A Hybrid-ARQ Protocol Using Channel Output Feedback Zachary Chance, Mayur Agrawal, David J. Love, and Venkataramanan Balakrishnan School of Electrical and Computer Engineering Purdue University, West Lafayette, IN 47907, USA {zchance, magrawal}@purdue.edu, {djlove, ragu}@ecn.purdue.edu Abstract—In recent years, hybrid-automatic repeat re- quest (ARQ) protocol has become one of the most popular packet transmission schemes. Hybrid-ARQ aims to combine the advantages of forward error correction codes with the traditional ARQ scheme to increase the reliability and throughput of the network. In this paper, we look at improving upon this performance for block fading channels (e.g., Rayleigh, Rician, etc.) by using feedback information from the destination; in particular, using a turbo code [1] in conjunction with a proposed linear feedback code under additive white Gaussian noise. The scheme is developed for the general case of multiple antennas at both the transmitter and receiver, and is analyzed for varying amounts of feedback information sent from the destination to the source. Simulations are presented to illustrate the gains in throughput offered by the proposed scheme over the existing ones. Index Terms—linear feedback, hybrid-ARQ, packet transmis- sion, MIMO fading channel, turbo coding I. I NTRODUCTION The need to reduce latency and improve the throughput of the communication networks has led to the proposal of variety of protocols. The traditional automatic repeat request (ARQ) com- bined with forward error correction (FEC) codes resulted in the development of hybrid-ARQ techniques [2], [3]. Further enhance- ments to the hybrid-ARQ schemes were proposed to leverage the advantages offered by soft-decoding of codes (e.g. LDPC, turbo codes) [4]–[6]. Some of these enhancements involved feeding back more than just the acknowledgment (ACK)/negative acknowledg- ment (NAK) for the packet received at the destination [7]–[9]. In this work, we look at the advantages offered by the presence of a very reliable communication link from the destination to the source of the packet. This would enable the destination to feedback more than just the ACK/NAK for the received packet. In particular, we will focus our attention on feeding back the received packet at the destination (either completely or partially) back to the source. We will call this feedback channel output feedback (COF) to distinguish it from the channel state information (CSI) feedback that is so common in the wireless communication. COF was one of the earliest feedback techniques to have been explored in the literature. Schalkwijk-Kailath explored it for the additive white Gaussian noise (AWGN) channel. In the seminal work [10], they showed that although the COF cannot lead to any improvement in the capacity of the forward channel, it has the potential to dramatically increase the reliability of the forward link. This was accomplished by a technique known as linear feedback coding in which the transmitter sends a strictly linear function of the feedback side-information and the message to be sent. Because this class of codes is constrained to be linear, they have low complexity and are often less difficult to analyze. In combining COF with traditional hybrid-ARQ, we show ap- preciable gains in the throughput of the wireless network over the existing schemes. Furthermore, this gain is achieved by introducing a very low complexity linear coding scheme at the source and destination. The paper is structured as follows. In Section II, we provide a brief description of the overall system model for the hybrid-ARQ scheme considered in this paper. In Section III, we propose a very simple linear feedback coding scheme for hybrid-ARQ schemes. Section IV is devoted to the discussion of variety of ways in which the proposed linear feedback scheme can be included in the existing hybrid-ARQ schemes. Section V provides simulation results to highlight the advantages offered by the use of proposed linear feedback scheme in hybrid-ARQ schemes. Finally, Section VI concludes the paper with possible future directions emanating from this work. Notation: The symbol C represents the set of all complex numbers. The vectors (matrices) are represented by lower (upper) boldface letters while scalars by lower italicized letters. The vectors are always assumed to be column vectors unless otherwise stated. The opera- tors (·) * , (·) T and ‖·‖ F denote complex conjugate, transpose and Frobenius norm of a complex matrix/vector, respectively, and E[·] represents the expectation of a random variable. II. MATHEMATICAL FRAMEWORK Consider the transmission of binary information vector w ∈ GF (2) L inf o M over a discrete-time multiple-input multiple-output (MIMO) block fading channel with M t transmit antennas and Mr receive antennas where the number of spatial channel is referred to as M = min{Mr ,M t }. The schematic for the complete system is shown in Figure 1. The information vector w corresponding to packet θ is first encoded using an FEC code of rate L inf o /L coded to produce a codeword c ∈ GF (2) L coded M . This codeword c is then modulated using a source constellation, Θ[N ], to create vector θ containing LM symbols. It is assumed that no more than N trans- missions (N − 1 retransmissions) of a single packet θ is allowed. The LM modulated symbols are subsequently divided into L sub- blocks each of length M, with each sub-block transmitted over one MIMO channel use. It is assumed that the MIMO channel remains constant over the transmission of one complete packet involving L channel uses. The overall packet transmission can be represented as: Y[k]= H[k]X[k]+ Z[k], 1 ≤ k ≤ N, (1)