跨封包極化編碼混合式自動重送請求規約之設計與效能分析

Abstract

吞吐量是用來衡量混合式自動請求規約之主要效能指標參數。這個參數對於使用的通道編碼的封包錯誤率會很敏感，尤其是在低信號雜音比區。為改善吞吐量效能，我們除了要選擇好的通道編碼外，還要去改進傳統混合式自動請求規約的設計。極化碼(polar code)是唯一有具體結構可以達到任何對稱的二元通道(binary discrete memoryless channel, B-DMC)容量的改錯碼。但若碼長有限，雖然在低信號雜音比(SNR)時它的封包錯誤率仍優於低密度奇偶校驗碼，但在高SNR區前者的效能就較差。幸好此區的封包錯誤率相對的低，對吞吐量的效能的影響不明顯，因此在本論文中我們選用極化碼作為規約的前向錯誤更正用。 我們所提的規約得在每次重傳將部份舊訊息位元與新訊息一倂編碼。亦即每當解碼後的封包無法通過循環冗餘校驗(CRC)時，部分的舊訊息位元會和新的訊息位元一起編碼，這個過程稱為重複編碼而此流程稱為跨封包混合式自動重送請求規約。因重傳時只需傳新的訊息位元和奇偶校驗位元，所以重傳的舊封包的位元數也比較少。如果重複編碼的封包能夠成功解出，重複編碼的位元可以用來幫助重解之前無法解對的封包。我們又進一步將訊息位元分割成數塊並個別做CRC編碼以便在解碼時可分別檢查是否已解碼成功。此外，我們對所提出的規約的吞吐量效能進行統計分析。電腦模擬顯示我們新設計的規約之吞吐量在低信號雜音比時優於結合LDPC碼的規約和極化穿刺碼(punctured polar code)的遞增冗餘(incremental redundancy)規約，多區塊分割與CRC個別檢驗也有助於縮短解碼時程並改善其封包錯誤率，且統計分析的預測的確與真正的規約表現一致。

Throughput is one of the most important performance metric for an HARQ system.The achievable rate of such a system is determined by the coding rate and the frame error rate (FER) performance of the channel codes used. To improve the throughput performance, we should not only select a powerful channel code but also have a proper retransmission procedure and decoding schedule. Polar codes have been proved to be capacity-achieving codes for binary symmetric channels. However, the FER performance of a finite length polar code outperforms a LDPC code of the same rate and comparable length at low SNRs but in general yields inferior performance when SNR is high and retransmission events are rare. Based on this observation, we develop an efficient polar code based increment redundant (IR) HARQ protocol. The proposed polar coded HARQ differs from the conventional IR-HARQ in that retransmission packets are coupled algebraically. The inter-packet coupling is established through (re-)encoding a portion of the message bits of the failed packet along with the new message bits to produce a retransmission codeword. A systematic recoding method as well as the corresponding decoding schedules are proposed. We call this new scheme as an inter-packet polar coded (IPPC) HARQ and verify that it provides improved throughput performance at the low SNRs against an LDPC coded IR-HARQ protocol and the conventional puncture based IR-HARQ using the same polar code. We also present a Markov analysis on the throughput performance of the proposed IPPC HARQ system. The accuracy of our analysis is confirmed by computer simulations as well.