Publication number | USRE43212 E1 |
Publication type | Grant |
Application number | US 10/973,100 |
Publication date | Feb 21, 2012 |
Filing date | Oct 25, 2004 |
Priority date | May 19, 1999 |
Fee status | Paid |
Also published as | CA2337918A1, CA2337918C, CN1171393C, CN1271795C, CN1271796C, CN1274096C, CN1318225A, CN1497866A, CN1520044A, CN1520058A, CN1520059A, CN1520060A, CN100442679C, CN100574116C, DE20023169U1, DE60032441D1, DE60032441T2, EP1097516A1, EP1097516A4, EP1097516B1, EP1367726A1, EP1367726B1, EP1367728A1, EP1367729A1, EP1367730A1, EP1367731A1, US6598202, WO2000070771A1 |
Publication number | 10973100, 973100, US RE43212 E1, US RE43212E1, US-E1-RE43212, USRE43212 E1, USRE43212E1 |
Inventors | Min-goo Kim, Beong-Jo Kim, Soon-Jae Choi, Young-Hwan Lee |
Original Assignee | Samsung Electronics Co., Ltd |
Export Citation | BiBTeX, EndNote, RefMan |
Patent Citations (23), Non-Patent Citations (44), Referenced by (1), Classifications (21), Legal Events (1) | |
External Links: USPTO, USPTO Assignment, Espacenet | |
This application claims priority to an application entitled “Turbo Interleaving Apparatus and Method” filed in the Korean Industrial Property Office on May 19, 1999 and assigned Serial No. 99-18928 and an application filed in the Korean Industrial Property Office on May 21, 1999 and assigned Serial No. 99-18560, the contents of which are hereby incorporated by reference.
1. Field of the Invention
The present invention relates generally to a turbo encoder used for radio communication systems (including satellite, ISDN, digital cellular, W-CDMA, and IMT-2000 systems), and in particular, to an internal interleaver of a turbo encoder.
2. Description of the Related Art
In general, an interleaver used for a turbo encoder randomizes an address of input information word and improves a distance property of a codeword. In particular, it has been decided that a turbo code will be used in a supplemental channel (or data transmission channel) of IMT-2000 (or CDMA-2000) and IS-95C air interfaces and in a data channel of UMTS (Universal Mobile Telecommunication System) proposed by ETSI (European Telecommunication Standards Institute). Thus, a method for embodying an interleaver for this purpose is required. In addition, the invention relates to an error correction code which greatly affects performance improvement of the existing and future digital communication systems.
For an existing internal interleaver for a turbo encoder (hereinafter, referred to as a turbo interleaver), there have been proposed various interleavers such as PN (Pseudo Noise) random interleaver, random interleaver, block interleaver, non-linear interleaver, and S-random interleaver. However, so far, such interleavers are mere algorithms designed to improve their performances in terms of scientific researches rather than implementation. Therefore, when implementing an actual system, the hardware implementation complexity must be taken into consideration. A description will now be made of properties and problems associated with the conventional interleaver for the turbo encoder.
Performance of the turbo encoder is dependent upon its internal interleaver. In general, an increase in the input frame size (i.e., the number of information bits included in one frame) enhances the effectiveness of the turbo encoder. However, an increase in interleaver size causes a geometric increase in calculations. Therefore, in general, it is not possible to implement the interleaver for the large frame size.
Therefore, in general, the interleavers are implemented by determining conditions satisfying several given criteria. The criteria are as follows:
Although the above criteria are applicable to a general turbo interleaver, it is difficult to clearly analyze the properties when the interleaver increases in size.
In addition, another problem occurring when designing the turbo interleaver is that the minimum free distance of the turbo code varies according to the type of the input codeword. That is, when the input information word has a specific sequence pattern defined as a critical information sequence pattern (CISP), the free distance of the output code symbols generated from the turbo encoder has a very small value. If the input information word has a Hamming weight 2, the CISP occurs when the input information word has two information bits of ‘1’ and can also occur when the input information word has 3 or more information bits of ‘1’. However, in most cases, when the input information word has 2 information bits of ‘1’, the minimum free distance is formed and most error events occur in this condition. Therefore, when designing the turbo interleaver, an analysis is generally made on the case where the input information word has the Hamming weight 2. A reason that the CISP exists is because the turbo encoder generally uses RSC (Recursive Systematic Convolutional Codes) encoders for the component encoders shown in
In this case (in the prior art of turbo interleaver), to increase the free distance, the turbo interleaver randomly disperses the CISP input information word so as to prevent a decrease in the free distance at the output symbol of the other component RSC encoder.
The above-stated properties are fundamental features of the known turbo interleaver. However, for the CISP, it is conventional that the information word has the minimum Hamming weight, when the input information word has the Hamming weight 2. In other words, the fact that the CISP can be generated even when the input information word has the Hamming weight 1 (i.e., when the input information word has one information bit of ‘1’) was overlooked, when the information word input to the turbo encoder had the type of a block comprised of frames.
For example, a prime interleaver (PIL) designated as the working model of the turbo code interleaver specified by the present UMTS standard exhibits such problems, thus having a degraded free distance property. That is, the implementation algorithm of the model PIL turbo interleaver include 3 stages, of which the second stage, which plays the most important role, performs random permutation on the information bits of the respective groups. The second stage is divided into three cases of Case A, Case B and Case C, and the Case B always involves the case where the free distance is decreased due to the event where the input information word has the Hamming weight 1. In addition, even the Case C involves a possibility that such an event will occur. The detailed problems will be described later with reference to the PIL.
In conclusion, when various interleaver sizes are required and the hardware implementation complexity is limited in the IMT-2000 or UMTS system, the turbo interleaver should be designed to guarantee the optimal interleaver performance by taking the limitations into consideration. That is, the required interleaver should be able to guarantee uniform performance for the various interleaver sizes, while satisfying the above-stated properties. More recently, there have been proposed several types of the interleavers for a PCCC (Parallel Concatenated Convolutional Codes) turbo interleaver, and a LCS (Linear Congruential Sequence) turbo interleaver has been provisionally decided as the turbo interleaver in the IMT-2000 (or CDMA-2000) and IS-95C specifications. However, most of these turbo interleavers have the problems of the CSIP with Hamming weight 1, and the details of implementing these turbo interleavers are still not defined. Therefore, the present invention proposes a solution of the turbo interleaver's problems, and a new method for implementing the turbo interleaver. In addition, the invention shows the PIL interleaver which is a working assumption of the UMTS turbo interleaver, and proposes a solution of this interleaver's problem.
To sum up, the prior art has the following disadvantages.
It is, therefore, an object of the present invention to provide an interleaving device and method for analyzing properties of a turbo interleaver and a property of a critical information sequence pattern (CISP) to improve performance of the turbo interleaver.
It is another object of the present invention to provide an interleaving device and method for improving free distance performance of a turbo code for the case where an input information word has a Hamming weight 1 when the information word input to a turbo interleaver has a block type comprised of frames.
It is a further object of the present invention to provide an interleaving device and method for solving the problem that the free distance is decreased when an input information word has a Hamming weight 1 in a prime interleaver (PIL) that is the turbo interleaver specified in the UMTS specification.
To achieve the above objects, there is provided a 2-dimensional interleaving method comprising dividing a frame of input information bits into a plurality of groups and sequentially storing the divided groups in a memory; permuting the information bits of the groups according to a given rule and shifting an information bit existing at the last position of the last group to a position preceding the last position; and selecting the groups according to a predetermined order, and selecting one of the information bits in the selected group.
The above and other objects, features and advantages of the present invention will become more apparent from the following detailed description when taken in conjunction with the accompanying drawings in which:
A preferred embodiment of the present invention will be described herein below with reference to the accompanying drawings. In the following description, well-known functions or constructions are not described in detail since they would obscure the invention in unnecessary detail.
Prior to describing the invention, the specification will present the problems occurring when an input information word, which is one of the design criteria used in the existing turbo interleaver/deinterleaver, is processed on a frame unit basis, and then analyze an affect that the CISP with a Hamming weight 1 has on the Hamming weight of the output code symbols. Next, the specification will propose a method for solving the problems and verify the performance difference through analysis of the minimum free distance.
Referring to
Referring to
Referring to
In general, since the turbo code is a linear block code, a new information word obtained by adding a non-zero information word to an input information word has the same codeword distribution property. Therefore, even though the property is developed based on the all-zero information word, the same performance will be given as compared with the performance determined using the non-zero information word. Thus, a description below will be made with reference to the case where the input information word is the all-zero codeword. That is, performance of the turbo code will be analyzed on the assumption that the input information word has all zero bits and only a given information bit is ‘1’.
To improve performance of the turbo encoder, a primitive polynomial may be used for a feedback polynomial out of a generator polynomial for the component encoder. The feedback polynomial is given by expressing tapping which undergoes feedback in the RSC component encoders 111, 113 of
In this case, to increase the free distance, the turbo interleaver randomly disperses the CISP input information word so as to prevent a decrease in the free distance at the output symbol of the other component RSC encoder. Table 1 below shows a feedback sequence generated from gf(x)=1+x^{2}+x^{3}. In Table 1, X(t) indicates an input information bit at a time t of the input information word. Further, m(t), m(t−1) and m(t−2) indicate 3 memory states of the RSC encoder, respectively. Here, since the number of memories is 3, the period is 2^{3}−1=7.
TABLE 1 | ||||||
m(t) | m(t − 1) | m(t − 2) | ||||
1 | 0 | 0 | t = 0 | X(0) = 1 | ||
0 | 1 | 0 | t = 1 | X(1) = 0 | ||
1 | 0 | 1 | t = 2 | X(2) = 0 | ||
1 | 1 | 0 | t = 3 | X(3) = 0 | ||
1 | 1 | 1 | t = 4 | X(4) = 0 | ||
0 | 1 | 1 | t = 5 | X(5) = 0 | ||
0 | 0 | 1 | t = 6 | X(6) = 0 | ||
1 | 0 | 0 | t = 7 | if X(7) = 1 | ||
0 | 0 | 0 | t = 8 | |||
0 | 0 | 0 | t = 9 | |||
. . . | ||||||
. . . | ||||||
From Table 1, it is noted that if X(t)=1 at time t=7, then m(t), m(t−1) and m(t−2) become all zero states henceforth. Therefore, the Hamming weight of the following output symbols becomes always zero. In this case, if the turbo interleaver provides the RSC2 with the input information sequence ‘10000001000 . . . ’ as it is, the Hamming weight of the output symbols at the following time of t=7 will not change thereafter even in the RSC2 using the same feedback polynomial, for the same reason. This causes a decrease in the free distance of the whole output symbols of the turbo encoder. To prevent this, the turbo interleaver changes the original input information sequence ‘10000001000 . . . ’ to an input information sequence of a different pattern (for example, changes a position of the information bit ‘1’ such as 110000000 . . . ) and provides the resulting sequence to the RSC2. Therefore, even though an increase in the Hamming weight is stopped in the RSC1, the Hamming weight continuously increases in the RSC2, so that the total free distance of the turbo encoder increases. This is because the feedback polynomial, having the infinite impulse response (IIR) filter type, continuously IN generates the infinite output symbol ‘1’ even for one input information bit ‘1’. Equation 1 below shows the relationship between the RSC1 and the RSC2 in terms of the Hamming weight or free distance of the turbo encoder.
HW(Output code sequence)=HW(RSC1 code sequence)+HW(RSC2 code sequence) [Equation 1]
where HW is the Hamming weight.
From Equation 1, it is noted that a Hamming weight balance between RSC1 and RSC2 is very important. In particular, it is noted that the minimum free distance of the turbo code is generated for the minimum Hamming weight of the input information word, when the IIR (Infinite Impulse Response) characteristic of the RSC encoder is taken into consideration. In general, the minimum free distance is provided when the input information word has the Hamming weight 2, as mentioned above.
However, as described above, the minimum free distance occurs when the input information word has the Hamming weight 3, 4, 5 . . . , as well as when the input information word has the Hamming weight 2. This occurs when the input information word is received on a frame unit basis, as follows.
For example, when only the information bit located at the last position of the input information word, i.e., the last position of the frame, is ‘1’ and all the other information bits are 0's, the Hamming weight of the input information word becomes 1. In this case, the number of the symbols ‘1’ output from the RSC1 becomes very small, because there is no more input information word. Of course, when zero-tail bits are used, there exist two symbols but those are independently used rather than undergoing turbo interleaving. Therefore, it is assumed herein that the weight is slightly increased. Since the constant weight is added, this will be so excluded from an analysis of the interleaver. In this case, it is noted from Equation 1 that the RSC2 should generate a great number of the output symbols ‘1’ to increase the total free distance.
Now, with reference to
In
If, as shown in
In addition to the decreased free distance occurring when the internal interleaver shifts the input information bit ‘1’ located at the last position of the frame to the last position of the frame as show in
For example, if the internal interleaver operations in the frame mode shown in
This principle can be expanded to the case where the turbo interleaver operates in the frame mode shown in
In conclusion, when designing the turbo interleaver, the following conditions as well as the random property and the distance property should be satisfied to guarantee performance of the turbo decoder and the free distance of the turbo encoder.
These conditions are applicable to a 2-dimensional turbo interleaver as well as the above-described 1-dimensional interleaver. The 1-dimensional interleaver performs interleaving, regarding the input information frame as a group, as shown in
As illustrated, the input information bits are sequentially written in the respective groups (or rows). That is, the input information bits are sequentially written in the groups (or rows) r0, r1, . . . , r(R−1). In each group, the input information bits are sequentially written from the left to the right. Thereafter, a turbo interleaving algorithm randomly changes the positions of R×C elements (i.e., input information bits), where R is the number of rows, C is the number of columns or, equivalently, the number of information bits in a group. In this case, it is preferable to design the turbo interleaving algorithm such that the information bit located at the last position (or the rightmost position) of the last group should be located at the foremost position, if possible, during output. Of course, depending on the order of selecting the groups, the input information bit located at the last position may be shifted to the foremost position (or close thereto) of the corresponding group. Further, Condition 1 and Condition 2 can be normalized in a k-dimensional turbo interleaver (where k>2) as well as the 2-dimensional interleaver.
Next, a description will be made of the PIL interleaver having the problems of the prior art document TS25.212 V1.0.0 (1999-2000), and then a further description will be made of a solution of the problems that the PIL interleaver has.
First stage, (1) determine a row number such that R=10 at the case of when the number of input information bit K is 481 to 530 (i.e., case (1)) and R=20 at the case of when the number of input information bit K is any other block length except 481 to 530 (i.e., case (2)), (2) determine a column number C such that in case 1 is (1), C=p=53 where, p=minimum prime number, and in case 2 is (2),
A second stage, Case-B, if C=p+1 out of an interleaving algorithm for the PIL interleaver which was provisionally determined as the UMTS turbo interleaver will be first described. In Equation 2 below, R indicates the number of groups (or rows), and has a value of R=10 or R=20. Further, C indicates the size of each group and is determined by a the minimum prime number p which is closest to R/K satisfying 0=<(p+1)−K/R determined in Stage 1 according to a value K/R where K is the size of the actual input information bits of a frame. In Case-B, it is always that C=p+1. Therefore, the actual size of the PIL interleaver becomes a value determined by R×C, which is larger than C K. Further, Cj(i) indicates a position of the information bits obtained by randomly permuting the position of the input information bits in the group on the basis of an ith group, where i=0,1,2,3, . . . , p. In addition, Pj indicates an initial seed value given for an a jth row vector, and is initially given by the algorithm.
[Equation 2]
A third stage, Perform the row-permutation based on the following p_{(j) }(j=0,1,2 . . . , R−1) patterns, where p_{(j) }is the original row position of the j-th permuted row. The usage of these patterns is as follows; when the number of input information bit K is 320 to 480 bit perform group selection pattern p_{A}, when the number of input information bit K is 481 to 530 bit perform group selection pattern p_{c}, when the number of input information bit K is 531 to 2280 bit perform group selection pattern p_{A}, when the number of input information bit K is 2281 to 2480 bit perform group selection pattern p_{B}, when the number of input information bit K is 2481 to 3160 bit perform group selection pattern p_{A}, when the number of input information bit K is 3161 to 3210 bit perform group selection pattern p_{B}, and when the number of input information bit K is 3211 to 5114 bit perform group selection pattern p_{A}. The group selection pattern is as follow;
It should be noted herein that the last operation of B-5) is defined as C_{j}(p)=p. That is, this means that when the position of the input information bit before interleaving is p, the position of the input information bit is maintained at the position p even after PIL interleaving. Therefore, for the last group (j=19), the information bits C_{R-1}(P)=C_{19}(p) existing at the last position maintain the same position i=P which is the last position of the 19th group. Therefore, Condition 2 for designing the turbo interleaver is not satisfied.
That is, to solve the problem that the PIL interleaver has, algorithm step B-5) may be modified by performing an additional step after step B-5 as follows. The invention presents six methods of B-5-1) to B-5-6), by way of example. Among these, an optimal performance can be determined through simulations in the light of the properties of the turbo interleaver.
One of the following 6 methods are selected.
Referring to
C(i)=[g0×C(i−1)]mod p, i=1,2,3, . . . ,p−2, C(0)=1
Thereafter, in step 1015, a minimum prime number set {q_{j}, j=0,1,2, . . . , R−1} given for the algorithm is calculated. Then, in step 1017, a prime number set {p_{j}=0,1,2, . . . , R−1} is calculated from the calculated minimum prime number set. Next, in step 1019, the elements of an jth group are randomized in the following method.
C_{j}(i)=c([i×p_{j}]mod(p−1), i=0,1,2,3, . . . , p−2,
C_{j}(p−1)=0
Here, in order to increase the minimum free distance of the turbo encoder while randomizing the elements of the group, one of B-5-1) to B-5-6) is selected to permute (or shift) the information bits existing at the last position of the frame to other positions after interleaving.
B-5-1) means that the positions of the first information bit and the last information bit in the last group are exchanged with each other. B-5-2) means that the last two information bits in the last group are exchanged with each other. B-5-3) means that for every group, the information bit existing at the last position and the information bit existing at the foremost position are exchanged with each other. B-5-4) means that for every group, the positions of the last two information bits are exchanged. B-5-5) means that for every group, an optimal position k for a given interleaving rule is searched to exchange a position of the information bit existing at the last position of each row with a position of the information bit existing at the position k. Finally, B-5-6) means that for the last group, an optimal position k for a given interleaving rule is searched to exchange a position of the information bit existing at the last position with a position of the information bit existing at the position k.
By applying the modified algorithm to the PIL interleaver, it is possible to prevent a decrease in the free distance of the turbo encoder. Table 2 below shows a weight spectrum of the PIL interleaver before modification, and Table 3 below shows a weight spectrum of the PIL interleaver after modification.
In Tables 2 and 3, K indicates the size of the input information frame, Dfree(1) indicates a free distance calculated with the CISP for which the input information word has the Hamming weight 1, and Dfree(2) indicates a free distance calculated with the CISP for which the input information word has the Hamming weigh 2. For example, for K=600, Dfree(1) of the original PIL interleaver is indicated by 25/39/49/53/57/ . . . in Table 2, and this means that the minimum free distance is 25 and the next minimum free distance is 39. Similarly, Dfree(2)=38/38/42/ . . . means that the minimum free distance is 38. Therefore, it is noted that the minimum free distance is determined according to the free distance by the CISP with the Hamming weight 1. To prevent a decrease in the free distance by the CISP with the Hamming weight 1, the invention uses the B-5-1) method in this example. That is, Dfree(1) is improved by removing the CISP with the Hamming 1.
Table 2 below shows a weight spectrum of the PIL interleaver before modification.
TABLE 2 | ||
K | Dfree(1) | Dfree(2) |
600 | Pos. = 599, Min. Weight = 25 | Pos. = 29, min_pl = 36, Min. Weight = 38 |
25/39/49/53/57/61/65/67/67/77/ | 38/38/42/42/42/42/42/42/42/42/ | |
640 | Pos. = 630, Min. Weight = 25 | Pos. = 440, min_pl = 447, Min. Weight = 40 |
25/37/53/53/53/69/71/73/75/77/ | 40/40/42/42/44/44/46/46/46/48/ | |
760 | Pos. = 759, Min. Weight = 25 | Pos. = 33, min_{ }pl = 40, Min. Weight = 38 |
25/41/57/57/59/69/75/77/81/83/ | 38/38/38/42/42/42/42/44/44/50/ | |
840 | Pos. = 839, Min. Weight = 25 | Pos. = 461, min_{ }pl = 468, Min. Weight = 36 |
25/45/57/65/65/79/79/83/85/87/ | 36/38/40/42/42/42/44/46/46/46/ | |
880 | Pos. = 879, Min. Weight = 25 | Pos. = 294, min_{ }pl = 308, Min. Weight = 40 |
25/47/57/61/65/71/83/89/93/93/ | 40/44/46/46/46/48/54/56/56/58/ | |
960 | Pos. = 959, Min. Weight = 25 | Pos. = 568, min_{ }pl = 575, Min. Weight = 36 |
25/45/61/65/69/71/73/87/87/89/ | 36/38/38/42/42/42/42/44/44/46/ | |
1080 | Pos. = 1079, Min. Weight = 25 | Pos. = 1016, min_{ }pl = 1030, Min. Weight = 42 |
25/49/61/65/67/77/85/89/93/97/ | 42/42/46/48/48/50/52/52/54/54/ | |
1200 | Pos. = 1199, Min. Weight = 25 | Pos. = 953, min_{ }pl = 967, Min. Weight = 38 |
25/53/65/69/85/85/89/89/95/103/ | 38/38/42/42/42/42/46/48/50/50/ | |
1240 | Pos. = 1239, Min. Weight = 25 | Pos. = 1053, min_{ }pl = 1060, Min. Weight = 38 |
25/53/67/69/71/85/93/93/103/105/ | 38/38/40/40/42/42/46/46/46/48/ | |
1360 | Pos. = 1359, Min. Weight = 25 | Pos. = 64, min_{ }pl = 71, Min. Weight = 38 |
25/57/65/73/85/91/93/105/107/107/ | 38/42/42/42/42/44/46/46/46/50/ | |
1440 | Pos. = 1439, Min. Weight = 25 | Pos. = 497, min_{ }pl = 504, Min. Weight = 36 |
25/53/63173/77/87/89/97/105/109/ | 36/42/42/46/46/50/50/52/54/58/ | |
1480 | Pos. = 1479, Min. Weight = 25 | Pos. = 1103, min_{ }pl = 1110, Min. Weight = 42 |
25/61/65/77/77/83/95/101/109/117/ | 42/42/44/48/50/50/50/50/54/54/ | |
1600 | Pos. = 1599, Min. Weight = 25 | Pos. = 315, min_{ }pl = 322, Min. Weight = 38 |
25/61/65/83/83/93/97/105/105/113/ | 38/38/38/40/42/44/50/50/50/54/ | |
1680 | Pos. = 1679, Min. Weight = 25 | Pos. = 504, min_{ }pl = 518, Min. Weight = 44 |
25/69/69/81/89/95/103/113/117/125/ | 44/46/50/50/52/52/54/62/62/62/ | |
1800 | Pos. = 1799, Min. Weight = 25 | Pos. = 1439, min_{ }pl = 1446, Min. Weight = 34 |
25/69/81/85/105/105/109/109/117/ | 34/42/42/42/46/48/50/58/60/62/ | |
1960 | Pos. = 1959, Min. Weight = 25 | Pos. = 1161, min_{ }pl = 1175, Min. Weight = 40 |
25/77/79/83/89/91/97/109/113/125/ | 40/44/44/46/48/50/50/52/54/64/ | |
2040 | Pos. = 2039, Min. Weight = 25 | Pos. = 1932, min_{ }pl = 1939, Min. Weight = 38 |
25/75/77/77/93/109/109/113/129/133/ | 38/40/54/54/56/64/64/74/74/74/ | |
2080 | Pos. = 2079, Min. Weight = 25 | Pos. = 928, min_{ }pl = 935, Min. Weight = 40 |
25/69/77/81/93/103/109/111/119/121/ | 40/42/46/54/54/56/58/72/76/88/ | |
2160 | Pos. = 2159, Min. Weight = 25 | Pos. = 644, min_{ }pl = 651, Min. Weight = 38 |
25/77/81/93/93/97/99/105/107/129/ | 38/42/46/50/52/54/54/54/54/60/ | |
2200 | Pos. = 2199, Min. Weight = 25 | Pos. = 1973, min_{ }pl = 1980, Min. Weight = 42 |
25/57/63/81/97/101/117/121/133/141/ | 42/42/44/52/52/54/54/54/60/62/ | |
2280 | Pos. = 2279, Min. Weight = 25 | Pos. = 1136, min_{ }pl = 1150, Min. Weight = 42 |
25/75/87/89/97/101/113/121/133/139/ | 42/42/42/44/50/54/54/54/62/62/ | |
2560 | Pos. = 2559, Min. Weight = 25 | Pos. = 1663, min_{ }pl = 1670, Min. Weight = 42 |
25/71/73/95/97/109/119/149/149/153/ | 42/42/46/48/54/56/56/56/62/62/ | |
2640 | Pos. = 2639, Min. Weight = 25 | Pos. = 1582, min_{ }pl = 1589, Min. Weight = 38 |
25/87/93/101/109/117/119/133/141/143/ | 38/42/42/42/44/46/50/56/62/66/ | |
2760 | Pos. = 2759, Min. Weight = 25 | Pos. = 820, min_{ }pl = 834, Min. Weight = 42 |
25/97/101/103/113/113/121/141/143/ | 42/48/52/54/58/62/62/66/66/66/ | |
2800 | Pos. = 2799, Min. Weight = 25 | Pos. = 412, min_{ }pl = 419, Min. Weight = 44 |
25/85/97/97/101/101/113/119/137/137/ | 44/58/62/62/70/72/72/76/80/82/ | |
3000 | Pos. = 2999, Min. Weight = 25 | Pos. = 2396, min_{ }pl = 2403, Min. Weight = 34 |
25/85/89/105/123/127/155/157/165/171/ | 34/38/40/50/54/54/54/58/74/76/ | |
3040 | Pos. = 3039, Min. Weight = 25 | Pos. = 604, min_{ }pl = 611, Min. Weight = 38 |
25/61/89/95/105/115/121/133/135/141/ | 38/38/42/46/46/52/52/64/66/76/ | |
3160 | Pos. = 3159, Min. Weight = 25 | Pos. = 2524, min_{ }pl = 2538, Min. Weight = 38 |
25/101/101/105/109/125/127/141/145/149/ | 38/42/46/56/68/76/76/78/90/90/ | |
3280 | Pos. = 3279, Min. Weight = 25 | Pos. = 3109, min_{ }pl = 3123, Min. Weight = 42 |
25/93/105/113/121/125/125/131/131/133/ | 42/50/52/62/62/76/90/90/90/90/ | |
3360 | Pos. = 3359, Min. Weight = 25 | Pos. = 3019, min_{ }pl = 3026, Min. Weight = 42 |
25/71/73/107/117/129/141/141/153/169/ | 42/52/54/66/76/80/88/90/90/90/ | |
3480 | Pos. = 3479, Min. Weight = 25 | Pos. = 1042, min_{ }pl = 1049, Min. Weight = 38 |
25/87/99/105/113/117/133/133/141/145/ | 38/38/54/54/56/58/58/58/60/62/ | |
3600 | Pos. = 3599, Min. Weight = 25 | Pos. = 1438, min_{ }pl = 1445, Min. Weight = 42 |
25/97/109/121/137/139/153/167/167/177/ | 42/46/48/54/54/62/74/76/90,90/ | |
3640 | Pos. = 3639, Min. Weight = 25 | Pos. = 3262, min_{ }pl = 3276, Min. Weight = 54 |
25/87/97/125/137/137/137/149/163/169/ | 54/58/58/62/66/68/72/74/82/88/ | |
3840 | Pos. = 3839, Min. Weight = 25 | Pos. = 759, min_{ }pl = 773, Min. Weight = 42 |
25/53/97/115/117/129/145/147/151/153/ | 42/56/58/62/62/62/62/66/70/72/ | |
3880 | Pos. = 3879, Min. Weight = 25 | Pos. = 383 min_{ }pl = 397, Min. Weight = 54 |
25/91/93/121/129/133/145/173/173/177/ | 54/56/60/62/66/74/86/90/90/90/ | |
3960 | Pos. = 3959, Min. Weight = 25 | Pos. = 1372 min_{ }pl = 1386, Min. Weight = 40 |
25/91/105/125/125/133/135/137/141/143/ | 40/62/68/78/88/90/90/90/90/90/ | |
4000 | Pos. = 3999, Min. Weight = 25 | Pos. = 797 min_{ }pl = 804, Min. Weight = 38 |
25/75/85/133/149/149/149/153/161/175/ | 38/42/42/50/54/54/54/54/54/56/ | |
4240 | Pos. = 4239, Min. Weight = 25 | Pos. = 3392, min_{ }pl = 3399, Min. Weight = 40 |
25/109/119/143/151/153/157/165/169/193/ | 40/42/42/46/50/66/80/90/90/90/ | |
4480 | Pos. = 4479, Min. Weight = 25 | Pos. = 892, min_{ }pl = 899, Min. Weight = 38 |
25/89/89/89/117/119/137/149/159/161/ | 38/38/42/42/42/46/54/64/90/90/ | |
4560 | Pos. = 4559, Min. Weight = 25 | Pos. = 1368, min_{ }pl = 1382, Min. Weight = 44 |
25/113/121/125/137/149/161/165/175/177/ | 44/58/66/68/70/70/82/84/86/88/ | |
4600 | Pos. = 4599, Min. Weight = 25 | Pos. = 3676, min_{ }pl = 3683, Min. Weight = 34 |
25/69/107/121/129/149/151/153/159/161/ | 34/48/50/58/62/66/66/76/86/90/ | |
4680 | Pos. = 4679, Min. Weight = 25 | Pos. = 928, min_{ }pl = 942, Min. Weight = 42 |
25/99/109/137/143/153/171/177/179/187/ | 42/44/50/58/62/62/64/68/84/86/ | |
4800 | Pos. = 4799, Min. Weight = 25 | Pos. = 949, min_{ }pl = 963, Min. Weight = 42 |
25/65/83/129/133/141/157/159/165/169/ | 42/42/50/56/58/66/66/66/70/70/ | |
4840 | Pos. = 4839, Min. Weight = 25 | Pos. = 3858, min_{ }pl = 3872, Min. Weight = 42 |
25/95/129/141/145/151/157/161/173/177/ | 42/72/80/82/84/90/90/90/90/90/ | |
5040 | Pos. = 5039, Min. Weight = 25 | Pos. = 4534, min_{ }pl = 4548, Min. Weight = 46 |
25/157/165/165/175/177/189/189/193/197/ | 46/54/54/58/60/60/62/76/82/90/ | |
5160 | Pos. = 5159, Min. Weight = 25 | Pos. = 2314, min_{ }pl = 2321, Min. Weight = 40 |
25/81/95/137/137/145/147/165/181/185/ | 40/40/46/50/58/58/58/62/66/84/ | |
5280 | Pos. = 5279, Min. Weight = 25 | Pos. = 1579, min_{ }pl = 1593, Min. Weight = 42 |
25/75/101/109/133/137/165/169/181/185/ | 42/50/62/66/70/72/82/82/90/90/ | |
5400 | Pos. = 5399, Min. Weight = 25 | Pos. = 5124, min_{ }pl = 5131, Min. Weight = 38 |
25/99/117/117/125/133/169/173/189/197/ | 38/50/52/54/58/72/90/90/90/90/ | |
5440 | Pos. = 5439, Min. Weight = 25 | Pos. = 4617, min_{ }pl = 4624, Min. Weight = 50 |
25/73/109/143/169/169/169/173/175/181/ | 50/58/60/62/76/90/90/90/90/90/ | |
5560 | Pos. = 5559, Min. Weight = 25 | Pos. = 4441, min_{ }pl = 4448, Min. Weight = 38 |
25/105/141/143/177/181/189/193/193/201/ | 38/42/46/54/66/78/84/88/88/90/ | |
5640 | Pos. = 5639, Min. Weight = 25 | Pos. = 1120, min_{ }pl = 1134, Min. Weight = 42 |
25/101/115/145/153/153/153/165/169/173/ | 42/62/76/86/86/90/90/90/90/90/ | |
5680 | Pos. = 5679, Min. Weight = 25 | Pos. = 851, min_{ }pl = 858, Min. Weight = 50 |
25/101/145/165/173/181/187/187/193/197/ | 50/54/62/74/78/80/82/84/88/88/ | |
5880 | Pos. = 5879, Min. Weight = 25 | Pos. = 4410, min_{ }pl = 4417, Min. Weight = 42 |
25/103/129/161/173/177/189/199/201/201/ | 42/52/72/80/90/90/90/90/90/90/ | |
6160 | Pos. = 6159, Min. Weight = 25 | Pos. = 5849, min_{ }pl = 5863, Min. Weight = 42 |
25/129/155/157/165/187/197/205/209/217/ | 42/44/46/58/90/90/90/90/90/90/ | |
6240 | Pos. = 6239, Min. Weight = 25 | Pos. = 305, min_{ }pl = 319, Min. Weight = 42 |
25/119/119/123/169/185/197/199/213/213/ | 42/42/62/80/90/90/90/90/90/90/ | |
6280 | Pos. = 6279, Min. Weight = 25 | Pos. = 5323, min_{ }pl = 5337, Min. Weight = 44 |
25/117/133/137/161/175/177/195/197/197/ | 44/68/72/72/80/88/90/90,90/90/ | |
6360 | Pos. = 6359, Min. Weight = 25 | Pos. = 5081, min_{ }pl = 5095, Min. Weight = 38 |
25/109/137/141/141/145/147/161/187/201/ | 38/42/46/62/78/86/90/90/90/90/ | |
6640 | Pos. = 6639, Min. Weight = 25 | Pos. = 3645, min_{ }pl = 3652, Min. Weight = 44 |
25/101/109/139/147/175/177/185/209/217/ | 44/54/58/60/64/90/90/90/90/90/ | |
6760 | Pos. = 6759, Min. Weight = 25 | Pos. = 6409, min_{ }pl = 6423, Min. Weight = 42 |
25/105/125/165/203/215/217/229/249/249/ | 42/50/70/84/90/90/90/90,90/90/ | |
6960 | Pos. = 6959, Min. Weight = 25 | Pos. = 5565, min_{ }pl = 5572, Min. Weight = 34 |
25/123/145/145/161/209/211/217/219/223/ | 34/50/54/62/66/80/82/88/90/90/ | |
7000 | Pos. = 6999, Min. Weight = 25 | Pos. = 3846, min_{ }pl = 3853, Min. Weight = 38 |
25/111/145/145/197/221/221/233/235/237/ | 38/52/54/60/62/72/84/90/90/90/ | |
7080 | Pos. = 7079, Min. Weight = 25 | Pos. = 2122, min_{ }pl = 2129, Min. Weight = 38 |
25/117/129/161/165/169/171/175/175/177/ | 38/42/50/54/54/58/72/84/88/90/ | |
7200 | Pos. = 7199, Min. Weight = 25 | Pos. = 6833, min_{ }pl = 6840, Min. Weight = 44 |
25/167/169/173/185/185/215/217/225/225/ | 44/50/66/84/90/90/90/90/90/90/ | |
7360 | Pos. = 7359, Min. Weight = 25 | Pos. = 1836, min_{ }pl = 1843, Min. Weight = 46 |
25/81/157/169/173/173/183/221/221/221/ | 46/60/72/82/82/90/90/90/90/90/ | |
7480 | Pos. = 7479, Min. Weight = 25 | Pos. = 1865, min_{ }pl = 1872, Min. Weight = 46 |
25/117/153/201/207/217/217/227/229/233/ | 46/66/66/72/82/82/90/90/90/90/ | |
7600 | Pos. = 7599, Min. Weight = 25 | Pos. = 1893, min_{ }pl = 1900, Min. Weight = 46 |
25/125/155/157/201/221/223/239/245/251/ | 46/56/58/72/84/90/90/90/90/90/ | |
7680 | Pos. = 7679, Min. Weight = 25 | Pos. = 2865, min_{ }pl = 2872, Min. Weight = 78 |
25/133/153/157/189/207/237/241/243/253/ | 78/90/90/90/90/90/90/90/90/90/ | |
7800 | Pos. = 7799, Min. Weight = 25 | Pos. = 1170, min_{ }pl = 1184, Min. Weight = 44 |
25/115/151/157/181/193/209/241/249/251/ | 44/50/64/72/76/80/86/90/90/90/ | |
7960 | Pos. = 7959, Min. Weight = 25 | Pos. = 398, min_{ }pl = 405, Min. Weight = 40 |
25/135/145/153/169/169/185/217/223/223/ | 40/80/86/88/90/90/90/90/90/90/ | |
8040 | Pos. = 8039, Min. Weight = 25 | Pos. = 7054, min_{ }pl = 7068, Min. Weight = 56 |
25/109/109/111/141/185/201/219/241/249/ | 56/68/90/90/90/90/90/90/90/90/ | |
Table 3 below shows a weight spectrum of the PIL interleaver after modification, where one modification step is selected and used for all frames.
TABLE 3 | ||
K | Dfree(1)/PILSS | Dfree(2)/PILSS |
600 | pos. = 569, Min. Weight = 39 | pos. = 29, min_{ }pl = 36, Min. Weight = 38 |
39/41/49/53/57/61/65/67/67/77/ | 38/38/42/42/42/42/42/42/42/42/ | |
640 | Pos. = 607, Min. Weight = 37 | pos. = 440, min_{ }pl = 447, Min. Weight = 40 |
37/43/53/53/53/69/71/73/75/77/ | 40/40/42/42/44/44/46/46/46/48/ | |
760 | Pos. = 721, Min. Weight = 41 | pos. = 33, min_{ }pl = 40, Min. Weight = 38 |
41/45/57/57/59/69/75/77/81/83/ | 38/38/38/42/42/42/42/44/44/50/ | |
840 | pos. = 797, Min. Weight = 45 | pos. = 461, min_{ }pl = 468, Min. Weight = 36 |
45/45/57/65/65/79/79/83/85/87/ | 36/38/40/42/42/42/44/46/46/46/ | |
880 | pos. = 835, Min. Weight = 47 | pos. = 294, min_{ }pl = 308, Min. Weight = 40 |
47/49/57/61/65/71/83/89/93/93/ | 40/44/46/46/46/48/54/56/56/58/62/ | |
960 | pos. = 911, Min. Weight = 45 | pos. = 568, min_{ }pl = 575, Min. Weight = 36 |
45/49/61/65/69/71/73/87/87/89/ | 36/38/38/42/42/42/42/44/44/46/ | |
1080 | pos. = 1025, Min. Weight = 49 | pos. = 1016, min_{ }pl = 1030, Min. Weight = 42 |
49/53/61/65/67/77/85/89/93/97/ | 42/42/46/48/48/50/52/52/54/54/ | |
1200 | pos. = 1139, Min. Weight = 25 | pos. = 953, min_{ }pl = 967, Min. Weight = 38 |
53/59/65/69/85/85/89/89/95/103/ | 38/38/42/42/42/42/46/48/50/50/ | |
1240 | pos. = 1177, Min. Weight = 53 | pos. = 1053, min_{ }pl = 1060, Min. Weight = 38 |
53/57/67/69/71/85/93/93/103/105/ | 38/38/40/40/42/42/46/46/46/48/ | |
1360 | pos. = 1291, Min. Weight = 53 | pos. = 64, min_{ }pl = 71, Min. Weight = 38 |
57/61/65/73/85/91/93/105/107/107/ | 38/42/42/42/42144/46/46/46/50/ | |
1440 | pos. = 1429, Min. Weight = 53 | pos. = 497, min_{ }pl = 504, Min. Weight = 36 |
53/63/65/73/77/87/89/97/105/109/ | 36/42/42/46/46/50/50/52/54/58/ | |
1480 | pos. = 1405, Min. Weight = 61 | pos. = 1103, min_{ }pl = 1110, Min. Weight = 42 |
61/65/67/77/77/83/95/101/109/117/ | 42/42/44/48/50/50/50/50/54/54/ | |
1600 | pos. = 1573, Min. Weight = 61 | pos. = 315, min_{ }pl = 322, Min. Weight = 38 |
61/65/69/83/83/93/97/105/105/113/ | 38/38/38/40/42/44/50/50/50/54/ | |
1680 | pos. = 1595, Min. Weight = 69 | pos. = 504, min_{ }pl = 518, Min. Weight = 44 |
69/69/69/81/89/95/103/113/117/125/ | 44/46/50/50/52/52/54/62/62/62/ | |
1800 | pos. = 1709, Min. Weight = 69 | pos. = 1439, min_{ }pl = 1446, Min. Weight = 34 |
69/73/81/85/105/105/109/109/117/ | 34/42/42/42/46/48/50/58/60/62/ | |
1960 | pos. = 1861, Min. Weight = 77 | pos. = 1161, min_{ }pl = 1175, Min. Weight = 40 |
77/77/79/83/89/91/97/109/113/125/ | 40/44/44/46/48/50/50/52/54/64/ | |
2040 | pos. = 2014, Min. Weight = 75 | pos. = 1114, min_{ }pl = 1121, Min. Weight = 40 |
75/77/77/83/93/109/109/113/129/133/ | 40/54/54/56/64/64/74/74/74/80/ | |
2080 | pos. = 2038, Min. Weight = 69 | pos. = 928, min_{ }pl = 935, Min. Weight = 40 |
69/77/81/81/93/103/109/111/119/121/ | 40/42/46/54/54/56/58/72/76/88/ | |
2160 | pos. = 2106, Min. Weight = 77 | pos. = 644, min_{ }pl = 651, Min. Weight = 38 |
77/81/85/93/93/97/99/105/107/129/ | 38/42/46/50/52/54/54/54/54/60/ | |
2200 | pos. = 2181, Min. Weight = 57 | pos. = 1973, min_{ }pl = 1980, Min. Weight = 42 |
57/63/81/95/97/101/117/121/133/141/ | 42/42/44/52/52/54/54/54/60/62/ | |
2280 | pos. = 2254, Min. Weight = 75 | pos. = 1136, min_{ }pl = 1150, Min. Weight = 42 |
75/87/89/89/97/101/113/121/133/139/ | 42/42/42/44/50/54/54/54/62/62/ | |
2560 | pos. = 2545, Min. Weight = 71 | pos. = 1663, min_{ }pl = 1670, Min. Weight = 42 |
71/73/95/97/97/109/119/149/149/153/ | 42/46/48/54/56/56/56/62/64/72/ | |
2640 | pos. = 2574, Min. Weight = 87 | pos. = 1582, min_{ }pl = 1589, Min. Weight = 38 |
87/93/97/101/109/117/119/133/141/143/ | 38/42/42/42/44/46/50/56/62/66/ | |
2760 | pos. = 2621, Min. Weight = 97 | pos. = 820, min_{ }pl = 834, Min. Weight = 42 |
97/101/101/103/113/113/121/141/143/ | 42/48/52/54/58/62/62/66/66/66/ | |
2800 | pos. = 2730, Min. Weight = 85 | pos. = 412, min_{ }pl = 419, Min. Weight = 44 |
85/97/97/101/101/101/113/119/137/137/ | 44/58/62/62/66/70/72/72/76/80/ | |
3000 | pos. = 2962, Min. Weight = 85 | pos. = 2396, min_{ }pl = 2403, Min. Weight = 34 |
85/89/105/109/123/127/155/157/165/171/ | 34/38/40/50/54/54/54/58/74/76/ | |
3040 | pos. = 3014, Min. Weight = 61 | pos. = 604, min_{ }pl = 611, Min. Weight = 38 |
61/89/95/105/109/115/121/133/135/141/ | 38/38/42/46/46/52/52/64/66/76/ | |
3160 | pos. = 3065, Min. Weight = 101 | pos. = 2524, min_{ }pl = 2538, Min. Weight = 38 |
101/101/105/109/115/125/127/141/145/149/ | 38/42/46/56/68/76/76/78/90/90/ | |
3280 | pos. = 3198, Min. Weight = 93 | pos. = 3109, min_{ }pl = 3123, Min. Weight = 42 |
93/105/113/117/121/125/125/131/131/133/ | 42/50/52/62/62/76/90/90/90/90/ | |
3360 | pos. = 3339, Min. Weight = 71 | pos. = 3019, min_{ }pl = 3026, Min. Weight = 42 |
71/73/107/117/117/129/141/141/153/169/ | 42/52/54/66/76/80/88/90/90/90/ | |
3480 | pos. = 3436, Min. Weight = 87 | pos. = 1042, min_{ }pl = 1049, Min. Weight = 38 |
87/99/105/113/117/121/133/133/141/145/ | 38/38/54/54/56/58/58/58/60/62/ | |
3600 | pos. = 3510, Min. Weight = 97 | pos. = 1438, min_{ }pl = 1445, Min. Weight = 42 |
97/109/121/125/137/139/153/167/167/177/ | 42/46/48/54/54/62/74/76/90/90/ | |
3640 | pos. = 3594, Min. Weight = 87 | pos. = 3262, min_{ }pl = 3276, Min. Weight = 54 |
87/97/125/125/137/137/137/149/163/169/ | 54/58/58/62/66/68/72/74/82/88/ | |
3840 | pos. = 3829, Min. Weight = 53 | pos. = 759, min_{ }pl = 773, Min. Weight = 42 |
53/97/115/117/129/133/145/147/151/153/ | 42/56/58/62/62/62/62/66/70/72/ | |
3880 | pos. = 3825, Min. Weight = 91 | pos. = 383 min_{ }pl = 397, Min. Weight = 54 |
91/93/121/129/133/133/145/173/173/177/ | 54/56/60/62/66174/86/90/90/90/ | |
3960 | pos. = 3910, Min. Weight = 91 | pos. = 1372 min_{ }pl = 1386, Min. Weight = 40 |
91/105/125/125/133/135/137/137/141/143/ | 40/62/68/78/88/90/90/90/90/90/ | |
4000 | pos. = 3977, Min. Weight = 75 | pos. = 797 min_{ }pl = 804, .Min. Weight = 38 |
75/85/133/139/149/149/149/153/161/175/ | 38/42/42/50/5454/54/54/54/56/ | |
4240 | pos. = 4134, Min. Weight = 109 | pos. = 3392, min_{ }pl = 3399, Min. Weight = 40 |
109/119/143/145/151/153/157/165/169/193/ | 40/42/42/46/50/66/80/90/90/90/ | |
4480 | pos. = 4405, Min. Weight = 89 | pos. = 892, min_{ }pl = 899, Min. Weight = 38 |
89/89/89/117/119/137/149/149/159/161/ | 38/38/42/42/42/46/54/64/90/90/ | |
4560 | pos. = 4446, Min. Weight = 113 | pos. = 1368, min_{ }pl = 1382, Min. Weight = 44 |
113/121/125/137/149/155/161/165/175/177/ | 44/58/66/68/70/70/82/84/86/88/ | |
4600 | pos. = 4561, Min. Weight = 69 | pos. = 3676, min_{ }pl = 3683, Min. Weight = 34 |
69/107/121/129/149/151/153/153/159/161/ | 34/48/50/58/62/66/66/76/86/90/ | |
4680 | pos. = 4656, Min. Weight = 99 | pos. = 928, min_{ }pl = 942, Min. Weight = 42 |
99/109/137/143/153/171/171/177/179/187/ | 42/44/50/58/62/62/64/68/84/86/ | |
4800 | pos. = 4765, Min. Weight = 65 | pos. = 949, min_{ }pl = 963, Min. Weight = 42 |
65/83/129/133/141/157/159/161/165/169/ | 42/42/50/56/58/66/66/66/70/70/ | |
4840 | pos. = 4780, Min. Weight = 95 | pos. = 3858, min_{ }pl = 3872, Min. Weight = 42 |
95/129/141/145/151/157/161/163/173/177/ | 42/72/80/82/84/90/90/90/90/90/ | |
5040 | pos. = 5029, Min. Weight = 157 | pos. = 4534, min_{ }pl = 4548, Min. Weight = 46 |
157/165/165/165/175/177/189/189/193/197/ | 46/54/54/58/60/60/62/76/82/90/ | |
5160 | pos. = 5140, Min. Weight = 81 | pos. = 2314, min_{ }pl = 2321, Min. Weight = 40 |
81/95/137/137/145/147/165/169/181/185/ | 40/40/46/50/58/58/58/62/66/84/ | |
5280 | pos. = 5285, Min. Weight = 75 | pos. = 1579, min_{ }pl = 1593, Min. Weight = 42 |
75/101/109/133/137/165/169/173/181/185/ | 42/50/62/66/70/72/82/82/90/90/ | |
5400 | pos. = 5332, Min. Weight = 99 | pos. = 1883, min_{ }pl = 1890, Min. Weight = 50 |
99/117/117/125/133/169/173/179/189/197/ | 50/52/54/58/72/90/90/90/90/90/ | |
5440 | pos. = 5394, Min. Weight = 73 | pos. = 4617, min_{ }pl = 4624, Min. Weight = 50 |
73/109/143/169/169/169/173/175/177/181/ | 50/58/60/62/76/90/90/90/90/90/ | |
5560 | pos. = 5520, Min. Weight = 105 | pos. = 4441, min_{ }pl = 4448, Min. Weight = 38 |
105/141/143/177/181/181/189/193/193/201/ | 38/42/46/54/6628/84/88/88/90/ | |
5640 | pos. = 5587, Min. Weight = 101 | pos. = 1120, min_{ }pl = 1134, Min. Weight = 42 |
101/115/145/153/153/153/165/169/173/173/ | 42/62/76/86/86/90/90/90/90/90/ | |
5680 | pos. = 5585, Min. Weight = 101 | pos. = 851, min_{ }pl = 858, Min. Weight = 50 |
101/145/165/173/181/187/187/187/193/197/ | 50/54/62/14/78/80/82/84/88/88/ | |
5880 | pos. = 5806, Min. Weight = 103 | pos. = 4410, min_{ }pl = 4417, Min. Weight = 42 |
103/129/161/173/177/189/189/199/201/201/ | 42/52/72/80/90/90/90/90/90/90/ | |
6160 | pos. = 6111, Min. Weight = 129 | pos. = 5849, min_{ }pl = 5863, Min. Weight = 42 |
129/155/157/165/187/197/197/205/209/217/ | 42/44/46/58/90/90/90/90/90/90/ | |
6240 | pos. = 6140, Min. Weight = 119 | pos. = 305, min_{ }pl = 319, Min. Weight = 42 |
119/119/123/169/185/197/199/203/213/213/ | 42/42/62/80/90/90/90/90/90/90/ | |
6280 | pos. = 6234, Min. Weight = 117 | pos. = 5323, min_{ }pl = 5337, Min. Weight = 44 |
117/133/137/161/175/177/195/197/197/199/ | 44/68/72/72/80/88/90/90/90/90/ | |
6360 | pos. = 6280, Min. Weight = 109 | pos. = 5081, min_{ }pl = 5095, Min. Weight = 38 |
109/137/141/141/145/147/161/187/201/205/ | 38/42/46/62/78/86/90/90/90/90/ | |
6640 | pos. = 6590, Min. Weight = 101 | pos. = 3645, min_{ }pl = 3652, Min. Weight = 44 |
101/109/139/147/175/177/185/209/213/217/ | 44/54/58/60/64/90/90/90/90/90/ | |
6760 | pos. = 6658, Min. Weight = 105 | pos. = 670, min_{ }pl = 677, Min. Weight = 50 |
105/125/165/203/215/217/217/229/249/249/ | 50/70/84/90/90/90/90/90/90/90/ | |
6960 | pos. = 6894, Min. Weight = 123 | pos. = 5565, min_{ }pl = 5572, Min. Weight = 34 |
123/145/145/161/209/211/217/219/221/223/ | 34/50/54/62/66/80/82/88/90/90/ | |
7000 | pos. = 6912, Min. Weight = 111 | pos. = 3846, min_{ }pl = 3853, Min. Weight = 38 |
111/145/145/197/221/221/221/233/235/237/ | 38/52/54/60/62/72/84/90/90/90/ | |
7080 | pos. = 7018, Min. Weight = 117 | pos. = 2122, min_{ }pl = 2129, Min. Weight = 38 |
117/129/161/165/169/171/175/175/177/181/ | 38/42/50/54/54/58/72/84/88/90/ | |
7200 | pos. = 6994, Min. Weight = 167 | pos. = 6833, min_{ }pl = 6840, Min. Weight = 44 |
167/169/173/185/185/215/217/225/225/229/ | 44/50/66184/90/90/90/90/90/90/ | |
7360 | pos. = 7298, Min. Weight = 81 | pos. = 1836, min_{ }pl = 1843, Min. Weight = 46 |
81/157/169/173/173/183/221/221/221/229/ | 46/60/72/82/82/90/90/90/90/90/ | |
7480 | pos. = 7386, Min. Weight = 117 | pos. = 1865, min_{ }pl = 1872, Min. Weight = 46 |
117/153/201/207/217/217/227/229/233/233/ | 46/66/66/72/82/82/90/90/90/90/ | |
7600 | pos. = 7528, Min. Weight = 125 | pos. = 1893, min_{ }pl = 1900, Min. Weight = 46 |
125/155/157/201/221/223/239/241/245/251/ | 46/56/58/72/84/90/90/90/90/90/ | |
7680 | pos. = 7526, Min. Weight = 133 | pos. = 2865, min_{ }pl = 2872, Min. Weight = 78 |
133/153/157/189/207/237/241/241/243/253/ | 78/90/90/90/90/90/90/90/90/90/ | |
7800 | pos. = 7702, Min. Weight = 115 | pos. = 1170, min_{ }pl = 1184, Min. Weight = 44 |
115/151/157/181/193/209/241/245/249/251/ | 44/50/64/72176/80/86/90/90/90/ | |
7960 | pos. = 7832, Min. Weight = 135 | Pos. = 398, min_{ }pl = 405, Min. Weight = 40 |
135/145/153/169/169/185/217/223/223/237 | 40/80/86188/90/90/90190/90/90/ | |
8040 | pos. = 8006, Min. Weight = 109 | pos. = 7054, min_{ }pl = 7068, Min. Weight = 56 |
109/109/111/141/185/201/219/241/249/253 | 56/68/90/90/90/90/90/90/90/90/ | |
As described above, the novel turbo encoder suppresses a decreases in the free distance dfree caused by one or more information bits of ‘1’ located at the last period of a data frame input to the component encoder, using the internal interleaver, thereby contributing to implementation of a turbo encoder with high performance.
While the invention has been shown and described with reference to a certain preferred embodiment thereof, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.
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U.S. Classification | 714/786, 714/788 |
International Classification | H03M13/27, H04L1/00, H03M13/29, H03M13/03, G06F11/10 |
Cooperative Classification | H03M13/2957, G11B2220/2562, H03M13/27, H03M13/2714, H03M13/2771, H03M13/276, H03M13/2764, H03M13/271 |
European Classification | H03M13/29T, H03M13/27A2G, H03M13/27T, H03M13/27A2, H03M13/27O1, H03M13/27O |