Future Work

The normalization factor β and the offset factor α influence the decoder BER performance quite large. Through our research, we found that our proposed dynamic normalized-offset technique and dynamic normalization technique [23] have

similar BER decoding performance. The other idea is to dynamically adjust the two factors α and β in the same time. The threshold values of α and β may be obtained through simulations. Moreover, as mentioned in Appendix A, there are a lot of different codeword lengths and code rates in 802.16e standard. Our future work is to integrate the multi-mode 802.16e LDPC decoder design.

Appendix A

LDPC Codes Specification in IEEE 802.16e

OFDMA

The LDPC code in IEEE802.16e is a systematic linear block code, where k systematic information bits are encoded to n coded bits by adding m= −n k parity-check bits. The code-rate is k n/ .

The LDPC code in IEEE802.16e is defined based on a parity-check matrix H of size m n× that is expanded from a binary base matrix H with size _b m_b× , where n_b m= ⋅z mb and n= ⋅ . In this standard, there are six different base matrices. One z n_b for the rate 1/2 code is depicted in Figure A.1. Two different ones for two rate 2/3 codes, type A is in Figure A.2 and type B is in Figure A.3. Two different ones for two rate 3/4 codes, type A is in Figure A.4 and type B is in Figure A.5. One for the rate 5/6 code is depicted in Figure A.6. In these base matrices, size n is an integer equal to _b 24 and the expansion factor z is an integer between 24 and 96. Therefore, we can compute the minimal code length as n_min =24 24 576× = bits and the maximum code length as n_max =24 96 2304× = bits.

For codes 1/2, 2/3B, 3/4A, 3/4B, and 5/6, the shift sizes ( , , )p f i j for a code size corresponding to the expansion factor z are derived from _f p i j , which is the ( , ) element at the i-th row, j-th column in the base matrices, by scaling ( , )p i j proportionally as

0 permutation matrix. The permutation matrix represents a circular right shift by

( , , )

Figure A.1 Base matrix of the rate 1/2 code

Rate 2/3 A code:

Figure A.2 Base matrix of the rate 2/3, type A code

Rate 2/3 B code:

Figure A.3 Base matrix of the rate 2/3, type B code

Rate 3/4 A code:

Figure A.4 Base matrix of the rate 3/4, type A code

Rate 3/4 B code:

Figure A.5 Base matrix of the rate 3/4, type A code

Rate 5/6 code:

Figure A.6 Base matrix of the rate 5/6 code

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自 傳

邱敏杰，1982 年 6 月 15 日出生，高雄縣人。2004 年自國立暨南 國際大學電機工程學系畢業，隨即進入國立交通大學電子研究所攻讀 碩士學位。研究興趣為通訊系統與數位信號處理，碩士論文題目為低 密度對偶檢查碼解碼演算法之改進以及其高速解碼器架構之設計。