A Comment on "A New Degree of Freedom For Energy Efficiency of Digital Communication Systems"

TL;DR

This paper critiques a recent random number modulation scheme, highlighting its error propagation issues and arguing that minimal energy consumption is achieved by transmitting all bits rapidly with low latency.

Contribution

It provides a critical analysis of the RNM scheme, emphasizing its drawbacks and proposing that maximum speed and minimal latency optimize energy efficiency.

Findings

RNM suffers from severe error propagation

Energy is minimized with fast, low-latency transmission

Critique of existing encoding schemes

Abstract

This comment recalls a previously proposed encoding scheme involving two synchronized random number generators (RNGs) to compress the transmission message. It is also claimed that the recently proposed random number modulation (RNM) scheme suffers considerably from the severe error propagation, and that, in general, the overall energy consumption is minimized when all information bits are transmitted as fast as possible with the minimum latency.

Full text

The paper [1] proposes a random number modulation (RNM) to trade-off the transmission latency with the energy efficiency. It uses a RNG at the transmitter and a RNG at the receiver. These two generators are synchronized to produce identical sequences of $B$ random bits in every time slot. If the random $B$ bit sequence at the transmitter in a given time slot matches one of the $M<2^{B}$ binary sequences representing the $B$ information bits to be transmitted, the corresponding $M$-ary modulation symbol is transmitted in that time slot.

Previously, the use of pseudo-random sequences to exploit the degrees-of-freedom of the communication link was advocated in the paper [2]. Therein, an encoding scheme using two synchronized RNGs at the transmitter and at the receiver is devised to greatly reduce the number of message bits that need to be actually transmitted over a feedback link. The RNGs generate $2^{C}$ random sequences at each time slot until one of the random sequences matches the feedback message, and then $C\ll\log_{2}N!$ bits are reported to the transmitter where $N!$ is the number of permutations of $N$ bits. The value of $C$ in [2] and the value of $B$ in [1] can be set to trade-off the transmission latency.

More importantly, the scheme in [2] assumes an ideal noise-less feedback channel which is a common assumption adopted in the literature. The compressed feedback message can be then perfectly recovered at the transmitter. On the other hand, the RNM signaling in [1] cannot reliably identify the time slots containing the transmitted $M$-ary modulation symbols. Consequently, the RNM scheme in [1] suffers from three types of symbol errors having the comparable probabilities. The first type of symbol error inserts an incorrect non-zero modulation symbol into the received sequence even though no symbol was transmitted in that time slot. The second type of symbol error assumes an empty time slot, so the transmitted non-zero modulation symbol is incorrectly deleted. The third type of symbol error interchanges the transmitted non-zero symbol for another incorrect non-zero symbol. The probability of symbol error (11) in [1] can be used to account for this third type of symbol errors. However, calculating the overall symbol error probability involving all these three types of symbol errors is rather non-trivial. The random insertion and deletion of modulation symbols in the transmitted sequence corresponding to the first two types of symbol errors causes a misalignment of the transmitted and the received symbol sequences which gives rise to yet another type of symbol errors. This misalignment will produce the prolonged error propagations, and the overall error performance will be significantly worse than reported in the paper [1]. The consideration of error propagation is even more important in multiantenna and multiuser scenarios with co-channel interference.

Hence, the symbol errors in [1] are correlated, and the optimum detector at the receiver have to consider the complete received sequences which affects the transmission latency. In order to avoid the detection complexity, a sub-optimum two-stage detection scheme for signalings employing $M$-ary modulation constellations extended with a zero symbol was considered in the paper [3]. The signaling in [3] assumes that there is exactly one non-zero $M$-ary modulation symbol transmitted within a predefined number of time slots. The non-coherent detection is used to find the likely transmission time slot which is followed by a conventional coherent symbol detection. In this case, there is no symbol error propagation, so the performance analysis is more straightforward.

It is also useful to make other general comments about the signaling schemes employing a zero modulation symbol. The frequent antenna switching is highly undesirable, especially when it is done at the level of individual modulation symbols. Such switching considerably expands the signaling spectrum as shown in [3] which affects the spectral efficiency. In addition, the electronic circuits have non-zero turn-on and turn-off times which is limiting the achievable switching frequency. In terms of the energy efficiency, it is shown in [3] that, in general, the faster the transmission, i.e., the smaller the latency, the smaller the overall energy consumption consisting of the overhead energy and the energy expended for the radio-frequency (RF) transmissions. However, it is correct that when only the RF portion of the overall energy consumption is considered, one can trade-off the latency for the energy consumption as discussed in [1].