On the use of ordered statistics decoders for low-density parity-check codes in space telecommand links

The performance of short low-density parity-check (LDPC) codes that will be included in the standard for next-generation space telecommanding is analyzed. The paper is focused on the use of a famous ordered statistics decoder known as most reliable basis (MRB) algorithm. Despite its complexity may appear prohibitive in space applications, this algorithm is shown to actually represent a realistic option for short LDPC codes, enabling significant gains over more conventional iterative algorithms. This is possible by a hybrid approach which combines the MRB decoder with an iterative decoding procedure in a sequential manner. The effect of quantization is also addressed, by considering two different quantization laws and comparing their performance. Finally, the impact of limited memory availability onboard of spacecrafts is analyzed and some solutions are proposed for efficient processing, towards a practical onboard decoder implementation

Advanced channel coding for space mission telecommand links

We investigate and compare different options for updating the error correcting code currently used in space mission telecommand links. Taking as a reference the solutions recently emerged as the most promising ones, based on Low-Density Parity-Check codes, we explore the behavior of alternative schemes, based on parallel concatenated turbo codes and soft-decision decoded BCH codes. Our analysis shows that these further options can offer similar or even better performance.Comment: 5 pages, 7 figures, presented at IEEE VTC 2013 Fall, Las Vegas, USA, Sep. 2013 Proc. IEEE Vehicular Technology Conference (VTC 2013 Fall), ISBN 978-1-6185-9, Las Vegas, USA, Sep. 201

An efficient NB-LDPC decoder architecture for space telecommand links

In the framework of error correction in space telecommand (TC) links, the Consultative Committee for Space Data Systems (CCSDS) currently recommends short block-length BCH and binary low-density parity-check (LDPC) codes. Other alternatives have been discarded due to their high decoding complexity, such as non-binary LDPC (NB-LDPC) codes. NB-LDPC codes perform better than their binary counterparts over AWGN and jamming channels, being great candidates for space communications. We show the feasibility of NB-LDPC coding for space TC applications by proposing a highly efficient decoding architecture. The proposed decoder is implemented for a (128,64) NB-LDPC code over GF(16) and the design is particularized for a space-certified Virtex-5QV FPGA. The results prove that NB-LDPC coding is an alternative that outperforms the standardized binary LDPC, with a coding gain of 0.7 dB at a reasonable implementation cost. Given that the maximum rate for TC recommended by the CCSDS is 2 Mbps, the proposed architecture achieves a throughput of 2.03 Mbps using only 9615 LUTs and 5637 FFs (no dedicated memories are used). In addition, this architecture is suitable for any regular (2,4) NB-LDPC (128,64) code over GF(16) independently of the H matrix, allowing flexibility in the choice of the code. This brief places NB-LDPC codes as the excellent candidates for future versions of the telecommand uplink standard.This work was supported by Spanish MICINN/AEI under Project TEC2017-86722-C4-3-R

Next generation earth‑to‑space telecommand coding and synchronization: ground system design, optimization and software implementation

The Consultative Committee for Space Data Systems, followed by all national and international space agencies, has updated the Telecommand Coding and Synchronization sublayer to introduce new powerful low-density parity-check (LDPC) codes. Their large coding gains significantly improve the system performance and allow new Telecommand services and profiles with higher bit rates and volumes. In this paper, we focus on the Telecommand transmitter implementation in the Ground Station baseband segment. First, we discuss the most important blocks and we focus on the most critical one, i.e., the LDPC encoder. We present and analyze two techniques, one based on a Shift Register Adder Accumulator and the other on Winograd convolution both exploiting the block circulant nature of the LDPC matrix. We show that these techniques provide a significant complexity reduction with respect to the usual encoder mapping, thus allowing to obtain high uplink bit rates. We then discuss the choice of a proper hardware or software platform, and we show that a Central Processing Unit-based software solution is able to achieve the high bit rates requested by the new Telecommand applications. Finally, we present the results of a set of tests on the real-time software implementation of the new system, comparing the performance achievable with the different encoding options

An Efficient NB-LDPC Decoder Architecture for Space Telecommand Links

In the frame of error correction in space telecommand (TC) links, the Consultative Committee for Space Data Systems (CCSDS) currently recommends short block-length BCH and binary LDPC codes. Other alternatives have been discarded due to their high decoding complexity, such as LDPC and eBCH codes with MRB decoding and NB-LDPC codes. NBLDPC codes perform better than their binary counterparts over AWGN and jamming channels, being excellent candidates for space communications. In this brief, we show the feasibility of NB-LDPC coding for space TC applications by proposing a highly efficient decoding architecture. The proposed decoder is implemented for a (128,64) NB-LDPC code over GF(16) and the design is particularized for a space-certified Virtex-5QV FPGA. The results prove that NB-LDPC coding is an alternative outperforming the standardized binary LDPC at a reasonable cost. Given that the maximum rate for TC recommended by the CCSDS is 2 Mbps, the proposed architecture achieves a throughput of 2.4 Mbps using only 8797 LUTs and 5460 FFs (no dedicated memories are used). In addition, this architecture is suitable for any regular (2,4) NB-LDPC (128,64) code over GF(16) independently of the H matrix, allowing great flexibility for the use with the recently proposed short block-length NBLDPC codes in upcoming telecommand uplink standards

State-of-the-art space mission telecommand receivers

Since their dawning, space communications have been among the strongest driving applications for the development of error correcting codes. Indeed, space-to-Earth telemetry (TM) links have extensively exploited advanced coding schemes, from convolutional codes to Reed-Solomon codes (also in concatenated form) and, more recently, from turbo codes to low-density parity-check (LDPC) codes. The efficiency of these schemes has been extensively proved in several papers and reports. The situation is a bit different for Earth-to-space telecommand (TC) links. Space TCs must reliably convey control information as well as software patches from Earth control centers to scientific payload instruments and engineering equipment onboard (O/B) spacecraft. The success of a mission may be compromised because of an error corrupting a TC message: a detected error causing no execution or, even worse, an undetected error causing a wrong execution. This imposes strict constraints on the maximum acceptable detected and undetected error rates

Trapping Sets of Quantum LDPC Codes

Iterative decoders for finite length quantum low-density parity-check (QLDPC) codes are attractive because their hardware complexity scales only linearly with the number of physical qubits. However, they are impacted by short cycles, detrimental graphical configurations known as trapping sets (TSs) present in a code graph as well as symmetric degeneracy of errors. These factors significantly degrade the decoder decoding probability performance and cause so-called error floor. In this paper, we establish a systematic methodology by which one can identify and classify quantum trapping sets (QTSs) according to their topological structure and decoder used. The conventional definition of a TS from classical error correction is generalized to address the syndrome decoding scenario for QLDPC codes. We show that the knowledge of QTSs can be used to design better QLDPC codes and decoders. Frame error rate improvements of two orders of magnitude in the error floor regime are demonstrated for some practical finite-length QLDPC codes without requiring any post-processing.Comment: Revised version - 19 pages, 12 figures - Accepted for publication in Quantu