IEEE C802.16e-04/526r1. IEEE Broadband Wireless Access Working Group <

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1 24--2 IEEE C826e-4/526r Project itle IEEE 826 Broadand Wireless Access Woring Group < LDPC coding for OFDMA PHY Date Sumitted Source(s) Brian Classon Yufei Blanenship Motorola Jerry Kim Panyuh Joo Gyuum Kyung Hongsil Jeong Sang-Hyo Kim Hanju Kim DS Par Jaeho Jeon Samsung Eric Jacosen Bo Xia Intel Kyuhyu Chung Min-seo Oh LG Electronics Brian Johnson Ale Purovic Nina Burns Sergey Suoo Nortel Networs Eli Sasha Zion Hadad Yigal Leia Itzi Kitroser Yossi Segal Oren Elayam Runcom echnologies

2 24--2 IEEE C826e-4/526r Simon Litsyn Eran Sharon el-aviv University Dale Hocevar Anuj Batra exas Instruments Victor Stolpman Jianzhong (Charlie) Zhang Nico Van Waes Noia Masoud Olfat Nextel Communications Re: Astract Purpose Notice Release Patent Policy and Procedures IEEE P826-REVe/D5-24, sponsor allot his contriution contains additional text output from an informal LDPC group Provide additional LDPC specification text his document has een prepared to assist IEEE 826 It is offered as a asis for discussion and is not inding on the contriuting individual(s) or organization(s) he material in this document is suject to change in form and content after further study he contriutor(s) reserve(s) the right to add, amend or withdraw material contained herein he contriutor grants a free, irrevocale license to the IEEE to incorporate material contained in this contriution, and any modifications thereof, in the creation of an IEEE Standards pulication; to copyright in the IEEE s name any IEEE Standards pulication even though it may include portions of this contriution; and at the IEEE s sole discretion to permit others to reproduce in whole or in part the resulting IEEE Standards pulication he contriutor also acnowledges and accepts that this contriution may e made pulic y IEEE 826 he contriutor is familiar with the IEEE 826 Patent Policy and Procedures < including the statement "IEEE standards may include the nown use of patent(s), including patent applications, provided the IEEE receives assurance from the patent holder or applicant with respect to patents essential for compliance with oth mandatory and optional portions of the standard" Early disclosure to the Woring Group of patent information that might e relevant to the standard is essential to reduce the possiility for delays in the development process and increase the lielihood that the draft pulication will e approved for pulication Please notify the Chair <mailto:chair@wirelessmanorg> as early as possile, in written or electronic form, if patented technology (or technology under patent application) might e incorporated into a draft

3 24--2 IEEE C826e-4/526r standard eing developed within the IEEE 826 Woring Group he Chair will disclose this notification via the IEEE 826 we site < 2

4 24--2 IEEE C826e-4/526r Overview An informal LDPC group has een woring on the goal of achieving consensus on a proposed LDPC code design as an optional advanced code for the OFDMA PHY Many excellent code designs have een sumitted he codes have een qualitatively and quantitatively characterized, and it is clear that a LDPC code with excellent flexiility and performance, as well as low encoding and decoding complexity, can e defined for 826e his contriution provides additional LDPC specification text Recommended ext Changes: Add the following text to 826e_D5, adjusting the numering as required: <Add a new paragraph to section Code Description, the new paragraph to precede the last paragraph of the section H is partitioned into two sections > he permutations used are circular right shifts, and the set of permutation matrices contains the z z identity matrix and circular right shifted versions of the identity matrix Because each permutation matrix is specified y a single circular right shift, the inary ase matrix information and permutation replacement information can e comined into a single compact model matrix H m he model matrix H m is the same size as the inary ase matrix H, with each inary entry (i,j) of the ase matrix H replaced to create the model matrix H m Each in H is replaced y a lan or negative value (eg, y ) to denote a z z all-zero matrix, and each in H is replaced y a circular shift size p(i,j) he model matrix H m can then e directly expanded to H <Add the material elow to the end of section LDPC encoding, directly after the sentence he LDPC codes are defined such that very low complexity encoding directly from H is possile > he following informative susection shows two such methods Direct Encoding (Informative) For the two methods, descried elow, section H 2 is further partitioned into two sections, where vector h has odd weight, and H 2 has a dual-diagonal structure with matrix elements at row i, column j equal to for ij, for ij+, and elsewhere: H h H 2 [ 2] h ( ) h ( ) h O O ( m ) he ase matrix has h (), h (m -), and a third value h (j), <j<(m -) equal to he ase matrix structure avoids having multiple weight- columns in the expanded matrix 3

5 24--2 IEEE C826e-4/526r In particular, the non-zero sumatrices are circularly right shifted y a particular circular shift value Each in H 2 is assigned a shift size of, and is replaced y a z z identity matrix when expanding to H he two s located at the top and the ottom of h are assigned equal shift sizes, and the third in the middle of h is given an unpaired shift size he unpaired shift size is Method Encoding is the process of determining the parity sequence p given an information sequence s o encode, the information loc s is divided into n m groups of z its Let this grouped s e denoted u, u u u L u, [ ( ) ( ) ( )] where each element of u is a column vector as follows u s s L s [ ] ( ) iz iz+ ( i+ ) i z Using the model matrix H m, the parity sequence p is determined in groups of z Let the grouped parity sequence p y denoted v, v v v L v m, [ ( ) ( ) ( )] where each element of v is a column vector as follows v p p L p [ ] ( ) iz iz+ ( i+ ) i z Encoding proceeds in two steps, (a) initialization, which determines v(), and () recursion, which determines v(i+) from v(i), i m 2 An expression for v() can e derived y summing over the rows of H m to otain p m ( x, ) v( ) Pp ( i, j ) u( j) P () j i where x, x m 2, is the row index of h m where the entry is nonnegative and unpaired, and P i represents the z z identity matrix circularly right shifted y size i Equation () is solved for v() y multiplying y P p( x, ), and P P since p(x, ) represents a circular shift p ( x, ) z p ( x, ) Considering the structure of H 2, the recursion can e derived as follows, where p i, j p i, j ( ) P ( ) u( j) + P ( ) v( ), i v, (2) p i, j p i, j ( i ) v( i) + P ( ) u( j) + P ( ) v( ), i,, m 2 + v (3) P z z hus all parity its not in v() are determined y evaluating Equation (2) for i m 2 Equations () and (2)to (3) completely descrie the encoding algorithm hese equations also have a straightforward interpretation in terms of standard digital logic architectures Since the non-zero elements p(i,j) of H m represent circular shift sizes of a vector, all products of the form P p(i,j) u(j) can e implemented y a size-z arrel shifter 4

6 24--2 IEEE C826e-4/526r Method 2 For efficient encoding of LDPC, H are divided into the form A B H () C D E N g N m z z N g g m z m z where A is ( m z) ( p ) C is z g N, D is z z g g expanded h and ( ), B is ( ) ( p ), and finally, E is z ( m z), is ( ) ( ) g ( N g p ) h m, respectively he asic structure of the H matrix is ( N g p ) ( N g p ), B D and D correspond to the A B C D E Further, all these matrices are sparse and is lower triangular with ones along the diagonal B and D part have the column degree 3 and D has shift value of a (a is an integer, <a<z-) B is with the shift value a of the first entry and shift value in the middle of the column his other entry is non-zero Let v(u, p, p 2 ) that where u denotes the systematic part, p and p 2 comined denote the parity part, p has length zg, and p 2 has length ( m z) (N p -g) he definition equation H v t splits into two equations, as in equations (2) and (3) 3 and 4 namely and 5 Au + Bp + p (2) ( E A+ C ) u + ( E B+ D ) p (- ) ( ) E A+ C u + -E B+ D p (3) - - Define φ : E B+ Dφ : -E B+ D and when we usewith the parity chec matrix as indicated appendix we can get, f and I hen from (34) we conclude that - p ( E A+ C ) u - (- + ) 2 - ( ) p E A C u (45) p Au + Bp (56) As a result, the encoding procedures and the corresponding operations can e summarized elow and illustrated in Fig Encoding procedure Step ) Compute Au and Step 2) Compute ( ) Step 3) Compute Cu E Au p E Au + Cu p y ( )

7 24--2 IEEE C826e-4/526r Step 4) Compute p 2 y p 2 Au + Bp Fig 2 Bloc diagram of the encoder architecture for the loc LDPC code 6