## An erasure code based on Vandermonde matrices

I've been looking at an erasure code by Luigi Rizzo which is based on Vandermonde matrices, since this code is used in Outernet. In fact, it is the code implemented by the zfec library. Luigi Rizzo describes his code in a paper from 1997, but the paper can be very confusing and misleading because it describes the mathematics in very little detail. I needed to go to the source code to understand how it works. Actually, the idea behind this code is very simple. Here I do a mathematical description of the code and show that it is the same as a Reed-Solomon code. This is rather weird, because Luigi Rizzo makes no mention of Reed-Solomon codes, which were first described in 1960.

## free-outernet gets LDPC decoding

In my previous post I talked about some small updates made by George Hopkins to my free-outernet project. In fact, George has been reverse engineering the ondd binary quite in depth and he has been able to reverse engineer the LDPC code which is used for file FEC. This solves a long-standing issue of free-outernet. Formerly, LDPC decoding was not implemented, so to recover a file successfully all the file blocks had to be received correctly. Now, with LDPC decoding the file can be recovered even if some of the file blocks are lost. Thus, the performance of free-outernet in this aspect should now be the same as the performance of the closed source ondd binary included in the official Outernet receiver. Many thanks to George, as this is a substantial improvement of free-outernet. Here I describe the latest changes made by George in free-outernet.

## Updated format for Outernet LDP protocol

After my talk in 33C3, George Hopkins has been doing some further reverse engineering of the Outernet protocols. By looking at the ondd binary, he has discovered that the length of the LDP header is not 6 bytes, but rather 4 bytes. He has sent a pull request with these changes. I have already merged it into free-outernet.

Thus, the last field of the LDP header as described in my previous post, which was formerly known as "B field", gets now included in the payload of the package. The former "A field" is now the only field that identifies the port or service, and therefore it is now known as "type". For file and FEC blocks, this change is small, because the former "B field" was always 0, so it gets incorporated into the "file id" field of the payload, which is now 24 bits long instead of 16 bits. For time packets it provides a nice way to interpret the packet as a variable record field structure. This interpretation now explains all the contents of the time packet.

After reviewing and merging George's changes and while I still have these details fresh in my mind, I have updated the slides I used in my 33C3 talk to reflect these changes. These are the updated slides.

## Open telecommand for BY70-1

Recently, Wei BG2BHC has published instructions for the use of BY70-1's camera by Amateurs. Essentially, there are three commands that can be used: 0x00 to take a picture and send it, 0x55 to take a picture and store it in memory, and 0xaa to send the picture stored in memory. He also gives the modulation and coding details for the commands. They use AX.25 with 1000baud FM-AFSK with tones at 1000Hz and 1833.33Hz. The AX.25 frames are UI frames containing a single byte with the command (0x00, 0x55 or 0xaa as described above). For ease of use, he also gives WAV recordings of the three commands, so they can be played back easily into an FM transmitter by any Amateur. Here I look at the contents of these WAV files and how to process and create this kind of packets.

## Coding for HIT satellites (and other CCSDS satellites)

The Harbin Institute of Technology satellites LilacSat-2, BY70-1 and the upcoming LilacSat-1 all use a concatenated code with an $r=1/2, k=7$ convolutional code and a (255,223) Reed-Solomon code according to the CCSDS TM Synchronization and Channel Coding blue book specifications. The GNU Radio decoder gr-lilacsat by Wei BG2BHC includes a custom implementation of the relevant part of the CCSDS stack, probably ported into GNU Radio from some other software.

Recently, I have been working on decoding KS-1Q and I've seen that it uses the same CCSDS coding as the HIT satellites. This has made me realise that most of this CCSDS coding can be processed using stock GNU Radio blocks, without the need for custom blocks. The only exception is Reed-Solomon decoding. This can be done easily with gr-libfec, which provides an easy interface from GNU Radio to Phil Karn's libfec. Here I look at the details of the CCSDS coding and how to process it with GNU Radio. I've updated the decoders in gr-satellites to use this kind of processing. I'll also talk about the small advantages of doing it in this way versus using the custom implementation in gr-lilacsat.

## KS-1Q decoded

In a previous post, I talked about my attempts to decode KS-1Q. Lately, WarMonkey, who is part of the satellite team, has been giving me some extra information and finally I have been able to decode the packets from the satellite. The decoder is in gr-ks1q, together with a sample recording contributed by Scott K4KDR. I've also added support for KS-1Q in gr-satellites. Here I look at the coding of the packets in more detail.