IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 57, NO. 11, NOVEMBER 2009 3177 Transactions Letters Policy Allocation for Transmission of Embedded Bit Streams over Noisy Channels with Feedback Jinshi Qiu and Amir H. Banihashemi, Senior Member, IEEE Abstract—An efficient policy allocation algorithm for the transmission of embedded bit streams over noisy channels with feedback is proposed. The transmission is based on the type- II hybrid ARQ/FEC protocol and uses a nested sequence C of channel codes to protect the packets. There are also constraints on the total bit budget and on the allowed number of retrans- missions per packet. The allocation algorithm assigns different protection policies, each policy being a subset of C, to different packets to maximize the average number of correctly received source bits. We study the performance and the complexity of the proposed scheme through the transmission of images encoded by JPEG2000 over mobile channels with correlated Rayleigh fading. We demonstrate by simulations that the proposed multiple- policy scheme provides significant improvements over a purely FEC scheme with no feedback and also the existing fixed-policy schemes. Our results show that feedback is particularly helpful for poor channel conditions and that the proposed scheme is very robust against changes in the channel signal-to-noise ratio (SNR) and the mobile speed. Index Terms—Joint source-channel coding, unequal error pro- tection, feedback channels, noisy channels, policy allocation, rate allocation, hybrid ARQ/FEC protocols, rate-compatible codes, image transmission, JPEG2000, fading channels. I. I NTRODUCTION AND MOTIVATION E MBEDDED bit streams are generated by many source coders to allow the progressive reconstruction of the source at different bit rates from the prefixes of a single bit stream. In a packet transmission system, such bit streams are packetized and transmitted over noisy channels. To protect the packets against channel errors, one can use forward error correction (FEC), automatic repeat request (ARQ), or a hybrid FEC/ARQ scheme. While in the absence of a feedback channel, FEC is the only possible choice, for channels with feedback, ARQ or hybrid schemes can be employed as well. In particular, the type II hybrid ARQ/FEC scheme can provide higher throughputs compared to the other protocols [1]. There is a vast literature on the transmission of embedded bit streams over noisy channels in a joint source-channel Paper approved by F. Alajaji, the Editor for Source and Source/Channel Coding of the IEEE Communications Society. Manuscript received September 11, 2008; revised January 8, 2009. J. Qiu was with the Broadband Communications and Wireless Systems (BCWS) Centre, Dept. of Systems and Computer Engineering, Carleton University, 1125 Colonel By Drive, Ottawa, Ontario, Canada K1S 5B6. He is now with RIM, Waterloo, Ontario, Canada (e-mail: jinshiq@gmail.com). A. Banihashemi is with the Broadband Communications and Wireless Systems (BCWS) Centre, Dept. of Systems and Computer Engineering, Carleton University, 1125 Colonel By Drive, Ottawa, Ontario, Canada K1S 5B6 (e-mail: ahashemi@sce.carleton.ca). Digital Object Identifier 10.1109/TCOMM.2009.11.080460 coding (JSCC) framework using FEC [2]-[11]. For such a framework, due to the difference in importance of the packets, the unequal error protection (UEP) of the packets usually results in a better end-to-end performance compared to the less sophisticated equal error protection (EEP) [2]. In the context of UEP, rate-compatible (RC) codes are often used for their advantages including a single encoder/decoder pair for the whole sequence of codes [2]-[7], [9], [10]. In addition to having a low complexity, RC schemes provide an efficient framework for the transmission of information using type II hybrid ARQ/FEC protocols, where incremental parity bits of the next lower rate code are transmitted in response to a negative acknowledgement (NACK) from the receiver. The NACK signal indicates the failure of the last code in correcting the errors in the transmitted packet. As an essential part of a JSCC with FEC and UEP, one would have to solve the problem of assigning channel codes of different rates to different source packets under a constraint on the total bit budget or the total transmission rate. This problem is called rate allocation. Well-known cost functions for rate allocation are the average mean squared error (MSE) distortion, the average peak signal-to-noise-ratio (PSNR), and the average number of correctly received source bits [2], [3]. We indiscriminately refer to the corresponding optimal solutions for the first two cost functions as distortion optimal, and to the optimal solution for the last cost function as rate optimal. While the rate optimal solution has a lower complexity and enjoys other advantages such as independence from the source, e.g., the image, and from the source coder performance, it results in some performance loss compared to the distortion optimal solution [2], [3]. Distortion and rate optimal solutions for variable-length transmitted packets using FEC were proposed in [2]. An efficient distortion optimal solution for fixed-length transmitted packets was recently de- rived in [12]. Suboptimal approaches for finding the distortion optimal solution with FEC were also proposed in [3], [4], [6], [8]-[11]. While much research has been devoted to the problem of JSCC and the associated rate allocation problem in the context of FEC, the size of the literature on JSCC over channels with feedback is much smaller (examples are [5], [13]-[17]). This is while feedback routes are available in many existing systems including standard wireless channels. It is therefore of great practical interest to study the JSCC problem under ARQ or hybrid ARQ/FEC protocols and examine the full 0090-6778/09$25.00 © 2009 IEEE