通道編碼為現今無線通訊中一大熱門議題。在嚴重雜訊與有限頻寬的無線衰減通道中傳輸，通道編碼為必要的技術。其中低密度同位檢測碼已被證實擁有非常好的效能。
多根傳送與接收天線的無線通訊中，空時區塊碼是利用多根傳送天線，提供多樣性增益來降低錯誤率。但在本論文中，我們是採用奇異值拆解機制讓錯誤率更有效地降低，通道響應使用奇異值拆解並搭配前置濾波器與後置濾波器使得系統之傳輸路徑轉成互相獨立且平行的傳輸路徑。因此，本論文利用二的冪次有限域之非二位元低密度同位檢測碼系統以及奇異值拆解機制並加入正交分頻多工系統來消除無線傳輸中由於多路徑影響所產生的訊號間干擾。
低密度同位檢測碼與正交分頻多工系統的結合，須搭配功率分配機制使每一個子通道訊雜比相同，幫助系統之效能更為提升，這是本論文最主要的議題。並由功率分配衍生出子通道選擇機制，捨棄通道響應較差的子通道傳輸訊息，而且子通道選擇可幫助我們把資料傳輸速率與錯誤率之效能做最佳的選擇。另外，本論文建構出最佳化子通道選擇與調變機制的方法，此方法可以在已知通道響應及系統限制的錯誤率與訊雜比的條件下，推論出最佳的調變機制以得到最高傳輸速率與保留子通道數目以及每一個被保留的子通道所需之能量。

Channel coding is one of the most popular topics of today’s wireless communications. It is an essential technique when the channel is noisy, fading and has inter-symbol interference (ISI). Among the channel coding techniques, LDPC (low density parity check) codes have been shown to exhibit excellent performance.
When there are multiple transmitting and receiving antennas in wireless communication, using the space-time block code is a popular technique because it provides diversity gain and thus reduce BER. However, in this thesis, we will try a SVD-based technique and compare it to the space-time block code. The SVD computation gives us a pre-filter and a post-filter so that when they are cascaded with the channel, the overall system becomes several parallel paths that are independent to each other. Then, we use non-binary LDPC codes and OFDM systems in this SVD-decomposed channel.
In combining OFDM system and LDPC codes, power allocation is the main topic of this thesis. Power allocation makes every subchannels have the same SNR (signal-to-noise ratio). One extended technique from power allocation is subchannel selection, in which very bad subchannels are discarded. Subchannel selection helps us to make the best choice between data rate and BER (bit error rate) performance. In addition, we construct a scheme to determine the modulation scheme, number of subchannels to be retained and the energies of every retained subchannel needs when the channel state information, the acceptable BER, and the SNR are specified.

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