## 1 Introduction  
Wireless multiple access schemes, where correlated signals, observed at different nodes, need to be transferred to one or more collectors, model several communication scenarios. For example, these schemes apply to wireless sensor networks, where a set of nodes collect and transmit correlated data to a common sink [1]. In the case of a single collector node (the access point, AP), the design of efficient transmission mechanisms is often referred to as reach-back channel problem [2, 3, 4]. Assuming orthogonal additive white Gaussian noise (AWGN) channels between the nodes and the collector, the separation between source and channel coding is known to be optimal [4, 5]. This means that the theoretical limit can be achieved by, first, compressing each source up to its Slepian-Wolf (SW) limit and, then, utilizing independent capacity-achieving channel codes (one per source) [6]. In an attempt to exploit such correlation, many works have recently focused on the design of distributed source coding schemes that approach the SW fundamental limit on the achievable compression rate [7, 8, 9, 10]. An alternative solution to distributed source coding is based on joint source channel coding (JSCC) schemes, where the correlated sources are not source encoded but only channel encoded. If one compares a JSCC system with a system based on source/channel coding separation with the same information rate, the channel codes used in a JSCC scheme must be less powerful (i.e., they have higher rates). In fact, this apparent weakness is compensated by exploiting the source correlation at the decoder, which jointly recovers the information signals of all sources. For this reason, this approach is also referred to as joint channel decoding (JCD). In this case, it can be shown that the final system performance can approach the theoretical limits. This approach has attracted the attention of several researchers in the recent past, also because of its implementation simplicity [11, 12, 13, 14, 15]. Note that, in the JCD approach, the sources are encoded independently of each other (i.e., for a given source neither the realizations from the other sources nor the correlation model are available at each encoder) and transmitted through the channel. In this case, the correlation between the sources has to be available at the (common) receiver. In the introduced scenario, we study the performance of wireless multiple access schemes, with binary correlated sources communicating to an AP and with block faded communication links. It is well known that the presence of block-faded channels may dramatically degrade the performance of wireless multiple access systems, unless some countermeasures are taken at the transmitters to protect highly faded links. For instance, the performance of multiple access schemes can be improved by the use of \"feedback.\" In general terms, the AP can provide the sources with supplementary information (e.g., on the links' states) to allow them to counter-act the effects of fading. From an information-theoretic viewpoint, while feedback does not increase the capacity of a memoryless channel with one sender and one receiver [16], the capacity region of multiple access channels increases through the use of feedback [17; 18]. In [19; 20], the authors devise JSCC strategies for multiple-access channels with feedback and correlated sources. In this paper, we refer to block faded multiple access schemes with correlated sources and JCD. In particular, we consider serially concatenated convolutional coding (SCCCing) or low-density parity-check (LDPC) coding at the sources. We first investigate, in the absence of non idealities (besides fading), feedback power control strategies which can guarantee theoretically error-free communications, i.e., that the system operational point lies in the feasible signal-to-noise ratio (SNR) region of the multiple access channel.