纜線數據機的更誤解碼與渦輪等化器研究

Abstract

由於高速傳輸需求的增加新的科技遂興起，一種基於正交調幅調變器(quadrature amplitude modulation)纜線數據機(cable modem)的網路標準ITU-T J.83B產生了。 本論文研究基於ITU-T J.83B主要包含兩個方面：更誤解碼與渦輪等化器。 ITU-T J.83B的前置更誤碼主要包含四個層次，分別為里德-所羅門碼(Reed-Solomon code)，交錯器(interleaver)，隨機性發生器(randomizer)，和格狀編碼調變器(trellis-coded modulation)。我們首先分別對於每個層次分析它們的特性。對於里德-所羅門碼，我們得到它的錯誤檢查矩陣和理論錯誤率。對於格狀編碼調變器，我們解釋它具有的旋轉不變性，也藉由既有的編碼架構展延出1024-正交調幅調變器。此外，我們透過其穿孔迴旋碼(punctured convolutional code)的重量分配頻譜得到她的理論錯誤率。最後，我們在模擬里德-所羅門碼和在白色高斯雜訊通道下的格狀編碼調變器，這些結果和分析值在高的訊號雜訊比下是相當接近的。 關於渦輪等化器，我們結合格狀編碼調變器和使用最小平均平方演算法(least mean square)及多模量演算法(multi-modulus algorithm)的等化器得到兩種渦輪等化器的演算法。我們在纜線的通道下模擬而結果證明了使用軟性輸出的維特比解碼器(soft-output Viterbi decoding)可以獲得比傳統維特比解碼器多0.2 dB增益。

Due to the demand for high data transmission rate, a cable modem networks standard, ITU-T J.83B, based on QAM (quadrature amplitude modulation) technique is produced. This work mainly contains two parts established on ITU-T J.83B: the error correction decoding and turbo equalization for cable modem receivers. For forward error correction, we analyze the property of the coding schemes respectively containing Reed-Solomon code, interleaver, randomizer and trellis-coded modulation (TCM). As to the extended RS code, we derive its parity check matrix, symbol error rate bound. For the TCM we explain the rotational invariance characteristic of the QAM mapper, and also expand the exiting QAM modes scheme to 1024-QAM. Besides, we acquire its upper bound through the weight distribution spectrum of the punctured convolutional code and modulation mapping. Finally, we simulate the RS code and the TCM under AWGN, and the analytic results are close to the simulation. Concerning the turbo equalization, we combine the TCM and decision feedback equalizer using least mean square and multi-modulus algorithm to obtain two turbo equalization algorithms. We simulate these algorithms in the cable modem channel, and the results show that soft-output Viterbi decoding gains more than Viterbi algorithm in the decoding of TCM by 0.2 dB.