適用於記憶性通道之訊源通道編碼研究

Abstract

向量量化是目前常見的影音壓縮處理技術，其目的在有效運用有限的網路傳輸頻寬與儲存容量，但通道失真會改變其編碼輸出的碼字索引進而影響通訊品質。本論文之目的旨在建立有效對抗無線通道失真的合併訊源通道編/解碼機制，加強其錯誤隱蔽功能以維持位元傳輸的強健性。但目前相關研究主要集中於無記憶性二元對稱通道，並不足以反應室內及室外無線通訊環境因多路衰減所衍生的叢發位元錯誤。因此，我們首先建立具有描述叢發位元錯誤能力的有限狀態馬可夫鏈通道模型，不僅能有效區隔其錯誤發生屬性也能反映不同程度的通道記憶特性。在編碼機制方面，我們成功地發展哈達瑪轉換的分群理論，並配合先前建立的通道模型進行分析，快速實現碼字索引指定的設計。至於限定向量碼書的建構，首先藉由哈達瑪分群理論發展一通道匹配的區段碼選擇機制，而對於相關對映矩陣的配置，我們重新規劃其組成向量的能量分布成為一非線性參數預估問題，並參考基因法則建立其最佳化訓練的隨機搜尋演算機制。進一步分析發現訊號經量化編碼所得的碼字索引序列仍存在諸多殘存的重覆訊息，依據接收索引值而查表輸出的傳統解碼機制仍有大量的改善空間。因此在解碼機制部分，本論文同時考慮存在於單一索引內及相鄰索引間位元組合的記憶特性，建立其區塊通道轉移機率的數學推導，再輔以索引序列殘存重覆訊息的運用，成功發展出一通道匹配的最小均方誤差解碼演算法。另外，我們亦將推導的區塊通道轉移機率成功地應用於串接式向量量化/迴旋解碼器，以提昇其對抗雜訊的能力。實驗結果證實本論文提出的哈達瑪轉換分群理論以及區塊通道轉移機率的數學推導，可以充分地利用通道記憶特性來改善合併訊源通道編/解碼機制，進而達到對抗無線傳輸雜訊之目的。

This study investigated the joint source-channel coding techniques for use with vector quantization (VQ) over channels with memory. Most previous research concentrated on memoryless binary symmetric channels, despite evidence showing that transmission errors encountered in indoor and outdoor wireless channels exhibit various degrees of statistical dependencies. To compensate for this shortage, the proposed joint source-channel coder design is based on Gilbert's two-state Markov chain model that better characterizes the observed error bursts. The first part of this study presents two encoding approaches that employ a Hadamard framework for analyzing VQ transmission over noisy channels. We proposed an index assignment algorithm in which pairwise swaps of VQ codevectors were arranged in accordance with Hadamard transform of channel transition probabilities. The decomposition of mapping vector indices becomes especially favorable when the complexity of searching the VQ for optimal indices is of primary concern. Also proposed is a new design approach to constrained VQ codebook design given by a linear mapping of a block code. The Hadamard transform proves effective in describing the VQ codebook, and use of it facilitates the search for a block code which better matches the expected channel condition. To optimize the mapping matrix to a given block code, we formulate its design as a combinatorial optimization problem that is amenable to the application of real-coded hybrid genetic algorithm. The second part of this study is concerned with the decoding algorithms having higher robustness against bursty channel errors. We developed a recursive algorithm for computing the a posteriori probability of a transmitted index sequence, and illustrated its performance in minimum mean-square error (MMSE) decoding of VQ data. The decoder is based on the Gilbert channel model that allows the exploitation of both intra-block and inter-block correlation of bit error sequences. Also proposed is a memory-enhanced convolutional decoder for use with a concatenated VQ/convolutional coding system. Simulation results indicated that with the aid of Gilbert channel characterization the joint source-channel coding algorithms can be developed to better track the intrinsic natures of channel errors.