格狀式空時碼的設計與性能模擬的關聯性分析

Performance Analysis Issue in Designing Good r-Space-Time-Trellis-Code

劉宗慶(Tsung-Ching Liu)

《華岡工程學報》 19期 (2005/06) Pp. 101-106

https://doi.org/10.29987/CCUHKJE.200506.0010

摘要

有別於一般疲乏式搜尋，我們曾提出了一種2-STTC的解析性設計的法則[1]，該設計的碼優於目前所知的碼。但合乎該法則的碼有476*476種（相比於疲乏式搜尋需上億種），且並無解析性的方法得知那一組是最好的，雖然我們亦提出一種非對稱調變架構去提高碼增益以最佳化[2]，但仍無法解析性證實每一組皆能達到同樣的最佳性能，因此仍需某種範圍的疲乏式搜尋。在此我們擴大討論於位元錯誤率(BER)而非碼框錯誤率(FER)時，Tarokh的Chernoff Bound所算得的兩個準則的有效性與爭議性（之前符合該兩項準則的模擬皆使用FER），也就是原先最佳碼的搜尋是根據差分矩陣的特徵值乘積（碼增益）來判定，而不需Monte Carlo模擬來尋找（Monte Carlo模擬只是當找到後之驗證用），探討BER時，於我們所設計的476*476種碼中的搜尋，為了加快模擬的速度使用Importance sampling以取代Monte Carlo模擬，以尋求最佳碼。其中Large Deviation Technique被用於biased density的選取，模擬的結果印證2-STTC Chernoff bound 設計的有效性，並可提供進一步分析r-STTC r為任意值的設計參考。

並列摘要

As a promising analytic design strategy studied in [1], the design of 2-Space-Time Trellis code by using function range set expansion shows its superiority among the existing codes. The designed codes can also be further optimized its coding gain by using asymmetric constellation. However, the codes obtained by function range set expansion in the 4 states case amounts to 476*476, though those are better than the currently existing codes, cannot be analytically decided which one is the best. And also no clues show that all of them can be optimized to the same performance by using asymmetric constellation. Therefore light exhaustive search by computer is needed. Furthermore, when we deal with the case that under Bit Error Rate (BER) (not the Frame Error Rate (FER)) the Tarokh's rule using the Chernoff bound may not be effective. So the exhaustive search by merely using the eigenvalue product criterion is not applicable which renders the Monte Carlo simulations together with the necessary decoding has to be used. We deal with the Importance Sampling (IS) method used in the STTC for fast simulation. While for rare event the Large Deviation Technique can be applied for the biased density treatment in the IS, all these works (Performance analysis) will complete and justify the designed work of 2-STTC in [1] and also can be used as an extension to the r-STTC design when r is greater than 2.