1. Complexity analysis for decoding SFBCH Document Number: S80216m-09/0732 Date Submitted: 2009-03-09 Source: Changlong Xu,Hongmei Sun,Jong-Kae(JK) Fwu, Email: {hongmei.sun, changlong.xu, jong-kae.fwu }@ intel.com Hujun Yin, Roshni Srinivasan, Sassan Ahmadi Intel Corporation Re: Call for Comments on Amendment Working Document, IEEE 802.16m-09/0012 Target topic: UL PHY Control Base Contribution: This is the base contribution. Purpose: Discussion and adoption for 802.16m AWD Notice: This document does not represent the agreed views of the IEEE 802.16 Working Group or any of its subgroups. It represents only the views of the participants listed in the “Source(s)” field above. It is offered as a basis for discussion. It is not binding on the contributor(s), who reserve(s) the right to add, amend or withdraw material contained herein. Release: The contributor grants a free, irrevocable license to the IEEE to incorporate material contained in this contribution, and any modifications thereof, in the creation of an IEEE Standards publication; to copyright in the IEEE’s name any IEEE Standards publication even though it may include portions of this contribution; and at the IEEE’s sole discretion to permit others to reproduce in whole or in part the resulting IEEE Standards publication. The contributor also acknowledges and accepts that this contribution may be made public by IEEE 802.16. Patent Policy: The contributor is familiar with the IEEE-SA Patent Policy and Procedures: and.http://standards.ieee.org/guides/bylaws/sect6-7.html#6http://standards.ieee.org/guides/opman/sect6.html#6.3 Further information is located at and. :http://standards.ieee.org/board/pat/pat-material.htmlhttp://standards.ieee.org/board/pat S80216m-09/0732

2. 2 Outline: Complexity for linear block code using MLD Complexity for linear block code using trellis without sectionalization Complexity for WAVA Complexity comparison between linear block code using trellis and TBCC using WAVA Further discussion

3. 3 1. Complexity for linear block code using MLD Consider (N, K) cyclic linear block code –Number of add 2 K (N-1) –Number of compare (real) 2 k -1 –Number of compare (binary) 2 K N

4. 4 2. Complexity for linear block code using trellis without sectionalization Consider (N, K) cyclic linear block code [1] –Number of add (N-2K+4)*2 k -4 –Number of compare (real) 2 k -1 –Number of compare (binary) < (N-2K+4)*2 k -4 The N-section trellis for an (N,K) linear block codes can be generated from generate matrix or parity check matrix. Please refer to the chapter 4 “State labeling, trellis construction procedures and trellis symmetry” in [1] for the detailed procedures.

5. 5 3. Complexity for WAVA Considering codeword length N, coding rate 1/R, with Constraint length L, complexity of VA –Number of add N/R*2 L *2*(R-1) –Number of compare (real) (N/R+1)*2 L –Number of compare (binary) < N/R*2 L *2*R=2N*2 L Complexity of WAVA –Suppose max M iteration –Complexity will be M*complexity of VA

6. 6 4. Complexity comparison between linear block code using trellis and TBCC using WAVA AlgorithmNumber of addNumber of compare (real) Number of compare (binary) WAVAM*N/R*2 L *2*(R-1) M*(N/R+1)*2 ^L M* 2N*2 L MLD 2 K (N-1)2 k -1 2 K N Trellis without sectionaliz ation (N-2K+4)*2 k -4 2 k -1 <(N-2K+4)*2 k -4

7. 7 Complexity comparison for WAVA and Trellis Parameters for Trellis –N = 60, K = 7,8,…,12 –N = 30, two block of K = 6, 7, …, 12 Parameters for WAVA –N = 60, R = 5, constraint length L = 7 (128states), M = 4 –For simplification, do not consider complexity of puncturing –For simplification, complexity of (60,12) is used for different number of information bits Among the three kinds of operations: add, compare (real), and compare (binary), the complexity of add is dominant. Thus, only add operator is necessary to be compared.

8. 8 Complexity comparison for WAVA and Trellis

9. 9 Comparison Results Complexity of WAVA is lower for cases of 11,12, 22, 23, 24 information bits Complexity of Trellis decoding is lower for all the other 13 cases The average trellis decoding complexity is lower than that of WAVA around 20 %.

10. 10 Further discussion The decoding complexity of trellis can be further reduced using bit position permutation and sectionalization[1]. Linear block codes can be represented by a tail-biting trellis [2]. The trellis complexity of a tail-biting trellis is usually smaller than that of conventional trellis [2]. –This complexity reduction is attributed to the additional degree of freedom achieved by not constraining the diagram to begin in the all zero state.

11. 11 Reference 1.Shu Lin, Tadao Kasami, Marc Fossorier, “Trellis and trellis-based decoding algorithms for linear block codes,” Kluwer Academic Publishers, Norwell, MA, USA. 1998Shu LinTadao KasamiMarc Fossorier 2.Ilan Reuven and Yair Beery, “Tail-biting trellises of block codes: trellis complexity and Viterbi Decoding complexity”, IEICE Trans. Fundamentals, Vol.E82-A, No.10, Oct. 1999.