In this manuscript the authors claim to use SVD to decompose the channel matrix in order to optimize power allocation to different mode groups in a mode group multiplexed MMF transmission system.

While generally space division multiplexed optical systems are of great relevance and SVD has been proven a powerful tool in this context, the presented manuscript is full of flaws both in the assumptions made, the methodology pursued and the results obtained. The manuscript is further very difficult to read due to rather poor use of the English language. As a result the reviewer does not consider this manuscript publishable and would require a complete re-design and re-execution of the work before publication can be considered.

The major flaws in this work include:

1. The authors discuss the decomposition of the channel response H using SVD as H=U\SigmaV^H - which is common practice. However the authors then proceed to interpret U as post-coding and V^H as pre-coding applied at receiver and transmitter respectively. This is a) not correct, as both U and V^H are part of the channel response of the fiber itself and b) assuming they are part of the channel response the further discussion provided by the authors would require perfect knowledge of the precise channel response H. The latter is impossible, especially as the channel is dynamic over time and will vary on the order of milliseconds (as noted by the authors themselves in the introduction). In the authors discussion both V and V^H are applied at the transmitter and U and U^H are applied at the receiver - it is obvious that this will yield perfect results and bears no relation to reality in which V^H and U are unknown and their precise estimation is difficult, especially as they vary rather fast over time.
2. The treatment of the decomposed channel matrix reduces the channel to a diagonal matrix of channel loss/gain values of the same size as mode groups are employed in the system. However it is a central characteristic (and limitation) of typical graded index MMF that their number of modes and mode groups is large and coupling between them is significant. As a result, any treatment of the channel matrix must take into account a significantly larger number of modes/mode groups than those used for transmission and must model the resulting mode coupling. The authors further mention that in their simulation the dispersion (chromatic or modal?), delay and attenuation are applied on a per channel basis, rather then by emulating a channel matrix with modal coupling - as a result the conclusions drawn from the simulations will likely bear little relation to reality.
3. The authors do not discuss the realization of their mode multiplexers and appear to assume perfect mode multiplexing and coupling into the fiber.
4. It is not clear how the impulse responses in Fig.5 and Fig.6 are computed or how their horizontal axis represents, nor what the numbers beneath the mode summary are. These being impulse responses, the reviewer would expect the horizontal axes to represent time.
5. In their algorithm for allocation of power to the mode groups, the authors allow the allocation of zero power to a channel (step 6). This would obviously result in a mode group remaining unused and the system capacity bring reduced.
6. In their discussion of the results, the authors mention an improvement in power spectral density (there appears to be an error in that the vertical axes of the spectra in Fig.10 are labelled power, rather than the correct power spectral density) from -300dBm to +100dBm. The reviewer would like to point out that both values are well outside the range applicable to telecommunication system (and in case of the lower limit unphysical). A power of -300dBm corresponds to 1e-33W, i.e., 0.0000000001yW (yocto W) - far below thermal noise, while the upper limit corresponds to 10MW and is thus far above the power used in any communication system.
7. Similar to the previous point, the authors claim to simulate bit error rates down to 1e-17 (Fig.11) and 1e-40 (Fig.12) - to observe 1 error at the latter BER, the authors would need to simulate the transmission of 1e40 bits which is approx 1e39 byte or 1e21 exabyte. For comparison, the total computer memory in existence in the world was estimated to be 300exabyte in 2011 (https://www.zdnet.com/article/what-is-the-worlds-data-storage-capacity/) which at 50% annual growth results in 11500 exabyte or 1/1e18 of the amount of data the authors would have had to transmit.