer loop may be added that increments a block size N variable between a range of N₀ to Nm, where the N declaration in the inner loop of the exemplary script is changed from

"N=12240" to "N=Nk", for example, Nk set by the outer loop (not shown).

Returning to the example of the code below where N=12,240, it is noted that the prime factors of 12,240 are 2, 2, 2, 2, 3, 3, 5 and 17. Taking the product of unique prime factors thus yields 2*3*5*17= 510. Thus, the possible parameter set comprises 510 and multiples thereof for f2, and, as seen, the code runs through various odd integers as a possible fl for each f2 that satisfy various tests and conditions used by the script (which are explained in the comments to the code). It is understood, however, that the same script may be used for any arbitrary block size to generate Q.PP parameter pairs for testing according to various embodiments of the present invention. The exemplary script shown below constrains f2 to multiples of f2 up to and including 4*f2. Thus, in this particular example, f2 may be 510, 1020, 1530 and 2040. For each possible f2, fls are generated where, as noted above, fl > 3, and in this exemplary script, fl is also subject to other conditions which limit fl to 1999 or less.

The exemplary script (which may be an inner loop of a larger script, as noted) generates a set of Q.PP parameters for block size N, which can then be tested, as described above. The testing may be fully automated and implemented using distributed processing, wherein the set of Q.PP parameters at each block size N is divided into subsets, and each subset is initially tested to see if at a set Eb/No ratio - e.g., 0.4 - if any parameter pairs exceed a maximum BER, e.g., 10^"6 during decoding.

From the results of this first test, all "bad" Q.PP parameter sets that have a BER greater than the maximum allowable BER can be dropped. Then, for each block size, the surviving Q.PP parameter sets can then be tested at a lower Eb/No ratio, such as, for example, 0.3, and the decoding process can be run, for example, until they all reach a BER of 10^"4, the last one to reach it being the best for that block size. If some still survive, for example, then the Eb/No ratio may be further decremented by some increment, say by 0.1, for example, and the BER either (i) raised by some appropriate increment, or alternatively (ii) left where it is, and the decoding process run until all the remaining candidates reach the then set BER. This "whittling down" process may be continued until a "best" Q.PP parameter pair for each block size is found from the remaining candidates.

Finally the best overall Q.PP pair may be chosen from the "winners" at each block size, as described above, by (i) decrementing Eb/No ratios, or by (ii) decrementing Eb/No ratios and lowering BER tolerances.

Thus, due to the large number of possible sets that meet the Q.PP criterion, the inventive algorithm can be implemented across multiple computers, where each computer evaluates a subset of all possible sets in parallel with the other computers. The "winners" of each computer run can then compete against each other to determine the best overall Q.PP set in a final test or set of tests.

Exemplary Matlab Code For Generating QPP Interleaves

clear

N=12240; Smax=0 ;

InVL=0 :N-1;

F=factor (N) ;

s=0;

DF=0;

cnt=l ;

for j=l : length (F)

if (F(j) ~= s

s=F(j) ;

DF(cnt)=F(j) ;

cnt = cnt+1;

end

e d

f2inc=l ;

for j=l : length (DF)

f2inc=f2inc*DF prms=primes (500) ;

gppcnt=l ;

cnt=0 ;

bc=l ;

catalin= = [1 1 2 5 14 42 1

BigD= [1 0 0 0 0 0 0;

0 2 0 0 0 0 0;

0 0 6 0 0 0 0;

0 0 0 24 0 0 0;

0 0 0 0 120 0 0;

0 0 0 0 0 720 0;

0 0 0 0 0 0 5040] ;

f (fwon==l)

fnm=strcat ( ¹ OF?

fid = fopen(fnm,

nd disp ( ^{! s} )

disp ( ^! " ) for p = 3:2:2000

fl=p;

cnt=0 ; for f2=f2inc : f2inc : 4*f2inc

terminate=0 ; for j=l : length (DF)

clear InV O tV chk s;

InV=0 : DF ( j ) -1;

OutV = mod(fl*InV + InV . * InV* f2 , DF ( j ) ) ;

chk (OutV+1) =1;

s=sum (chk) ; i (s ~= DF(j) )

% ciisp(^: Q?P p rens not valid' S

terminate=l ;

break

end

end

if (terminate ==0)

¾ s^'io i let:?, check, if the diverse to this GPP pair % ubic or quadratic or higher

ivd=-l ;

for K=l :7

v=factorial (K+l) *catalin (K) *f2^AK;

vm=mod (v, ) ;

if (vm ==0)

ivd=K;

break

end

end

¾ s^'io i coiiL ui ;:b.e inverse coe ί.^~1ρ, £2ρ,"

clear D U e

D=BigD ( 1 : ivd, 1 : ivd) ;

gppcnt=gppcnt+l ;

disp (strcat (^{! s} , num2str ( f1 ) , ^! ,. ^s , num2str ( f2 ) , ^! irxv degree = ' , num2str (ivd) ) )

if (fwon==l)

fprintf (fid, ^! %d %s %d\r; ' , f1 , ^! , f2 ) ;

end end

end

end

disp (strcat ( * $ QPP sets found ^~ ' , num2str (gppcnt-1 ))) ;

if (fwon==l)

fclose ( fid) ;

e d Exemplary Parameter Set for N=12,240.

7 , 510

7 , 1020

7 , 1530

7 , 2040

11 510

11 1020

11 1530

11 2040

13 510

13 1020

13 1530

13 2040

19 510

19 1020

19 1530

19 2040

23 510

23 1020

23 1530

23 2040

29 510

29 1020

29 1530

29 2040

31 510

31 1020

31 1530

31 2040

37 510

37 1020

37 1530

37 2040

41 510

41 1020

41 1530

41 2040

43 510

43 1020

43 1530

43 2040

47 510

47 1020

47 1530

47 2040

49 510

49 1020

49 1530

49 2040

53 510

53 1020 53 2040

59 510

59 1020

59 1530

59 2040

61 510

61 1020

61 1530

61 2040

67 510

67 1020

67 1530

67 2040

71 510

71 1020

71 1530

71 2040

73 510

73 1020

73 1530

73 2040

77 510

77 1020

77 1530

77 2040

79 510

79 1020

79 1530

79 2040

83 510

83 1020

83 1530

83 2040

89 510

89 1020

89 1530

89 2040

91 510

91 1020

91 1530

91 2040

97 510

97 1020

97 1530

97 2040

101 , 510

101 , 1020

101 , 1530

101 , 2040

103 , 510

103 , 1020

103 , 1530 103 2040

107 510

107 1020

107 1530

107 2040

109 510

109 1020

109 1530

109 2040

113 510

113 1020

113 1530

113 2040

121 510

121 1020

121 1530

121 2040

127 510

127 1020

127 1530

127 2040

131 510

131 1020

131 1530

131 2040

133 510

133 1020

133 1530

133 2040

137 510

137 1020

137 1530

137 2040

139 510

139 1020

139 1530

139 2040

143 510

143 1020

143 1530

143 2040

149 510

149 1020

149 1530

149 2040

151 510

151 1020

151 1530

151 2040

157 510

157 1020

157 1530

157 2040 161 1020

161 1530

161 2040

163 510

163 1020

163 1530

163 2040

167 510

167 1020

167 1530

167 2040

169 510

169 1020

169 1530

169 2040

173 510

173 1020

173 1530

173 2040

179 510

179 1020

179 1530

179 2040

181 510

181 1020

181 1530

181 2040

191 510

191 1020

191 1530

191 2040

193 510

193 1020

193 1530

193 2040

197 510

197 1020

197 1530

197 2040

199 510

199 1020

199 1530

199 2040

203 510

203 1020

203 1530

203 2040

209 510

209 1020

209 1530

209 2040

211 510 211 1020

211 1530

211 2040

217 510

217 1020

217 1530

217 2040

223 510

223 1020

223 1530

223 2040

227 510

227 1020

227 1530

227 2040

229 510

229 1020

229 1530

229 2040

233 510

233 1020

233 1530

233 2040

239 510

239 1020

239 1530

239 2040

241 510

241 1020

241 1530

241 2040

247 510

247 1020

247 1530

247 2040

251 510

251 1020

251 1530

251 2040

253 510

253 1020

253 1530

253 2040

257 510

257 1020

257 1530

257 2040

259 510

259 1020

259 1530

259 2040

263 510

263 1020 263 1530

263 2040

269 510

269 1020

269 1530

269 2040

271 510

271 1020

271 1530

271 2040

277 510

277 1020

277 1530

277 2040

281 510

281 1020

281 1530

281 2040

283 510

283 1020

283 1530

283 2040

287 510

287 1020

287 1530

287 2040

293 510

293 1020

293 1530

293 2040

299 510

299 1020

299 1530

299 2040

301 510

301 1020

301 1530

301 2040

307 510

307 1020

307 1530

307 2040

311 510

311 1020

311 1530

311 2040

313 510

313 1020

313 1530

313 2040

317 510

317 1020

317 1530 317 2040

319 510

319 1020

319 1530

319 2040

329 510

329 1020

329 1530

329 2040

331 510

331 1020

331 1530

331 2040

337 510

337 1020

337 1530

337 2040

341 510

341 1020

341 1530

341 2040

343 510

343 1020

343 1530

343 2040

347 510

347 1020

347 1530

347 2040

349 510

349 1020

349 1530

349 2040

353 510

353 1020

353 1530

353 2040

359 510

359 1020

359 1530

359 2040

361 510

361 1020

361 1530

361 2040

367 510

367 1020

367 1530

367 2040

371 510

371 1020

371 1530

371 2040 373 510

373 1020

373 1530

373 2040

377 510

377 1020

377 1530

377 2040

379 510

379 1020

379 1530

379 2040

383 510

383 1020

383 1530

383 2040

389 510

389 1020

389 1530

389 2040

397 510

397 1020

397 1530

397 2040

401 510

401 1020

401 1530

401 2040

403 510

403 1020

403 1530

403 2040

407 510

407 1020

407 1530

407 2040

409 510

409 1020

409 1530

409 2040

413 510

413 1020

413 1530

413 2040

419 510

419 1020

419 1530

419 2040

421 510

421 1020

421 1530

421 2040

427 510 427 1020

427 1530

427 2040

431 510

431 1020

431 1530

431 2040

433 510

433 1020

433 1530

433 2040

437 510

437 1020

437 1530

437 2040

439 510

439 1020

439 1530

439 2040

443 510

443 1020

443 1530

443 2040

449 510

449 1020

449 1530

449 2040

451 510

451 1020

451 1530

451 2040

457 510

457 1020

457 1530

457 2040

461 510

461 1020

461 1530

461 2040

463 510

463 1020

463 1530

463 2040

467 510

467 1020

467 1530

467 2040

469 510

469 1020

469 1530

469 2040

473 510

473 1020 473 1530

473 2040

479 510

479 1020

479 1530

479 2040

481 510

481 1020

481 1530

481 2040

487 510

487 1020

487 1530

487 2040

491 510

491 1020

491 1530

491 2040

497 510

497 1020

497 1530

497 2040

499 510

499 1020

499 1530

499 2040

503 510

503 1020

503 1530

503 2040

509 510

509 1020

509 1530

509 2040

511 510

511 1020

511 1530

511 2040

517 510

517 1020

517 1530

517 2040

521 510

521 1020

521 1530

521 2040

523 510

523 1020

523 1530

523 2040

529 510

529 1020

529 1530 529 2040

533 510

533 1020

533 1530

533 2040

539 510

539 1020

539 1530

539 2040

541 510

541 1020

541 1530

541 2040

547 510

547 1020

547 1530

547 2040

551 510

551 1020

551 1530

551 2040

553 510

553 1020

553 1530

553 2040

557 510

557 1020

557 1530

557 2040

559 510

559 1020

559 1530

559 2040

563 510

563 1020

563 1530

563 2040

569 510

569 1020

569 1530

569 2040

571 510

571 1020

571 1530

571 2040

577 510

577 1020

577 1530

577 2040

581 510

581 1020

581 1530

581 2040 583 510

583 1020

583 1530

583 2040

587 510

587 1020

587 1530

587 2040

589 510

589 1020

589 1530

589 2040

593 510

593 1020

593 1530

593 2040

599 510

599 1020

599 1530

599 2040

601 510

601 1020

601 1530

601 2040

607 510

607 1020

607 1530

607 2040

611 510

611 1020

611 1530

611 2040

613 510

613 1020

613 1530

613 2040

617 510

617 1020

617 1530

617 2040

619 510

619 1020

619 1530

619 2040

623 510

623 1020

623 1530

623 2040

631 510

631 1020

631 1530

631 2040

637 510 637 1020

637 1530

637 2040

641 510

641 1020

641 1530

641 2040

643 510

643 1020

643 1530

643 2040

647 510

647 1020

647 1530

647 2040

649 510

649 1020

649 1530

649 2040

653 510

653 1020

653 1530

653 2040

659 510

659 1020

659 1530

659 2040

661 510

661 1020

661 1530

661 2040

667 510

667 1020

667 1530

667 2040

671 510

671 1020

671 1530

671 2040

673 510

673 1020

673 1530

673 2040

677 510

677 1020

677 1530

677 2040

679 510

679 1020

679 1530

679 2040

683 510

683 1020 683 1530

683 2040

689 510

689 1020

689 1530

689 2040

691 510

691 1020

691 1530

691 2040

701 510

701 1020

701 1530

701 2040

703 510

703 1020

703 1530

703 2040

707 510

707 1020

707 1530

707 2040

709 510

709 1020

709 1530

709 2040

713 510

713 1020

713 1530

713 2040

719 510

719 1020

719 1530

719 2040

721 510

721 1020

721 1530

721 2040

727 510

727 1020

727 1530

727 2040

733 510

733 1020

733 1530

733 2040

737 510

737 1020

737 1530

737 2040

739 510

739 1020

739 1530 739 2040

743 510

743 1020

743 1530

743 2040

749 510

749 1020

749 1530

749 2040

751 510

751 1020

751 1530

751 2040

757 510

757 1020

757 1530

757 2040

761 510

761 1020

761 1530

761 2040

763 510

763 1020

763 1530

763 2040

767 510

767 1020

767 1530

767 2040

769 510

769 1020

769 1530

769 2040

773 510

773 1020

773 1530

773 2040

779 510

779 1020

779 1530

779 2040

781 510

781 1020

781 1530

781 2040

787 510

787 1020

787 1530

787 2040

791 510

791 1020

791 1530

791 2040 793 510

793 1020

793 1530

793 2040

797 510

797 1020

797 1530

797 2040

803 510

803 1020

803 1530

803 2040

809 510

809 1020

809 1530

809 2040

811 510

811 1020

811 1530

811 2040

817 510

817 1020

817 1530

817 2040

821 510

821 1020

821 1530

821 2040

823 510

823 1020

823 1530

823 2040

827 510

827 1020

827 1530

827 2040

829 510

829 1020

829 1530

829 2040

839 510

839 1020

839 1530

839 2040

841 510

841 1020

841 1530

841 2040

847 510

847 1020

847 1530

847 2040

851 510 851 1020

851 1530

851 2040

853 510

853 1020

853 1530

853 2040

857 510

857 1020

857 1530

857 2040

859 510

859 1020

859 1530

859 2040

863 510

863 1020

863 1530

863 2040

869 510

869 1020

869 1530

869 2040

871 510

871 1020

871 1530

871 2040

877 510

877 1020

877 1530

877 2040

881 510

881 1020

881 1530

881 2040

883 510

883 1020

883 1530

883 2040

887 510

887 1020

887 1530

887 2040

889 510

889 1020

889 1530

889 2040

893 510

893 1020

893 1530

893 2040

899 510

899 1020 899 1530

899 2040

907 510

907 1020

907 1530

907 2040

911 510

911 1020

911 1530

911 2040

913 510

913 1020

913 1530

913 2040

917 510

917 1020

917 1530

917 2040

919 510

919 1020

919 1530

919 2040

923 510

923 1020

923 1530

923 2040

929 510

929 1020

929 1530

929 2040

931 510

931 1020

931 1530

931 2040

937 510

937 1020

937 1530

937 2040

941 510

941 1020

941 1530

941 2040

943 510

943 1020

943 1530

943 2040

947 510

947 1020

947 1530

947 2040

949 510

949 1020

949 1530 949 2040

953 510

953 1020

953 1530

953 2040

959 510

959 1020

959 1530

959 2040

961 510

961 1020

961 1530

961 2040

967 510

967 1020

967 1530

967 2040

971 510

971 1020

971 1530

971 2040

973 510

973 1020

973 1530

973 2040

977 510

977 1020

977 1530

977 2040

979 510

979 1020

979 1530

979 2040

983 510

983 1020

983 1530

983 2040

989 510

989 1020

989 1530

989 2040

991 510

991 1020

991 1530

991 2040

997 510

997 1020

997 1530

997 2040

1001 , 510

1001 , 1020

1001 , 1530

1001 , 2040 1007 510

1007 1020

1007 1530

1007 2040

1009 510

1009 1020

1009 1530

1009 2040

1013 510

1013 1020

1013 1530

1013 2040

1019 510

1019 1020

1019 1530

1019 2040

1021 510

1021 1020

1021 1530

1021 2040

1027 510

1027 1020

1027 1530

1027 2040

1031 510

1031 1020

1031 1530

1031 2040

1033 510

1033 1020

1033 1530

1033 2040

1039 510

1039 1020

1039 1530

1039 2040

1043 510

1043 1020

1043 1530

1043 2040

1049 510

1049 1020

1049 1530

1049 2040

1051 510

1051 1020

1051 1530

1051 2040

1057 510

1057 1020

1057 1530

1057 2040

1061 510 1061 1020

1061 1530

1061 2040

1063 510

1063 1020

1063 1530

1063 2040

1067 510

1067 1020

1067 1530

1067 2040

1069 510

1069 1020

1069 1530

1069 2040

1073 510

1073 1020

1073 1530

1073 2040

1079 510

1079 1020

1079 1530

1079 2040

1081 510

1081 1020

1081 1530

1081 2040

1087 510

1087 1020

1087 1530

1087 2040

1091 510

1091 1020

1091 1530

1091 2040

1093 510

1093 1020

1093 1530

1093 2040

1097 510

1097 1020

1097 1530

1097 2040

1099 510

1099 1020

1099 1530

1099 2040

1103 510

1103 1020

1103 1530

1103 2040

1109 510

1109 1020 1109 1530

1109 2040

1111 510

1111 1020

1111 1530

1111 2040

1117 510

1117 1020

1117 1530

1117 2040

1121 510

1121 1020

1121 1530

1121 2040

1123 510

1123 1020

1123 1530

1123 2040

1127 510

1127 1020

1127 1530

1127 2040

1129 510

1129 1020

1129 1530

1129 2040

1133 510

1133 1020

1133 1530

1133 2040

1141 510

1141 1020

1141 1530

1141 2040

1147 510

1147 1020

1147 1530

1147 2040

1151 510

1151 1020

1151 1530

1151 2040

1153 510

1153 1020

1153 1530

1153 2040

1157 510

1157 1020

1157 1530

1157 2040

1159 510

1159 1020

1159 1530 1159 2040

1163 510

1163 1020

1163 1530

1163 2040

1169 510

1169 1020

1169 1530

1169 2040

1171 510

1171 1020

1171 1530

1171 2040

1177 510

1177 1020

1177 1530

1177 2040

1181 510

1181 1020

1181 1530

1181 2040

1183 510

1183 1020

1183 1530

1183 2040

1187 510

1187 1020

1187 1530

1187 2040

1189 510

1189 1020

1189 1530

1189 2040

1193 510

1193 1020

1193 1530

1193 2040

1199 510

1199 1020

1199 1530

1199 2040

1201 510

1201 1020

1201 1530

1201 2040

1211 510

1211 1020

1211 1530

1211 2040

1213 510

1213 1020

1213 1530

1213 2040 1217 510

1217 1020

1217 1530

1217 2040

1219 510

1219 1020

1219 1530

1219 2040

1223 510

1223 1020

1223 1530

1223 2040

1229 510

1229 1020

1229 1530

1229 2040

1231 510

1231 1020

1231 1530

1231 2040

1237 510

1237 1020

1237 1530

1237 2040

1243 510

1243 1020

1243 1530

1243 2040

1247 510

1247 1020

1247 1530

1247 2040

1249 510

1249 1020

1249 1530

1249 2040

1253 510

1253 1020

1253 1530

1253 2040

1259 510

1259 1020

1259 1530

1259 2040

1261 510

1261 1020

1261 1530

1261 2040

1267 510

1267 1020

1267 1530

1267 2040

1271 510 1271 1020

1271 1530

1271 2040

1273 510

1273 1020

1273 1530

1273 2040

1277 510

1277 1020

1277 1530

1277 2040

1279 510

1279 1020

1279 1530

1279 2040

1283 510

1283 1020

1283 1530

1283 2040

1289 510

1289 1020

1289 1530

1289 2040

1291 510

1291 1020

1291 1530

1291 2040

1297 510

1297 1020

1297 1530

1297 2040

1301 510

1301 1020

1301 1530

1301 2040

1303 510

1303 1020

1303 1530

1303 2040

1307 510

1307 1020

1307 1530

1307 2040

1313 510

1313 1020

1313 1530

1313 2040

1319 510

1319 1020

1319 1530

1319 2040

1321 510

1321 1020 1321 1530

1321 2040

1327 510

1327 1020

1327 1530

1327 2040

1331 510

1331 1020

1331 1530

1331 2040

1333 510

1333 1020

1333 1530

1333 2040

1337 510

1337 1020

1337 1530

1337 2040

1339 510

1339 1020

1339 1530

1339 2040

1349 510

1349 1020

1349 1530

1349 2040

1351 510

1351 1020

1351 1530

1351 2040

1357 510

1357 1020

1357 1530

1357 2040

1361 510

1361 1020

1361 1530

1361 2040

1363 510

1363 1020

1363 1530

1363 2040

1367 510

1367 1020

1367 1530

1367 2040

1369 510

1369 1020

1369 1530

1369 2040

1373 510

1373 1020

1373 1530 1373 2040

1379 510

1379 1020

1379 1530

1379 2040

1381 510

1381 1020

1381 1530

1381 2040

1387 510

1387 1020

1387 1530

1387 2040

1391 510

1391 1020

1391 1530

1391 2040

1393 510

1393 1020

1393 1530

1393 2040

1397 510

1397 1020

1397 1530

1397 2040

1399 510

1399 1020

1399 1530

1399 2040

1403 510

1403 1020

1403 1530

1403 2040

1409 510

1409 1020

1409 1530

1409 2040

1417 510

1417 1020

1417 1530

1417 2040

1421 510

1421 1020

1421 1530

1421 2040

1423 510

1423 1020

1423 1530

1423 2040

1427 510

1427 1020

1427 1530

1427 2040 1429 510

1429 1020

1429 1530

1429 2040

1433 510

1433 1020

1433 1530

1433 2040

1439 510

1439 1020

1439 1530

1439 2040

1441 510

1441 1020

1441 1530

1441 2040

1447 510

1447 1020

1447 1530

1447 2040

1451 510

1451 1020

1451 1530

1451 2040

1453 510

1453 1020

1453 1530

1453 2040

1457 510

1457 1020

1457 1530

1457 2040

1459 510

1459 1020

1459 1530

1459 2040

1463 510

1463 1020

1463 1530

1463 2040

1469 510

1469 1020

1469 1530

1469 2040

1471 510

1471 1020

1471 1530

1471 2040

1477 510

1477 1020

1477 1530

1477 2040

1481 510 1481 1020

1481 1530

1481 2040

1483 510

1483 1020

1483 1530

1483 2040

1487 510

1487 1020

1487 1530

1487 2040

1489 510

1489 1020

1489 1530

1489 2040

1493 510

1493 1020

1493 1530

1493 2040

1499 510

1499 1020

1499 1530

1499 2040

1501 510

1501 1020

1501 1530

1501 2040

1507 510

1507 1020

1507 1530

1507 2040

1511 510

1511 1020

1511 1530

1511 2040

1517 510

1517 1020

1517 1530

1517 2040

1519 510

1519 1020

1519 1530

1519 2040

1523 510

1523 1020

1523 1530

1523 2040

1529 510

1529 1020

1529 1530

1529 2040

1531 510

1531 1020 1531 1530

1531 2040

1537 510

1537 1020

1537 1530

1537 2040

1541 510

1541 1020

1541 1530

1541 2040

1543 510

1543 1020

1543 1530

1543 2040

1549 510

1549 1020

1549 1530

1549 2040

1553 510

1553 1020

1553 1530

1553 2040

1559 510

1559 1020

1559 1530

1559 2040

1561 510

1561 1020

1561 1530

1561 2040

1567 510

1567 1020

1567 1530

1567 2040

1571 510

1571 1020

1571 1530

1571 2040

1573 510

1573 1020

1573 1530

1573 2040

1577 510

1577 1020

1577 1530

1577 2040

1579 510

1579 1020

1579 1530

1579 2040

1583 510

1583 1020

1583 1530 1583 2040

1589 510

1589 1020

1589 1530

1589 2040

1591 510

1591 1020

1591 1530

1591 2040

1597 510

1597 1020

1597 1530

1597 2040

1601 510

1601 1020

1601 1530

1601 2040

1603 510

1603 1020

1603 1530

1603 2040

1607 510

1607 1020

1607 1530

1607 2040

1609 510

1609 1020

1609 1530

1609 2040

1613 510

1613 1020

1613 1530

1613 2040

1619 510

1619 1020

1619 1530

1619 2040

1621 510

1621 1020

1621 1530

1621 2040

1627 510

1627 1020

1627 1530

1627 2040

1631 510

1631 1020

1631 1530

1631 2040

1633 510

1633 1020

1633 1530

1633 2040 1637 510

1637 1020

1637 1530

1637 2040

1639 510

1639 1020

1639 1530

1639 2040

1643 510

1643 1020

1643 1530

1643 2040

1651 510

1651 1020

1651 1530

1651 2040

1657 510

1657 1020

1657 1530

1657 2040

1661 510

1661 1020

1661 1530

1661 2040

1663 510

1663 1020

1663 1530

1663 2040

1667 510

1667 1020

1667 1530

1667 2040

1669 510

1669 1020

1669 1530

1669 2040

1673 510

1673 1020

1673 1530

1673 2040

1679 510

1679 1020

1679 1530

1679 2040

1681 510

1681 1020

1681 1530

1681 2040

1687 510

1687 1020

1687 1530

1687 2040

1691 510 1691 1020

1691 1530

1691 2040

1693 510

1693 1020

1693 1530

1693 2040

1697 510

1697 1020

1697 1530

1697 2040

1699 510

1699 1020

1699 1530

1699 2040

1703 510

1703 1020

1703 1530

1703 2040

1709 510

1709 1020

1709 1530

1709 2040

1711 510

1711 1020

1711 1530

1711 2040

1721 510

1721 1020

1721 1530

1721 2040

1723 510

1723 1020

1723 1530

1723 2040

1727 510

1727 1020

1727 1530

1727 2040

1729 510

1729 1020

1729 1530

1729 2040

1733 510

1733 1020

1733 1530

1733 2040

1739 510

1739 1020

1739 1530

1739 2040

1741 510

1741 1020 1741 1530

1741 2040

1747 510

1747 1020

1747 1530

1747 2040

1753 510

1753 1020

1753 1530

1753 2040

1757 510

1757 1020

1757 1530

1757 2040

1759 510

1759 1020

1759 1530

1759 2040

1763 510

1763 1020

1763 1530

1763 2040

1769 510

1769 1020

1769 1530

1769 2040

1771 510

1771 1020

1771 1530

1771 2040

1777 510

1777 1020

1777 1530

1777 2040

1781 510

1781 1020

1781 1530

1781 2040

1783 510

1783 1020

1783 1530

1783 2040

1787 510

1787 1020

1787 1530

1787 2040

1789 510

1789 1020

1789 1530

1789 2040

1793 510

1793 1020

1793 1530 1793 2040

1799 510

1799 1020

1799 1530

1799 2040

1801 510

1801 1020

1801 1530

1801 2040

1807 510

1807 1020

1807 1530

1807 2040

1811 510

1811 1020

1811 1530

1811 2040

1813 510

1813 1020

1813 1530

1813 2040

1817 510

1817 1020

1817 1530

1817 2040

1823 510

1823 1020

1823 1530

1823 2040

1829 510

1829 1020

1829 1530

1829 2040

1831 510

1831 1020

1831 1530

1831 2040

1837 510

1837 1020

1837 1530

1837 2040

1841 510

1841 1020

1841 1530

1841 2040

1843 510

1843 1020

1843 1530

1843 2040

1847 510

1847 1020

1847 1530

1847 2040 1849 510

1849 1020

1849 1530

1849 2040

1859 510

1859 1020

1859 1530

1859 2040

1861 510

1861 1020

1861 1530

1861 2040

1867 510

1867 1020

1867 1530

1867 2040

1871 510

1871 1020

1871 1530

1871 2040

1873 510

1873 1020

1873 1530

1873 2040

1877 510

1877 1020

1877 1530

1877 2040

1879 510

1879 1020

1879 1530

1879 2040

1883 510

1883 1020

1883 1530

1883 2040

1889 510

1889 1020

1889 1530

1889 2040

1891 510

1891 1020

1891 1530

1891 2040

1897 510

1897 1020

1897 1530

1897 2040

1901 510

1901 1020

1901 1530

1901 2040

1903 510 1903 1020

1903 1530

1903 2040

1907 510

1907 1020

1907 1530

1907 2040

1909 510

1909 1020

1909 1530

1909 2040

1913 510

1913 1020

1913 1530

1913 2040

1919 510

1919 1020

1919 1530

1919 2040

1927 510

1927 1020

1927 1530

1927 2040

1931 510

1931 1020

1931 1530

1931 2040

1933 510

1933 1020

1933 1530

1933 2040

1937 510

1937 1020

1937 1530

1937 2040

1939 510

1939 1020

1939 1530

1939 2040

1943 510

1943 1020

1943 1530

1943 2040

1949 510

1949 1020

1949 1530

1949 2040

1951 510

1951 1020

1951 1530

1951 2040

1957 510

1957 1020 1957 1530

1957 2040

1961 510

1961 1020

1961 1530

1961 2040

1963 510

1963 1020

1963 1530

1963 2040

1967 510

1967 1020

1967 1530

1967 2040

1969 510

1969 1020

1969 1530

1969 2040

1973 510

1973 1020

1973 1530

1973 2040

1979 510

1979 1020

1979 1530

1979 2040

1981 510

1981 1020

1981 1530

1981 2040

1987 510

1987 1020

1987 1530

1987 2040

1991 510

1991 1020

1991 1530

1991 2040

1993 510

1993 1020

1993 1530

1993 2040

1997 510

1997 1020

1997 1530

1997 2040

1999 510

1999 1020

1999 1530

1999 2040 Non-Limiting Software and Hardware Examples

Various exemplary embodiments of the invention as described above can be

implemented as one or more program products, software applications and the like, for use with a computer system, both as to transmission from preparation and as to receiver operations and processes. The terms program, software application, and the like, as used herein, are defined as a sequence of instructions designed for execution on a computer system or data processor. A program, computer program, or software application may include a subroutine, a function, a procedure, an object method, an object implementation, an executable application, an applet, a servlet, a source code, an object code, a shared library/dynamic load library and/or other sequence of instructions designed for execution on a computer system.

The program(s) of the program product or software may define functions of the embodiments (including the methods described herein) and can be contained on a variety of computer readable media. Illustrative computer readable media include, but are not limited to: (i) information permanently stored on non-writable storage medium (e.g., read-only memory devices within a computer such as CD-ROM disk readable by a CD-ROM drive); (ii) alterable information stored on writable storage medium (e.g., floppy disks within a diskette drive or hard-disk drive); or (iii) information conveyed to a computer by a communications medium, such as through a computer or telephone network, including wireless communications. The latter embodiment specifically includes information downloaded from the Internet and other networks. Such computer readable media, when carrying computer-readable instructions that direct the functions of the present invention, represent embodiments of the present invention.

In general, the routines executed to implement the embodiments of the present invention, whether implemented as part of an operating system or a specific application, component, program, module, object or sequence of instructions may be referred to herein as a "program." A computer program typically is comprised of a multitude of instructions that will be translated by the native computer into a machine-readable format and hence executable instructions. Also, programs are comprised of variables and data structures that either reside locally to the program or are found in memory or on storage devices. In addition, various programs described herein may be identified based upon the application for which they are implemented in a specific embodiment of the invention. However, it should be appreciated that any particular program nomenclature that follows is used merely for convenience, and thus the invention should not be limited to use solely in any specific application identified and/or implied by such nomenclature.

It is also clear that given the typically endless number of manners in which computer programs may be organized into routines, procedures, methods, modules, objects, and the like, as well as the various manners in which program functionality may be allocated among various software layers that are resident within a typical computer (e.g., operating systems, libraries, API's, applications, applets, etc.) It should be appreciated that the invention is not limited to the specific organization and allocation or program functionality described herein.

The present invention may be realized in hardware, software, or a combination of hardware and software. A system according to a preferred embodiment of the present invention can be realized in a centralized fashion in one computer system on the transmit side, and one receiver on the receive side, or in a distributed fashion where different elements are spread across several interconnected computer systems, including cloud connected computing systems and devices. Any kind of computer system— or other apparatus adapted for carrying out the methods described herein— is suited. A typical combination of hardware and software could be a general purpose computer system with a computer program that, when being loaded and executed, controls the computer system such that it carries out the methods described herein.

Each computer system may include, inter alia, one or more computers and at least a signal bearing medium allowing a computer to read data, instructions, messages or message packets, and other signal bearing information from the signal bearing medium. The signal bearing medium may include non-volatile memory, such as ROM, Flash memory, Disk drive memory, CD-ROM, and other permanent storage. Additionally, a computer medium may include, for example, volatile storage such as RAM, buffers, cache memory, and network circuits. Furthermore, the signal bearing medium may comprise signal bearing information in a transitory state medium such as a network link and/or a network interface, including a wired network or a wireless network, that allow a computer to read such signal bearing information. Although specific embodiments of the invention have been disclosed, those having ordinary skill in the art will understand that changes can be made to the specific embodiments without departing from the spirit and scope of the invention. The scope of the invention is not to be restricted, therefore, to the specific embodiments. The above-presented description and figures are intended by way of example only and are not intended to limit the present invention in any way except as set forth in the following claims. For example, while this disclosure speaks in terms of enhancing the bandwidth efficiency of satellite radio broadcasts, its techniques and systems are applicable to any type of communications system, transmitting, broadcasting or exchanging audio, video or other data content. It is particularly noted that persons skilled in the art can readily combine the various technical aspects of the various elements of the various exemplary embodiments that have been described above in numerous other ways, all of which are considered to be within the scope of the invention.

It will thus be seen that the objects made apparent from the preceding description are efficiently attained, and since certain changes may be made without departing from the spirit and scope of the invention, it is intended that all matter contained in the above description shall be interpreted as illustrative and not in a limiting sense.

Claims

WHAT IS CLAIMED:

1. A computerized method of generating and testing Q.PP parameter sets for large code block sizes, comprising:

generating a set of possible Q.PP parameter pairs {fl,f2} for a given block size N greater than 10,000 bits;

first testing the bit error performance of each pair of the set at a given SNR;

eliminating any Q.PP parameter pair that does not meet a defined performance threshold;

subsequently testing the remaining Q.PP pairs by changing at least one of (i) number of bits decoded error free , (ii) SNR, or (iii) bit error rate, to find an optimal pair or pairs; and

outputting one or more optimal pair or pairs of Q.PP parameters to a user.

2. The method of claim 1, wherein the defined SNR for the first test is an Eb/No ratio between 0.2 and 0.8, inclusive.

3. The method of claim 1, wherein the defined SNR for the first test is an Eb/No ratio between 0.3 and 0.5, inclusive.

4. The method of claim 1, wherein the defined performance threshold for the first test is at least one of:

a maximal BER, or a minimum number of bits successfully decoded at a defined BER.

5. The method of claim 1, wherein for the subsequent test the defined SNR is 0.3 Eb/No and the defined performance threshold is a maximal BER of 10^"4'

6. The method of claim 1, wherein for the subsequent test the defined SNR is 0.4 Eb/No and the defined performance threshold is a maximal BER of 10^"6'

7. The method of claim 1, wherein for the subsequent test either (i) the SNR is lowered and the bit error rate raised, (ii) the SNR lowered and the bit error rate maintained the same, (iii) the SNR maintained the same and the bit error rate lowered, or (iv) the SNR lowered and the number of bits to be decoded error free is raised .

8. The method of claim 1, further comprising testing over a range of possible block sizes, each possible bock size tested as the given block size.

9. The method of claim 1, wherein said subsequently testing includes incrementally increasing/decreasing the Eb/No and decreasing/increasing the number of bits being decoded one or more times.

10. The method of claim 9, wherein the last parameter pair to meet the BER threshold is chosen as a winner of the subsequent testing.

11. A computerized method of generating and testing Q.PP parameter sets for a given code block size, comprising:

generating a set of possible Q.PP parameter pairs for a given block size;

separating the set into I subsets;

first testing in parallel the performance of each subset of pairs at a given SNR;

eliminating any Q.PP parameter pair from each subset that does not meet a defined performance threshold;

subsequently testing the remaining Q.PP pairs from each subset by at least one of decoding larger numbers of bits and decoding a signal of a lower SNR ratio to find an optimal pair or pairs to obtain an optimal Q.PP pair for that subset;

testing the optimal pair from each subset by some combination of decoding larger numbers of bits and decoding a signal of a lower SNR ratio to find an optimal pair or pairs for the set; and

outputting one or more optimal pair or pairs of Q.PP parameters to a user.

12. The method of claim 11, wherein each subset of Q.PP pairs is first tested on a separate data processing device.

13. The method of claim 12, wherein the remaining Q.PP pairs from each subset are also tested in parallel on separate data processing devices.

14. The method of claim 12, wherein the optimal pairs from each subset are tested on one data processing device in a head to head comparison.

15. A system, comprising:

at least one processor;

a display; and

memory containing instructions that, when executed, cause the at least one processor to: generate a set of possible Q.PP parameter pairs {fl,f2} for a given block size N greater than 10,000 bits;

first test the bit error performance of each pair of the set at a given SNR;

eliminate any Q.PP parameter pair that does not meet a defined performance threshold; subsequently test the remaining Q.PP pairs by changing at least one of (i) number of bits decoded error free , (ii) SNR, or (iii) bit error rate, to find an optimal pair or pairs; and outputting one or more optimal pair or pairs of Q.PP parameters.

16. The system of claim 15, wherein the defined SNR for the first test is an Eb/No ratio between 0.2 and 0.8, inclusive.

17. The system of claim 15, wherein the defined SNR for the first test is an Eb/No ratio between 0.3 and 0.5, inclusive.

18. The system of claim 15, wherein the defined performance threshold for the first test is at least one of:

a maximal BER, or a minimum number of bits successfully decoded at a defined BER.

19. The system of claim 15, wherein for the subsequent test the defined SNR is 0.3 Eb/No and the defined performance threshold is a maximal BER of 10^"4'

20. The system of claim 15, wherein for the subsequent test the defined SNR is 0.4 Eb/No and the defined performance threshold is a maximal BER of 10^"6'

21. The system of claim 15, wherein for the subsequent test either (i) the SNR is lowered and the bit error rate raised, (ii) the SNR lowered and the bit error rate maintained the same, (iii) the SNR maintained the same and the bit error rate lowered, or (iv) the SNR lowered and the number of bits to be decoded error free is raised .

22. The system of claim 15, wherein the instructions further cause the at least one processor to test over a range of possible block sizes, each possible bock size tested as the given block size.

23. The system of claim 15, wherein said subsequently test includes incrementally increasing/decreasing the Eb/No and decreasing/increasing the number of bits being decoded one or more times.

24. The system of claims 19-23, wherein the last parameter pair to meet a then prevailing BER threshold is chosen as a winner of the subsequent testing.

25. The system of claim 22 where the range of possible block sizes are divided into one or more layers of subsets and tested in parallel.

26. The system of claim 15, wherein the optimal pair is a parameter set {fl,f2} = {217,1560} for a block size of N=12,168 bits, and a parameter set {fl,f2} = {299, 510} for a block size of N=12,240 bits.

27. The method of claim 1, wherein the optimal pair is a parameter set {fl,f2} = {217,1560} for a block size of N=12,168 bits, and a parameter set {fl,f2} = {299, 510} for a block size of N=12,240 bits.