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

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

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

An improved bound on the list error probability and list distance properties

List decoding of binary block codes for the additive white Gaussian noise channel is considered. The output of a list decoder is a list of the $L$ most likely codewords, that is, the L signal points closest to the received signal in the Euclidean-metric sense. A decoding error occurs when the transmitted codeword is not on this list. It is shown that the list error probability is fully described by the so-called list configuration matrix, which is the Gram matrix obtained from the signal vectors forming the list. The worst-case list configuration matrix determines the minimum list distance of the code, which is a generalization of the minimum distance to the case of list decoding. Some properties of the list configuration matrix are studied and their connections to the list distance are established. These results are further exploited to obtain a new upper bound on the list error probability, which is tighter than the previously known bounds. This bound is derived by combining the techniques for obtaining the tangential union bound with an improved bound on the error probability for a given list. The results are illustrated by examples

Simulation and Performance Evaluation of Algorithms for Unmanned Aircraft Conflict Detection and Resolution

The problem of aircraft conflict detection and resolution (CDR) in uncertainty is addressed in this thesis. The main goal in CDR is to provide safety for the aircraft while minimizing their fuel consumption and flight delays. In reality, a high degree of uncertainty can exist in certain aircraft-aircraft encounters especially in cases where aircraft do not have the capabilities to communicate with each other. Through the use of a probabilistic approach and a multiple model (MM) trajectory information processing framework, this uncertainty can be effectively handled. For conflict detection, a randomized Monte Carlo (MC) algorithm is used to accurately detect conflicts, and, if a conflict is detected, a conflict resolution algorithm is run that utilizes a sequential list Viterbi algorithm. This thesis presents the MM CDR method and a comprehensive MC simulation and performance evaluation study that demonstrates its capabilities and efficiency

Simulation and Performance Evaluation of Algorithms for Unmanned Aircraft Conflict Detection and Resolution

The problem of aircraft conflict detection and resolution (CDR) in uncertainty is addressed in this thesis. The main goal in CDR is to provide safety for the aircraft while minimizing their fuel consumption and flight delays. In reality, a high degree of uncertainty can exist in certain aircraft-aircraft encounters especially in cases where aircraft do not have the capabilities to communicate with each other. Through the use of a probabilistic approach and a multiple model (MM) trajectory information processing framework, this uncertainty can be effectively handled. For conflict detection, a randomized Monte Carlo (MC) algorithm is used to accurately detect conflicts, and, if a conflict is detected, a conflict resolution algorithm is run that utilizes a sequential list Viterbi algorithm. This thesis presents the MM CDR method and a comprehensive MC simulation and performance evaluation study that demonstrates its capabilities and efficiency

Fast tree-trellis list viterbi decoding

A list Viterbi algorithm (LVA) finds n most likely paths in a trellis diagram of a convolutional code. One of the most efficient LVAs is the tree-trellis algorithm of Soong and Huang. We propose a new implementation of this algorithm. Instead of storing the candidate paths in a single list sorted according to the metrics of the paths, we show that it is computationally more efficient to use several unsorted lists, where all paths of the same list have the same metric. For an arbitrary integer bit metric, both the time and space complexity of our implementation are linear in n. Experimental results for a binary symmetric channel and an additive white Gaussian noise channel show that our implementation is much faster than all previous LVAs