US RE43212 E1 Abstract A 2-dimensional interleaving method is disclosed. The method comprises 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.
Claims(32) 1. A turbo encoder comprising:
a first encoder configured for encoding a frame of K input information bits to generate first coded symbols;
an interleaver configured for
receivingsequentially writing the K information bits into a Row (R)×Column (C) rectangular matrix, row by row, starting in a first column of a first row,
intra row permuting positions of the K information bits in the R×C rectangular matrix in each row according to a given interleaving rule,
exchanging a position of an information bit in a last column of a last row with a position of an information bit in the first column of the last row, after the intra row permuting,
performing inter-row permutations of the R×C rectangular matrix, and
and interleaving the information bits position such that an information bit existing at the last position of the frame is shifted to a position preceding the last position for not generating Critical Information Sequence Pattern (CISP)reading out the information bits from the permuted R×C rectangular matrix, column by column, starting in the first row of the first column; and
a second encoder configured for encoding the interleaved read out information bits to generate second coded symbols,
wherein the R×C rectangular matrix includes R rows and C columns, K=R×C, and K indicates a number of the information bits included in the frame.
2. The turbo encoder as claimed in
a controller for writing the information bits sequentially in memory and dividing the information bits into R groups each having the C information bits; permuting the an address of the an information bit written in a jth row (where, j=0,1,2, . . . , R−1) to positions C
_{j}(i) in the row in accordance with an algorithm given by
i) C(i)=[g
0×C(i−1)] mod p, i=1,2, . . . , (p−2) and C(0)=1ii) C
_{j}(i)=C([i×p_{j}] mod (p−1)),
j=0,1,2, . . . , (R−1), i=0,1,2, . . . , (p−1 2), C
_{j}(p−1)=0, and C_{j}(p)=piii) exchange C
_{R-1}(p) with C_{R-1}(0)where p (prime number) indicates a minimum prime number which is closest to K/R satisfying 0≦(p+1)−K/R, g
0 (primitive root) indicates a predetermined number corresponding to an associated primitive root for p, and p_{j }indicates a primitive number set.3. The turbo encoder as claimed in
a memory for storing the information bit frame sequentially; a randomizer for permuting the address of the stored informnation bits according as shifting the address of an informnation bit existing at the last position to a position preceding the last position in the last group. 4. The turbo encoder as claimed in
5. A device for permuting information bit addresses of an input frame which have R Row (R) groups, each of the R groups having C Column (C) information bits, in a prime interleaver (PIL) used as an internal interleaver for a turbo encoder, the device comprising:
a memory for storing the information bit frame sequentially; and
a randomizer for permuting the addresses of the information bit frame according to a given interleaving rule, and changing the exchanging an address of an a last information bit to a position preceding the position in the position with an address of an information bit existing at a first position of a last group, after the permuting.
6. The device as claimed in
7. A device for interleaving a frame of K information bits which have R Row (R) groups, each of the R groups having C Column (C) information bits, in a PIL interleaver prime interleaver (PIL) used as an internal interleaver for a turbo encoder, the device comprising:
a controller for writing input information bits of a frame in a memory sequentially and permuting the position positions of the information bits written in a jth row (where, j can be 0,1,2, . . . , or R−1) to position C
_{j}(i) in the row in accordance with an algorithm given by
i) permute a base sequence C(i)=[g
0×C(i−1)] mod p, i=1,2, . . . , (p−2) and C(0)=1ii) perform row permutation C
_{j}(i)=C([i×p_{j}] mod (p−1)),
j=0,1,2, . . . , (R−1), i=0,1,2, . . . , (p−1 2), C
_{j}(p−1)=0, and C_{j}(p)=piii) exchange C
_{R-1}(p) with C_{R-1}(0)where p (prime number) indicates a minimum prime number which is closest to K/R satisfying 0≦(p+1)−K/R, g
0 (primitive root) indicates a predetermined number corresponding to an associated primitive root for p, and p_{j }indicates a primitive number set.8. A 2-dimensional interleaving method comprising the steps of:
storing a frame of K input information bits into a memory sequentially and dividing an the information bits into R Row (R) groups, each of the R groups having C Column (C) information bits;
permuting the information bits addresses of the each group according to a given rule; and
changingexchanging an information bit address existing at thea last position of thea last group to a address preceding the last positionwith an information bit address existing at a first position of the last group, subsequent to the permuting.
9. A The 2-dimensional interleaving method as claimed in
determining a minimum prime number p which is closest to K/R satisfying 0≦(p+1)−K/R, sequentially writing input sequences of information bits of a frame in a memory;
selecting a primitive root g
0 corresponding to the minimum prime number p, and generating a base sequence C(i) for intra-row permuting the input sequences written in the rows in accordance with
C(i)=[g 0×C(i−1)] mod p, i=1,2, . . . , (p−2), and C(0)=1;
calculating a minimum prime integer set {q
_{j}}(j=0,1,2, . . . , R−1) by determining
g.c.d{q _{j},p−1}=1
q _{j}>6, q_{j}>q_{(j-1) } where g.c.d is a greatest common divider and q
_{0}=1;intra-row permuting {q
_{j}} using
p _{P(j)}=q_{j}, j=0,1, . . . , R−1
where P(j) indicates a predetermined selecting order for selecting the R rows;
when C=p+1, permuting sequences in a jth row in accordance with
C _{j}(i)=C([i×p_{j}] mod(p−1)),
where j=0,1,2, . . . , (R−1), i=0,1,2, . . . , (p−1 2), C
_{j}(p−1)=0, and C_{j}(p)=p,and if (K=C×R), then C
_{R-1}(p) is exchanged with C_{R-1}(0).10. The 2-dimensional interleaving method as claimed in
11. A 2-dimensional interleaving method comprising the steps of:
writing input sequences of a frame of input information bits which have R Row (R) groups, each of the R groups having C Column (C) information bits, in a memory;
permuting the address addresses of the information bits written in the memory according to a given rule; and
shiftingexchanging an address of an information bit written in thea last position of thea last group to a position precedingwith an address of an information written in a first position of the last group, subsequent to the permuting.
12. The 2-dimensional interleaving method as claimed in
13. A method for interleaving a frame of input information bits which have R Row (R) groups, each of the R groups having C Column (C) information bits, in a PIL interleaver prime interleaver (PIL) used as an internal interleaver for a turbo encoder, the method comprising the steps of:
a) permuting the information bits position positions of the groups according to a predetermined PIL interleaving rule; and
b) changing exchanging an information bit existing at the a last position of the frame to a position preceding the last position a last group with an information bit existing at a first position of the last group, subsequent to the permuting.
14. The method as claimed in
15. The method as claimed in
_{j}(i) in the row in accordance with the steps of an algorithm given by the steps of
i) calculating C(i)=[g
0×c(i−1)] mod p, i=1,2, . . . , (p−2) and C(0)=1ii) calculating C
_{j}(i)=C([i×p_{j}] mod(p−1)), where
j=0,1,2, . . . , (R−1), i=0,1,2, . . . , (p−1 2), C
_{j}(p−1)=0, and C_{j}(p)=piii) exchanging C
_{R-1}(p) with C_{R-1}(0)
where p (prime number) indicates a minimum prime number which is closest to K/R satisfying 0≦(p+1)−K/R, K indicates a number of the input information bits in the frame, g
0 (primitive root) indicates a predetermined number corresponding to an associated primitive root for p, p_{j }indicates a primitive number set, and c_{j}(i) is the an input bit position of an ith output after the permutation of a jth row.16. A 2-dimensional interleaving method comprising the steps of:
sequentially writing input sequences of information bits of the a frame in an R a Row (R)×C Column rectangular matrix;
selecting a primitive root g
0 corresponding to the a minimum prime number p, and generating a base sequence c(i) for intra-row permuting the input sequences written in the rows of the R×C rectangular matrix in accordance with
C(i)=[g 0×C(i−1)] mod p, i=1,2, . . . , (p−2), and C(0)=1;
calculating a minimum prime integer set {q
_{j}}(j=0,1,2, . . . , R−1) by determining
g.c.d{q _{j},p−1}=1
q _{j}>6, q_{j}>q_{(j-1) } where g.c.d is a greatest common divider and q
_{0}=1;intra-row permuting {q
_{j}} using
p _{P(j)}=q_{j}, j=0,1, . . . , R−1
where P(j) indicates a predetermined selecting order for selecting the R rows;
when C=p+1, permuting sequences in a jth row in accordance with
C _{j}(i)=C([i×p_{j}] mod(p−1)),
where j=0,1,2, . . . , (R−1), i=0,1,2, . . . , (p−1 2), C
_{j}(p−1)=0, and C_{j}(p)=p,and if (K=C×R), then C
_{R-1}(p) is exchanged with C_{R-1}(0),selecting R rows according to a predetermined order P(j), and selecting one input sequence from the selected row; and
providing the selected input sequence as a read address for interleaving the information bits of the input frame.
17. The turbo encoder as claimed in claim 1, wherein the interleaver is further configured for permuting addresses of the information bits written in a jth row, where, j=0, 1, 2, . . . , R−1, to positions C
_{j}(i) in the row in accordance with an algorithm given by
i) C(i)=[g0×C(i−1)] mod p, i=1,2, . . . ,(p−2) and C(0)=1
ii) C
_{j}(i)=C([i×p_{j}] mod (p−1)), j=0,1,2, . . . ,(R−1), i=0,1,2, . . . ,(p−2), C_{j}(p−1)=0, and C_{j}(p)=piii) exchange C
_{R-1}(p) with C_{R-1}(0)where p indicates a minimum prime number satisfying 0≦(p+1)−K/R, g0 indicates an associated primitive root for p, and p
_{j }indicates a prime number set.18. A device for permuting information bit addresses of an input frame, the input frame having Row (R) groups, each of the R groups having Column (C) information bits, the device being configured in an internal interleaver for a turbo encoder, the device comprising:
a memory configured for storing the information bits frame sequentially; and a randomizer configured for
intra-row permuting an address of the stored information bits in each row according to a given interleaving rule,
exchanging an address of an information bit existing at a last position of a last group with an address of an information bit existing at a first position of the last group, after the intra-row permuting,
performing inter-row permutations, and
reading out the information bits, column by column, starting in the first row of the first column. 19. A device for interleaving a frame of K information bits, the frame having Row (R) groups, each the R groups having Column (C) information bits, the device comprising:
an interleaver for two-dimensional interleaving for a turbo encoder configured for sequentially writing input information bits of a frame in a memory and permuting positions of the information bits written in a jth row to a position C _{j}(i) in the row, where, j can be 0,1,2 . . . , or R−1, in accordance with an algorithm given byiv) permute a base sequence C(i)=[g0×C(i−1)] mod p, i=1,2, . . . ,(p−2) and C(0)=1, v) perform row permutation C _{j}(i)=C([i×p_{j}] mod (p−1)), j=0,1.2, . . ,(R−1), i=0,1,2, . . . , (p−2), C_{j}(p−1)=0, and C_{j}(p)=p,vi) exchange C _{R-1}(p) with C_{R-1}(0);where K specifies a number of input information bits in a frame, p indicates a minimum prime number satisfying 0≦(p+1)−K/R, g0 indicates an associated primitive root for p, and p _{j }indicates a prime number set.20. The device according to claim 19, further comprising a randomizer configured for permuting the addresses of the stored information bits in accordance with exchanged positions of the stored information bits.
21. A two-dimensional interleaving method comprising the steps of:
sequentially storing a frame of K input information bits, the frame having Row (R) groups, each of the R groups having Column (C) information bits; permuting information bit addresses of the each of the R groups according to a given interleaving rule; and exchanging an address of an information bit existing at a last position of a last group with an address of an information bit existing at a first position of the last group, subsequent to the permuting. 22. The two-dimensional interleaving method as claimed in claim 21, wherein the step of permuting comprises:
determining a minimum prime number p satisfying 0≦(p+1)−K/R; selecting a primitive root g0 associated with the minimum prime number p, and generating a base sequence C(i) for intra-row permuting of the input sequences written in the rows in accordance with C(i)=[g0×C(i−1)] mod p, i=1,2, . . . ,(p−2), and C(0)=1; calculating a minimum prime integer set {q _{j}}(j=0,1,2, . . . ,R−1) by determining
g.c.d{q
_{j},p−1}=1q
_{j}>6, q_{j}>q_{(j-1) } where g.c.d is a greatest common divider and q
_{0}=1;intra-row permuting {q _{j}} using
p
_{P(j)}=q_{j}, j=0,1, . . . ,R−1where P(j) indicates a predetermined selecting order for selecting the R rows; and
when C=p+1, permuting sequences in a jth row in accordance with
C
_{j}(i)=C([i×p_{j}] mod (p−1)),where j=0,1,2, . . . ,(R−1), i=0,1,2, . . . ,(p−2), C
_{j}(p−1)=0, and C_{j}(p)=p,and if (K=C×R), then C
_{R-1}(p) is exchanged with C_{R-1}(0).23. A two-dimensional interleaving method comprising the steps of:
writing input sequences of a frame of input information bits in a memory, the frame having Row (R) groups, each of the R groups having Column (C) information bits; permuting addresses of the information bits written in the memory according to a given interleaving rule; and exchanging an address of an information bit written in a last position of a last group with an information bit written in a first position of the last group, subsequent to the permuting. 24. A method for interleaving a frame of input information bits, the frame having Row (R) groups, each of the R groups having Column (C) information bits, the method for use in an internal interleaver of a turbo encoder, the method comprising the steps of:
a) permuting information bit positions of the groups according to predetermined interleaving rule; and b) exchanging an information bit existing at a last position of a last group with an information bit existing at a first position of the last group. 25. The method as claimed in claim 24, wherein in the step a) and b), the R groups are rows and the information bits positions of the frame written in a jth row, where j=0,1,2, . . . ,R−1, are permuted with positions C
_{j}(i) in the row in accordance with an algorithm given by
i) calculating C(i)=[g0×C(i−1)] mod p, i=1,2, . . . ,(p−2) and C(0)=1
ii) calculating C
_{j}(i)=C([i×p_{j}] mod (p−1)), where
j=0,1,2, . . . ,(R−1), i=0,1,2, . . . ,(p−2), C
_{j}(p−1)=0, and C_{j}(p)=piii) exchanging C
_{R-1}(p) with C_{R-1}(0)where k specifies a number of input information bits in a frame, p indicates a minimum prime number satisfying 0≦(p+1)−K/R, g0 indicates an associated primitive root for p, p
_{j }indicates a prime number set, and C_{j}(i) is the input bit position of an ith output after the permutation of a jth row.26. A two-dimensional interleaving method comprising the steps of:
sequentially writing input sequences of information bits of a frame in a Row (R)×Column (C) rectangular matrix, the frame having R groups, each of the R groups having C information bits; selecting a primitive root g0 corresponding to a minimum prime number p satisfying 0≦(p+1)−K/R; generating a base sequence C(i) for intra-row permuting the input sequences written in the rows in accordance with
C(i)=[g0×C(i−1)] mod p, i=1,2, . . . ,(p−2), and C(0)=1;
calculating a minimum prime integer set {q _{i}}(j=0,1,2, . . . ,R−1) by determining
g.c.d{q
_{j},p−1}=1q
_{j}>6, q_{j}>q_{(j-1) } where g.c.d is a greatest common divider and q
_{0}=1;intra-row permuting {q _{j}} using
p
_{P(j)}=q_{j}, j=0,1, . . . ,R−1where P(j) indicates a predetermined selecting order for selecting the R rows;
when C=p+1, permuting sequences in a jth row in accordance with
C
_{j}(i)=C([i×p_{j}] mod (p−1)),where j=0,1,2, . . . ,(R−1), i=0,1,2, . . . ,(p−2), C
_{j}(p−1)=0, and C_{j}(p)=p,and if (K=C×R), then C
_{R-1}(p) is exchanged with C_{R-1}(0),selecting R rows according to a predetermined order P(j); selecting an input sequence from the selected rows; and providing the selected input sequence as read addresses for interleaving the information bits of the input frame. 27. A two-dimensional interleaving method comprising the steps of:
sequentially storing a frame of K input information bits, the frame having Row (R) groups, each of the R groups having Column (C) information bits; permuting the information bits addresses of each of the R groups according to a given interleaving rule; and exchanging an address of an information bit existing at a last position of a last group with an information bit existing at a first position of the last group, subsequent to the permuting. 28. A method for interleaving a frame of input information bits, the frame having Row (R) groups, each of the R groups having Column (C) information bits, the method for use in an internal interleaver of a turbo encoder, the method comprising the steps of:
a) permuting the information bit positions of the groups according to predetermined interleaving rule; and b) exchanging an information bit position existing at a last position of a last group with an information bit existing at a first position of the last group. 29. The method as claimed in claim 28, wherein in the step a) and b), the R groups are rows and the information bit positions of the frame written in a jth row, where j=0, 1, 2, . . . , R−1, are permuted with positions C
_{j}(i) in the row in accordance with the steps of an algorithm given by
i) calculating C(i)=[g0×C(i−1)] mod p, i=1, 2, . . . , (p−2) and C(0)=1
ii) calculating C
_{j}(i)=C([i×p_{j}] mod (p−1)), j=0, 1, 2, . . . , (R−1), i=0, 1, 2, . . . , (p−21), C_{j}(p−1)=0, and C_{j}(p−1)=piii) exchanging C
_{R-1}(p) with C_{R-1}(0)where K specifies a number of input information bits in a frame, p indicates a minimum prime number, which is closest to K/R while satisfying 0≦(p+1)−K/R, g0 indicates an associated primitive root for predetermined number corresponding to p, p
_{j }indicates a primitive prime number set and C_{j}(i) is the information bit position of an ith output after the permutation of a jth row.30. A turbo encoder comprising:
a first encoder configured for encoding a frame of K input information bits to generate first coded symbols; an interleaver configured for
sequentially writing the K input information bits into a Row (R)×Column (C) rectangular matrix, row by row, starting in a first column of a first row,
intra row permuting positions of the information bits in the R×C rectangular matrix in each row according to a given interleaving rule,
exchanging a position of an information bit in a last column of a last row with a position within the last row which precedes the last column, after the intra row permuting,
performing inter-row permutations of the R×C rectangular matrix, and
reading out the information bits from the permuted R×C rectangular matrix, column by column, starting in the first row of the first column; and
a second encoder configured for encoding the read out information bits to generate second coded symbols, wherein the R×C rectangular matrix includes R rows and C columns, K=R×C, and K indicates a number of the input information bits included in the frame. 31. The turbo encoder as claimed in claim 30, wherein the turbo encoder is further configured to store the input information bits in a memory, to perform the interleaving of the information bits in the R×C rectangular matrix based on generated read addresses corresponding to the permuted R×C rectangular matrix, and to output the information bits from the memory using the generated read addresses.
32. The turbo encoder as claimed in claim 30, wherein the turbo encoder is further configured to exchange the position of the information bit in the last column of the last row with a position of an information bit in the first column of the last row.
Description 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: -
- Distance Property: The distance between adjacent codeword symbols should be maintained to a certain extent. This has the same function as a codeword distance property of the convolutional code, and as a criterion indicating this, a minimum free distance is used which is a value of a codeword path or a codeword sequence with the minimum Hamming weight out of the code symbol sequences (or codeword paths) output on the trellis. In general, it is preferable that the interleaver should be designed to have the longer free distance, if possible.
- Random Property: A correlation factor between output word symbols after interleaving should be much lower than a correlation factor between original input word symbols before interleaving. That is, randomization between the output word symbols should be completely performed. This makes a direct effect on the quality of extrinsic information generated in continuous decoding.
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 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 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 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 To sum up, the prior art has the following disadvantages. -
- (1) The turbo interleaver is designed for the infinite frame size on the basis of the CISP for which the input information word has the Hamming weight
**2**, without considering the fact that determining the CISP according to the type of the input information word is limited to the frame size. However, in an actual system, the frame has a finite size, thus causing a decrease in the free distance of the turbo code. - (2) In designing the existing turbo interleaver, the fact that the input information word may have Hamming weight
**1**was not considered. In other words, for the finite frame size, the turbo interleaver design rule should be determined in consideration of the fact that the minimum free distance generated in the PCCC turbo encoder is determined by the CISP having the Hamming weight**1**. However, this was not fully considered for the existing turbo interleavers. - (3) The Prime interleaver (PIL) designated as the working assumption of the turbo code interleaver defined by the UMTS specification involves such problems, thus having degraded free distance performance.
- (1) The turbo interleaver is designed for the infinite frame size on the basis of the CISP for which the input information word has the Hamming weight
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 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 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 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 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
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 RSC From Equation 1, it is noted that a Hamming weight balance between RSC However, as described above, the minimum free distance occurs when the input information word has the Hamming weight 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 RSC 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. -
- Condition 1: In designing every turbo interleaver, the information bits corresponding to a specific period from the last position of the frame should be shifted to the foremost position of the frame by interleaving to increase the free distance of the turbo code.
- Condition 2: The information bits corresponding to the last position of the frame should be shifted to a position preceding the last position (if possible, to the leading position of the frame) by interleaving, to increase the free distance of the turbo code.
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) r 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 - (i) find minimum prime number p such that, satisfying 0=<(p+1)−K/R
- (ii) if (0=<p−K/R) then go to (iii), else C=p+1
- (iii) if (0=<p−K/R) then C=p=1, else C=p.
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] -
- B-1) A primitive root g
**0**is selected from a given random initialization constant table (3GPP TS 25.212 table 2; table of prime number p and associated primitive root) such that g**0**is a the primitive root of a field based on the prime number p. - B-2) Construct base sequence C(i) to be used for row vector randomization is generated using the following formula.
C(i)=[g**0**×C(i−1)]mod p, i=1,2,3, . . . ,p−2, C(0)=1 - B-3) Select the minimum prime integer set {q
_{j}, j=0,1,2, . . . , R−1} such that g.c.d {q_{j},p−1}=1, q_{j}>6 and q_{j}>q_{(j-1)}, where g.c.d is a greatest common divider and q_{0}=1 - B-4) {p
_{j}, j=0,1,2, . . . , R−1} which is a new prime number set is calculated from {q_{j}, j=0,1,2, . . . , R−1} such that p_{p(j)}=q_{j }where, j=0, 1, . . . R−1 and p_{(j) }is the inter-row permutation pattern defined in the third stage. - B-5) Elements of the jth intra-row permutation as following method.
C_{j}(i)=C([i×p_{j}]mod(p−1)), i=0,1,2,3, . . . , p−2, C_{j}(p−1)=0, and C_{j}(p)=p
- B-1) A primitive root g
A third stage, Perform the row-permutation based on the following p - p
_{A}: {19, 9, 14, 4 0, 2, 5, 7, 12, 18, 10, 8, 13, 17, 3, 1, 16, 6, 15, 11} for R=20 - p
_{B}: {19, 9, 14, 4 0, 2, 5, 7, 12, 18, 16, 13, 17, 15, 3, 1, 6, 11, 8, 10} for R=20 - p
_{c}: {9,8,7,6,5,4,3,2,1,0} for R=10.
It should be noted herein that the last operation of B-5) is defined as C 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. -
- B-5-1) Positions of C
_{R-1},(0) and C_{R-1}(p) are interchanged. R=10 or 20 - B-5-2) Positions of C
_{R-1}(p−1) and C_{R-1}(p) are interchanged. R=10 or 20 - B-5-3) For every j, positions of C
_{j}(0) and C_{j}(p) are interchanged. j=0,1,2, . . . , R-1 - B-5-4) For every j, positions of C
_{j}(p−1) and C_{j}(p) are interchanged. j=0,1,2, . . , R−1 - B-5-5) For every j, an optimal exchanging position k for the used interleaving algorithm is searched to interchange positions of C
_{j}(k) and C_{j}(p). - B-5-6) For an (R−1)th row, an optimal exchanging position k for the used interleaving algorithm is searched to interchange positions of C
_{R-1}(k) and C_{R-1}(p), where K is determined by simulation.
- B-5-1) Positions of C
Referring to Thereafter, in step 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 Table 2 below shows a weight spectrum of the PIL interleaver before modification.
Table 3 below shows a weight spectrum of the PIL interleaver after modification, where one modification step is selected and used for all frames.
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. Patent Citations
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