在平行高斯通道下考慮固定碼長與碼率的編碼條件之吞吐量基準資源分配方式

Abstract

傳統探討平行無記憶性高斯通道資源分配的問題都是以最大化整體通道容量為目的，而所推得的最佳能量分配法為著名的充水(Water-Filling)演算法。但是此一能量分配法則的問題為，各管道達到最佳能量分配的碼率是總能量的函數，所得的最佳碼率常是一個實作上不易實現的實數，同時隨著訊號雜訊比增大還需不斷更換最佳編碼方式，如此才能達到原本設定的最大通道容量，另外最大通道容量是成立於碼長趨近於無限大的情況，在實際有限的碼長下，此種能量分配方式是否可以達到最佳系統效能(即系統有效吞吐量)值得探討，故而本論文直接探討在有限碼長、固定編碼方式下以達到最大有效系統吞吐量為目的的傳送能量分配策略。結果顯示，我們所提出的資源分配方式可以以類似充水演算法的概念以圖形詮釋，並且幾乎達到最大系統有效吞吐量。

The common criterion used in the power allocation problem for parallel memoryless Gaussian channels is to maximize overall mutual information (namely, to achieve the ca- pacity), resulting in the well-known water-filling policy. Such a capacity-achieving power allocation, although theoretically interesting and beneficial in conceptually elucidating the behavior of coding systems, does not match well with practical situations as capacity is an asymptotic rate requiring the codeword length to grow to infinity. In addition, the overall system capacity can only be achieved when the coding scheme of each channel is optimally and continuously adapted to the allotted power. However in a practical system, the adopted codes are by no means optimal in terms of achieving capacity and have only a finite number of rate choices. Furthermore, a common quantity of interest is the effective system through- put. In light of these observations, we study in this paper the problem of determining the power allocation strategy for a system of coded parallel Gaussian channels with the objective of maximizing effective throughput under finite-length and fixed-rate coding constraints. An approximating formula of the system’s effective throughput is proposed for the case of con- volutional codes and used to identify the optimal power allocation for each parallel channel. Our results show that the proposed power allocation policies can be graphically represented as a variation of the water-filling principle and achieves a near-optimal throughput.