fec – Daniel Estévez

LTE uplink: PUSCH

This post belongs to my series about LTE. In the LTE uplink, the PUSCH (physical uplink shared channel) is the channel used to trasmit data from the UEs (phones) to the eNB (base station). It plays a role analogous to the PDSCH (physical downlink shared channel), which is used to transmit data in the downlink. In this post I will decode the PUSCH in a recording that I made of my phone uplink a couple years ago.

The PUSCH uses the same kind of techniques as the PDSCH for transport block coding, so all the Turbo code implementation and related algorithms from my post about the PDSCH will be re-used here. However, there is an important difference between the PDSCH and the PUSCH that makes decoding the PUSCH much harder. The LTE downlink is, in a certain sense, a self-descriptive signal. The UEs don’t know in advance the configuration that will be used to transmit each transport block in the PDSCH, because the eNB decides it on the fly. Therefore, the eNB announces PDSCH transmissions in the PDCCH (physical downlink control channel).

When I decoded the PDCCH and PDSCH, the only slightly clever thing that I had to do was to find the RNTIs (radio network temporary indicators). These are 16-bit numbers that are used to address each PDSCH transmission. There are some of them which are statically allocated to some broadcast purpose (SI-RNTI, P-RNTI, RA-RNTI), and the C-RNTIs, which are individually assigned to each UE. The CRC-16 of the PDCCH DCIs is XORed with the RNTI to which the transmission is addressed. At any time, a UE knows the set of RNTIs that it is monitoring, so it calculates the CRC-16 of the received DCI, computes its XOR with each of its assigned RNTIs, and compares the result with the CRC-16 in the DCI. If there is a match, the DCI is accepted. This is a way of filtering out messages without spending additional bits to put the RNTI in a field in the DCI.

When we are monitoring an LTE downlink, we don’t know which RNTIs are being used. With some cleverness, if the SNR is good enough, we can detect and select each PDCCH transmission by hand (it is necessary to guess the REGs that it occupies and the DCI length) and then, assuming that we have decoded the DCI with no bit errors, obtain the RNTI as the XOR of the calculated CRC and the received CRC. This is what I did in the post about the PDCCH. If we were monitoring the LTE downlink for a longer time, this trick wouldn’t even be necessary. The C-RNTIs assigned to the UEs are communicated to them in a RAR transmitted with the RA-RNTI, as a response to their PRACH (see the post where I analyze this in Wireshark). So a downlink monitor application can simply watch the SI-RNTI, P-RNTI and RA-RNTI, and add any C-RNTIs to a list of known connected UEs when it sees a RAR. The C-RNTIs can be removed from this list after a period of inactivity, because the UE would have been sent to the idle state by the network. This idea really shows that it is possible to decode everything in the LTE downlink without doing clever blind decoding tricks.

In contrast, the LTE uplink is not self-descriptive. The eNB defines the configuration of each PUSCH transmission when it sends the uplink grant to the UE. So the UE doesn’t need to communicate this configuration again to the eNB when it transmits in the PUSCH. The information that describes the PUSCH transmissions is effectively in the PDCCH in the downlink, and in this case I don’t have a recording of the downlink that matches my uplink recording. This makes decoding the PUSCH much more difficult, but nevertheless not impossible. With some clever ideas and blind decoding tricks we can usually find all the information we’re missing. In the rest of this post, I describe how to do this in detail. It will be long and quite technical.

Decoding LTE MIMO with a single antenna

In my previous post I decoded LTE PDSCH (physical downlink shared channel) transmissions from an IQ recording that I had made of an eNB recording using an USRP B205mini and a single antenna. The eNB has two antenna ports, and it uses TM4 (closed-loop spatial multiplexing) to transmit the PDSCH to each individual UE. In the post, I repeated several times that two-codeword TM4 is intended for 2×2 MIMO and relies on the receiver having at least 2 antennas in order to separate the two transmitted codewords, so I couldn’t decode these transmissions with my recording.

In this post I will show that in some cases this is not true, and these two-codeword TM4 transmissions can be decoded with just one receive antenna. I will decode some of these two-codeword transmissions from my IQ recording by using the ideas I introduce below.

LTE downlink: PDSCH

This post is a continuation of my series about LTE, where I decode a recording of the downlink signal of an eNB using Jupyter notebooks written from scratch. Here I will decode the PDSCH (physical downlink shared channel), which contains the data transmitted by the eNB to the UEs, including PDUs from the MAC layer, and some broadcast information, such as the SIB (system information block) and paging. At first I planned this post to be about decoding the SIB1. This is the first block of system information, and it is the next thing that a UE must decode after decoding the MIB (located in the PBCH) to find the configuration of the cell. The SIB1 is always transmitted periodically, and its contents and format are relatively well known a priori (as opposed to a user data transmission, which could happen at any time and contain almost anything), so it is a good example to try to decode PDSCH transmissions.

After writing and testing all the code to decode the SIB1, it was too tempting to decode everything else. Even though at first I wrote my code thinking only about the SIB1, with a few modifications I could decode all the PSDCH transmissions (except those using two-codeword spatial multiplexing, since my recording was done with a single antenna). I will still use the SIB1 as an example to show how to decode the PDSCH step by step, but I will also show the rest of the data.

The post is rather long, but we will get from IQ samples to looking at packets in Wireshark using only Python, so I think it’s worth its length.

Trying to decode LEV-1

LEV-1 is a small lunar hopper that was carried by the SLIM lunar lander. It was released a few metres above the surface on January 19, as part of the lunar landing of SLIM. LEV-1 transmits telemetry in the 435 MHz amateur satellite band (it has an IARU satellite coordination approval), and also in S-band. Shortly after the landing, CAMRAS received the 437.410 MHz signal from LEV-1 using the 25 m radiotelescope at Dwingeloo. They have published a couple of IQ recordings in their directory of miscellaneous recordings (see the filenames starting by slim_).

The information about the telemetry signal of LEV-1 is scarce. Its website just says

Telemetry format of LEV-1 stands on CCSDS. The contents of telemetry are under developing.

The IARU coordination sheet contains other clues, such as the mention of PCM/PSK/PM, CW, and bitrates of 31, 31.25 and 32 bps, but not much else. Regardless of the mention of CCSDS, I have found that the signal from LEV-1 is quite peculiar. This post is an account of my attempt to decode the data.

ssdv-fec: an erasure FEC for SSDV implemented in Rust

Back in May I proposed an erasure FEC scheme for SSDV. The SSDV protocol is used in amateur radio to transmit JPEG files split in packets, in such a way that losing some packets only cases the loss of pieces of the image, instead of a completely corrupted file. My erasure FEC augments the usual SSDV packets with additional FEC packets. Any set of \(k\) received packets is sufficient to recover the full image, where \(k\) is the number of packets in the original image. An almost limitless amount of distinct FEC packets can be generated on the fly as required.

I have now written a Rust implementation of this erasure FEC scheme, which I have called ssdv-fec. This implementation has small microcontrollers in mind. It is no_std (it doesn’t use the Rust standard library nor libc), does not perform any dynamic memory allocations, and works in-place as much as possible to reduce the memory footprint. As an example use case of this implementation, it is bundled as a static library with a C-like API for ARM Cortex-M4 microcontrollers. This might be used in the AMSAT-DL ERMINAZ PocketQube mission, and it is suitable for other small satellites. There is also a simple CLI application to perform encoding and decoding on a PC.

ldpc-toolbox gets LDPC decoding

Recently I have implemented an FPGA LDPC decoder for a commercial project. The belief propagation LDPC decoder algorithm admits many different approximations in the arithmetic, and other tricks that can be used to trade off between decoding sensitivity (BER versus Eb/N0 performance) and computational complexity. To help me benchmark the different belief propagation algorithms, I have extended my ldpc-toolbox project to implement many different LDPC decoding algorithms and perform BER simulations.

ldpc-toolbox is a Rust library and command line tool for the design of LDPC codes. I initially created this project when I was trying to design a suitable LDPC code for a narrowband 32APSK modem to be used over the QO-100 amateur GEO transponder. The tool so far supported some classical pseudorandom constructions of LDPC codes, computed Tanner graph girths, and could construct the alists for all the DVB-S2 and CCSDS LDPC codes. Extending this tool to support LDPC encoding, decoding and BER simulation is a natural step.

An erasure FEC for SSDV

SSDV is an amateur radio protocol that is used to transmit images in packets, in a way that is tolerant to packet loss. It is based on JPEG, but unlike a regular JPEG file, where losing even a small part of the file has catastrophic results, in SSDV different blocks of the image are compressed independently. This means that packet loss affects only the corresponding blocks, and the image can still be decoded and displayed, albeit with some missing blocks.

SSDV was originally designed for transmission from high-altitude balloons (see this reference for more information), but it has also been used for some satellite missions, including Longjiang-2, a Chinese lunar orbiting satellite.

Even though SSDV is tolerant to packet loss, to obtain the full image it is necessary to receive all the packets that form the image. If some packets are lost, then it is necessary to retransmit them. Here I present an erasure FEC scheme that is backwards-compatible with SSDV, in the sense that the first packets transmitted by this scheme are identical to the usual \(k\) packets of standard SSDV, and augments the transmission with FEC packets in such a way that the complete image can be recovered from any set of \(k\) packets (so there is no encoding overhead). The FEC packets work as a fountain code, since it is possible to generate up to \(2^{16}\) packets, which is a limit unlikely to be reached in practice.

An error in the DSN Telecommunications Link Design Handbook description of Reed-Solomon

The DSN Telecommunications Link Design Handbook is a large document describing many aspects pertaining deep space communications and how they are implemented by the NASA Deep Space Network. One of the many things it contains is a description of a Reed-Solomon encoder for the CCSDS code using the Berlekamp bit-serial architecture. While following this description to implement an encoder, I have found an error. In this post, I explain the error and where I think it comes from.

Voyager 1 and Reed-Solomon

In one of my previous posts about Voyager 1, I stated that the Voyager probes used as forward error correction only the k=7, r=1/2 CCSDS convolutional code, and that Reed-Solomon wasn’t used. However, some days ago, Brett Gottula asked about this, citing several sources that stated that the Voyager probes used Reed-Solomon coding after their encounter with Saturn.

My source for stating that Reed-Solomon wasn’t used was some private communication with DSN operators. Since the XML files describing the configuration of the DSN receivers for Voyager 1 didn’t mention Reed-Solomon either, I had no reason to question this. However, the DSN only processes the spacecraft data up to some point (which usually includes all FEC decoding), and then passes the spacecraft frames to the mission project team without really looking at their contents. Therefore, it might be the case that it’s the project team the one who handles the Reed-Solomon code for the Voyagers. This would make sense specially if the code was something custom, rather than the CCSDS code (recall that Voyager predates the CCSDS standards). If this were true, the DSN wouldn’t really care if there is Reed-Solomon or not, and they might have just forgotten about it.

After looking at the frames I had decoded from Voyager 1 in more detail, I remarked that Brett might be right. Doing some more analysis, I have managed to check that in fact the Voyager 1 frames used Reed-Solomon as described in the references that Brett mentioned. In this post I give a detailed look at the Reed-Solomon code used by the Voyager probes, compare it with the CCSDS code, and show how to perform Reed-Solomon decoding in the frames I decoded in the last post. The middle section of this post is rather math heavy, so readers might want to skip it and go directly to the section where Reed-Solomon codewords in the Voyager 1 frames are decoded.

LDPC code design for my QO-100 narrowband modem

A couple months ago I presented my work-in-progress design for a data modem intended to be used through the QO-100 NB transponder. The main design goal for this modem is to give the maximum data rate possible in a 2.7 kHz channel at 50 dB·Hz CN0. For the physical layer I settled on an RRC-filtered single-carrier modulation with 32APSK data symbols and an interleaved BPSK pilot sequence for synchronization. Simulation and over-the-air tests of this modulation showed good performance. The next step was designing an appropriate FEC.

Owing to the properties of the synchronization sequence, a natural size for the FEC codewords of this modem is 7595 bits (transmitted in 1519 data symbols). The modem uses a baudrate of 2570 baud, so at 50 dB·Hz CN0 the Es/N0 is 15.90 dB. In my previous post I considered using an LDPC code with a rate of 8/9 or 9/10 for FEC, taking as a reference the target Es/N0 performance of the DVB-S2 MODCODs. After some performing some simulations, it turns out that 9/10 is a bit too high with 7595 bit codewords (the DVB-S2 normal FECFRAMEs are 64800 bits long, giving a lower LDPC decoding threshold). Therefore, I’ve settled on trying to design a good rate 8/9 FEC. At this rate, the Eb/N0 is 9.42 dB.