結合錯誤更正與通道估計的系統化編碼設計及其最大概度解碼

Abstract

傳統通訊系統是使用獨立的訓練序列於接收機來估計通道參數，之後再使用該通道參數來對錯誤更正碼進行解碼。在某些應用上，接收機通道估計值可能需要耗費極高的計算複雜度來獲取，即便如此甚至可能還不能達到所需要的精準估計。因此，非同調系統在此時就成為一個解決方案。基於上述的背景，本論文討論當傳送機與接收機兩者皆對通道參數完全一無所知的環境下之通道編碼設計，我們也提出一個相對應的有效率解碼演算法。

事實上，結合通道估計與錯誤更正的編碼方式最近受到相當的關注並且被視為對抗多路徑衰減的重要技術之一。與一般具有個別獨立的通道估計與錯誤更正裝置相較，在相同的碼率下，模擬證明結合考量通道估計的編碼設計可以顯著增進系統效能。然而，這類編碼的實際使用有個主要障礙，由於目前設計都是經由電腦搜尋而來，以至於所獲得的碼是不具結構，故亦無法有效率的解碼，導致複雜度最高的完全搜尋演算法成為唯一的解碼方法，所以解碼複雜度將會隨著碼的增長而巨幅增加。在本論文中，我們提出一個系統化的建碼方法來設計具有明確結構的結合通道估計與錯誤更正的編碼，用於多輸入多輸出通道的延伸設計也將會被討論。模擬顯示我們所提出的編碼與電腦搜尋所獲得最佳碼兩者效能幾乎不分軒輊。再者，基於系統化建碼所具備的結構，我們可以推導出具有遞迴關係的最大概度解碼量度，進而可以使用以碼樹為基礎的循序解碼演算法來 做最大概度解碼，因此可以避免使用完全搜尋解碼而大幅降低解碼複雜度。

A traditional communication system uses separate training sequence for the estimation of channel state information (CSI) at the receiver. This channel estimation will then be used as a base for error correction through channel codes. In applications that channel estimation at the receiver is either of infeasibly high complexity or statistically impossible, noncoherent system design apparently becomes the due selection. At this background, we study the coding scheme that can be applied in an environment that the channel coefficients are completely unknown to both the transmitters and receivers. We subsequently investigate efficient decoding algorithms for our proposed codes.

In fact, the coding technique that combines channel estimation and error correction has received attention recently, and has been regarded as a promising approach to counter the effects of multi-path fading. It has been shown by simulation that a proper code design that jointly considers channel estimation can improve the system performance subject to a fixed code rate as compared to a conventional system which performs channel estimation and error correction separately. Nevertheless, the major obstacle that prevents the practice of such coding technique is that the existing codes are mostly searched by computers, and subsequently exhibit no apparent structure for efficient decoding. Hence, the operation-intensive exhaustive search becomes the only decoding option, and the decoding complexity increases dramatically with codeword length. In this dissertation, a systematic construction is derived for a class of structured codes that support joint channel estimation and error correction. The extension designs that take into consideration the varying characteristic of channels and multiple-input multiple-output channels are also discussed. Simulations show that our codes have comparable performance to the best simulated-annealing-based computer-searched codes. Moreover, the systematically constructed codes can now be maximum-likelihoodly decoded with respect to the unknown-channel criterion in terms of a newly derived recursive metric for use by the priority-first search decoding algorithm. Thus, the decoding complexity is significantly reduced as compared with that of an exhaustive decoder.