Bandwidth efficient CCSDS coding standard proposals

The basic concatenated coding system for the space telemetry channel consists of a Reed-Solomon (RS) outer code, a symbol interleaver/deinterleaver, and a bandwidth efficient trellis inner code. A block diagram of this configuration is shown. The system may operate with or without the outer code and interleaver. In this recommendation, the outer code remains the (255,223) RS code over GF(2 exp 8) with an error correcting capability of t = 16 eight bit symbols. This code's excellent performance and the existence of fast, cost effective, decoders justify its continued use. The purpose of the interleaver/deinterleaver is to distribute burst errors out of the inner decoder over multiple codewords of the outer code. This utilizes the error correcting capability of the outer code more efficiently and reduces the probability of an RS decoder failure. Since the space telemetry channel is not considered bursty, the required interleaving depth is primarily a function of the inner decoding method. A diagram of an interleaver with depth 4 that is compatible with the (255,223) RS code is shown. Specific interleaver requirements are discussed after the inner code recommendations

CRC-Aided High-Rate Convolutional Codes With Short Blocklengths for List Decoding

Recently, rate-1/n zero-terminated (ZT) and tail-biting (TB) convolutional codes (CCs) with cyclic redundancy check (CRC)-aided list decoding have been shown to closely approach the random-coding union (RCU) bound for short blocklengths. This paper designs CRC polynomials for rate- (n-1)/n ZT and TB CCs with short blocklengths. This paper considers both standard rate-(n-1)/n CC polynomials and rate- (n-1)/n designs resulting from puncturing a rate-1/2 code. The CRC polynomials are chosen to maximize the minimum distance d_min and minimize the number of nearest neighbors A_(d_min) . For the standard rate-(n-1)/n codes, utilization of the dual trellis proposed by Yamada et al. lowers the complexity of CRC-aided serial list Viterbi decoding (SLVD). CRC-aided SLVD of the TBCCs closely approaches the RCU bound at a blocklength of 128. This paper compares the FER performance (gap to the RCU bound) and complexity of the CRC-aided standard and punctured ZTCCs and TBCCs. This paper also explores the complexity-performance trade-off for three TBCC decoders: a single-trellis approach, a multi-trellis approach, and a modified single-trellis approach with pre-processing using the wrap around Viterbi algorithm.Comment: arXiv admin note: substantial text overlap with arXiv:2111.0792

Trellis-Based Equalization for Sparse ISI Channels Revisited

Sparse intersymbol-interference (ISI) channels are encountered in a variety of high-data-rate communication systems. Such channels have a large channel memory length, but only a small number of significant channel coefficients. In this paper, trellis-based equalization of sparse ISI channels is revisited. Due to the large channel memory length, the complexity of maximum-likelihood detection, e.g., by means of the Viterbi algorithm (VA), is normally prohibitive. In the first part of the paper, a unified framework based on factor graphs is presented for complexity reduction without loss of optimality. In this new context, two known reduced-complexity algorithms for sparse ISI channels are recapitulated: The multi-trellis VA (M-VA) and the parallel-trellis VA (P-VA). It is shown that the M-VA, although claimed, does not lead to a reduced computational complexity. The P-VA, on the other hand, leads to a significant complexity reduction, but can only be applied for a certain class of sparse channels. In the second part of the paper, a unified approach is investigated to tackle general sparse channels: It is shown that the use of a linear filter at the receiver renders the application of standard reduced-state trellis-based equalizer algorithms feasible, without significant loss of optimality. Numerical results verify the efficiency of the proposed receiver structure.Comment: To be presented at the 2005 IEEE Int. Symp. Inform. Theory (ISIT 2005), September 4-9, 2005, Adelaide, Australi

Performance Improvement of Space Missions Using Convolutional Codes by CRC-Aided List Viterbi Algorithms

Recently, CRC-aided list decoding of convolutional codes has gained attention thanks to its remarkable performance in the short blocklength regime. This paper studies the convolutional and CRC codes of the Consultative Committee for Space Data System Telemetry recommendation used in space missions by all international space agencies. The distance spectrum of the concatenated CRC-convolutional code and an upper bound on its frame error rate are derived, showing the availability of a 3 dB coding gain when compared to the maximum likelihood decoding of the convolutional code alone. The analytic bounds are then compared with Monte Carlo simulations for frame error rates achieved by list Viterbi decoding of the concatenated codes, for various list sizes. A remarkable outcome is the possibility of approaching the 3 dB coding gain with nearly the same decoding complexity of the plain Viterbi decoding of the inner convolutional code, at the expense of slightly increasing the undetected frame error rates at medium-high signal-to-noise ratios. Comparisons with CCSDS turbo codes and low-density parity check codes highlight the effectiveness of the proposed solution for onboard utilization on small satellites and cubesats, due to the reduced encoder complexity and excellent error rate performance

Application of List Viterbi Algorithms to Improve the Performance in Space Missions using Convolutional Codes

Currently, several space missions are still using convolutional codes, which are among the available coding options of the CCSDS telemetry recommendation. When convolutional codes are employed, the CCSDS specification mandates the use of an outer CRC code to perform error detection over the transfer frame. Alternatively, the CRC code may be used, together with list Viterbi decoding of the inner convolutional code, to significantly improve the performance of the coding scheme. In this paper, we first compute the distance spectrum of the concatenation of the outer CRC code and the inner convolutional codes recommended by the CCSDS. By means of a union bound on the block error probability under maximum-likelihood decoding, we estimate the extra coding gain achievable by the concatenation with respect to the use of the Viterbi algorithm applied to the decoding of the inner convolutional code only. The extra coding gain is close to 3 dB. Then, we consider the application of the list Viterbi algorithm and we discuss some techniques useful to reduce its complexity in practical implementations. Results show that it is possible to approach the 3 dB extra coding gain with negligible increase in the decoding complexity with respect to Viterbi decoding of the inner convolutional code

Error control techniques for satellite and space communications

The results included in the Ph.D. dissertation of Dr. Fu Quan Wang, who was supported by the grant as a Research Assistant from January 1989 through December 1992 are discussed. The sections contain a brief summary of the important aspects of this dissertation, which include: (1) erasurefree sequential decoding of trellis codes; (2) probabilistic construction of trellis codes; (3) construction of robustly good trellis codes; and (4) the separability of shaping and coding

Sequential decoding of trellis codes through ISI channels

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1996.Includes bibliographical references (leaves 56-57).by Patrick M. Maurer.M.S