Finite Block Length Coding for Low-latency High-Reliability Wireless Communication Leah Dickstein ˚ , Vasuki Narasimha Swamy ˚ , Gireeja Ranade : , Anant Sahai ˚ ˚ University of California, Berkeley, CA, USA : Microsoft Research, Redmond, WA, USA Abstract—This paper takes a step towards making practical cooperative protocols for wireless low-latency high-reliability communication. We consider the effect of finite block-length error correction codes and the main message is that the demands on the error-correcting code are different in different phases of a diversity-seeking cooperative protocol: In the first hop where messages must reach potential relays, the code only has to achieve a moderate probability of error. The final hop from relays to the destination is where the code must be ultrareliable. The results are illustrated in the context of a simple concatenated Hamming+Reed Solomon code. I. I NTRODUCTION In [1], we introduced a wireless protocol framework that harvests diversity needed for high reliability by employ- ing cooperative communication. Cooperating nodes relay messages simultaneously using a space-time code so that spatial diversity is harvested while meeting low latency requirements. In [2], this protocol framework was extended to include network coding that exploits the bi-directional traffic (both uplink and downlink) and channel reciprocity. Both of those works ignored the effects of realistic error-correcting codes — instead assuming the existence of perfect capacity- achieving codes. In this paper, we analyze the effect of finite-block-length codes on such cooperative communication schemes. Our naive guess would be that we simply must add the error- correcting code’s gap-to-capacity at the desired probability of error to the transmit SNR predicted by using a perfect capacity-achieving code. The main finding of this paper is that this naive guess is too conservative. We can do a few dB better. The main insight is that the demands on the error- correcting code are different in different phases. In the initial phases of the cooperative protocols proposed in [1], [2], the key is to recruit as many relays as possible and for this, the error-correcting code does not have to be ultrareliable. Moderate reliability is fine. However, when the messages are finally delivered to their ultimate destination, there is no diversity with respect to the additive noise and it is vital that the error-correcting code be ultrareliable. Because multiple relays were very likely to have been recruited earlier in the protocol, there is less of a fear of simultaneous deep fades. The main challenge we encounter while analyzing such protocols is the computational complexity of actually eval- uating what SNRs would suffice. Since we want very high reliability (10 ´9 ), simulations would take far too long. Nu- merical integration could be used, but there is a curse of dimensionality since the number of independent fades grows quadratically with the number of nodes in the network. In Section III, this paper presents a simpler way of analyzing the impact of finite-block-length codes in cooperative com- munication before showing numerical results in Section IV. II. BACKGROUND A useful comm-theoretic perspective is to decompose the required SNR into three parts: (1) capacity: how much does the rate fundamentally require? (2) gap-to-capacity: given the target reliability and the specific code being used, how many extra dB do we need beyond capacity? (3) fading-margin: how many dB do we need to absorb bad wireless fades? Although it is useful to be able to think about these separately, they clearly interact with each other at the system level. For example, if overall “goodput” is what is desired and the higher layers will use ARQ to achieve high reliability, then lowering the target reliability on a link comes at the cost of more retransmissions and hence less overall rate. In [3] the authors propose that links which fail about 10% of the time (allowing more aggressive code rates) result in the best goodput. A similar finding is reported in [4] from a channel dispersion perspective. The core question in this paper is whether a similar story holds when we have a diversity- oriented cooperative communication protocol with a low la- tency requirement. In this section, we briefly provide pointers into the relevant background underlying diversity-oriented cooperative communication, finite block length effects on performance of error correction codes and the specific low- latency oriented protocols that we are considering. A. Cooperative Communication As discussed in [1], exploiting virtual multiple antennas are at the heart of cooperative communication [5]–[7]. The schemes used for cooperation can be broadly divided into: a) coded-cooperation; b) distributed space-time coding; and c) delay-diversity approaches. In coded-cooperation relays decode the message, then re-encode it and transmit a new helper code word [8]–[14]. Laneman et al. [5] proposed a simple distributed space-time block coding (DSTBC) scheme in which each relay transmits a different column of the space- time block code (STBC) matrix. A randomized strategy was addressed in [15] where each relay node transmits an 978-1-5090-4550-1/16/$31.00 ©2016 IEEE 908 Fifty-fourth Annual Allerton Conference Allerton House, UIUC, Illinois, USA September 27 - 30, 2016