隱藏式馬可夫通道下的RS碼之錯誤與擦去式解碼

Abstract

如果有適當的擦拭偵測(erasure detection)，錯誤和擦去式（errors-and-erasures, EE）解碼法會有比錯誤式（error-only, EO）解碼法更好的改錯效能。然而先前的研究大多集中在無記憶（memoryless）和非時變（time-invariant）通道下EE或EO解碼器的性能分析。本論文旨在探究一些時變（time-variant）通道中RS碼之EE式解碼器的效能。 從設計解碼器的觀點來看，通訊系統中「通道」這個部分一般是指編碼器的輸出端到解碼器的輸入端。在前人的研究中，雖然發現Gilbert模型在預測某些時變通道的解碼效能方面有令人滿意的結果。但是我們不難發現在一些情況下使用Gilbert模型是不夠充足也不適當的。本論文延伸前人的結果，就一般性隱藏式馬可夫通道對EE解碼器設計的影響做了有系統的研究。 在調變方法方面，我們考慮了兩種非同調的多維正交調變，一種是慢跳頻/MFSK信號，另一種是Walsh編碼的信號。我們除了提供EE式解碼的表現及其可能帶來的改善程度之數值預測外，也探討了交錯器大小，跳頻速率和編碼率等對解碼器表現的影響。

The advantage of errors-and-erasures (EE) decoding of 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 intends to examine the performance of EE-RS decoders under several time-varying channels. From the viewpoint of decoder design, the `channel' of concern is the part of a communication system with the encoder output as the channel input and the decoder input as the channel output. Although decoder performance evaluation using a two-state Markov channel model (i.e., Gilbert model) has recently been proposed and shown to render reasonably satisfactory prediction, this thesis finds that there are cases where the Gilbert model is deemed inappropriate and insufficient. We thus extend earlier investigations to study the impact of a general class of hidden Markov channels on EE decoder design. The associated modulation schemes under consideration are two noncoherent M-dimensional orthogonal waveforms: frequency-hopped MFSK and Walsh-coded signals. Numerical examples are presented to (i) examine the extent of the improvement of an EE decoder can bring about, (ii) explore the effect of the interleaver size, the hop rate and the code rate.