在時變通道中RS碼之錯誤和擦去式解碼的研究

Abstract

對於BCH碼或RS碼而言，錯誤和擦去式(errors-and-erasures)解碼的效能比錯誤式(errors-only)解碼好。然而，先前的研究大多討論錯誤和擦去式解碼在無記憶(memoryless)和不隨時間變化的(time-invariant)通道上。本論文主旨在研究RS碼之錯誤和擦去式解碼在時間變化通道中之應用。我們討論兩種不同的時變通道，一種為無記憶式的，另一種為有記憶式的。第一類的通道我們討論在慢跳頻系統中的干擾通道-部分頻帶干擾(partial band noise jamming)和帶頻多波道單音干擾(band multitone jamming)。第二類的通道我們討論Gilbert-Elliott (GE)通道模型。同時我們討論兩種不同系統之設計考量。第一種是慢跳頻/MFSK調變RS編碼系統，另一種是正交調變/RS編碼通訊系統。 在慢跳頻/MFSK調變RS編碼系統中，前人的研究只考慮完美的交錯(interleaving)和部分頻帶干擾通道，而RS碼在GE通道的應用上並沒有人討論錯誤和擦去式解碼的效能。因此，我們研究的主要目的(i)在干擾通道上我們分析有限交錯的影響和討論系統在帶頻多波道單音干擾通道的效能，(ii)我們分析錯誤和擦去式解碼在GE通道的效能，並且推導解碼錯誤率與通道，信號，不同碼之間的關係。此外我們提出利用兩個門檻(two-threshold)的方式來增加改錯能力。兩種門檻的方法需要用到通道與信號的參數，我們亦提出簡單而有效率的演算法來估計這些參數。 最後我們列出了數值結果來比較RS碼錯誤和擦去式解碼的有效性及跳頻率，交錯器大小和碼率(code rate)之間的關係以提供系統設計者參考。

The advantage of errors-and-erasures (EE) decoding of BCH or RS codes over conventional errors-only (EO) decoding has long been recognized. Most literature, however, deals with the applications of EE decoding in memoryless and time-invariant channels. This thesis intend to examine the effect of time-varying channels on the performance of EE/RS decoders. We consider two classes of time-varying channels, one is memoryless and the other one with memory. The first class of channels is slow frequency-hopped jammed channels in which a partial-band noise jammer (PBNJ) or a band multitone jammer (BMTJ) is present. The second class of channels is Gilbert-Elliott (GE) channels which had been shown to be suitable for characterizing the behavior of various fading multipath channels. Noncoherent MFSK signals, which are known to be very effective against jamming, are used in jammed channels while orthogonal Walsh signals with noncoherent detectors are employed in GE channels. In the RS-coded SFH/MFSK system, earlier investigations on its anti-jam (AJ) capability assumed an infinite interleaving length and concentrate on PBNJ only while those of GE channels did not consider EE decoding. We extend previous efforts by (i) analyzing the effect of finite interleaving length and the impact of BMTJ for jammed channels and (ii) examining the EE decoders' performance in GE channels. The codeword error probabilities as a function of various channel, signal and code parameters are given. Besides, the need to use two-threshold (2T) erasure-insertion methods (EIM) is justified and their performance is evaluated. The use of 2T EIMs necessitates the detection of the channel state and the estimation of several additional channel and signal parameters. Simple and effective detection and estimation algorithms are provided as well. Numerical examples are presented to examine the extent of the improvement of an EE decoder can bring about and to compare the effectiveness various EIMs and jammer types. Our numerical results are also useful in exploring the relationships and tradeoff among the hop rate, the interleaver size and the code rate.