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

Coding theorems for turbo code ensembles

This paper is devoted to a Shannon-theoretic study of turbo codes. We prove that ensembles of parallel and serial turbo codes are "good" in the following sense. For a turbo code ensemble defined by a fixed set of component codes (subject only to mild necessary restrictions), there exists a positive number γ0 such that for any binary-input memoryless channel whose Bhattacharyya noise parameter is less than γ0, the average maximum-likelihood (ML) decoder block error probability approaches zero, at least as fast as n -β, where β is the "interleaver gain" exponent defined by Benedetto et al. in 1996

Self-concatenated code design and its application in power-efficient cooperative communications

In this tutorial, we have focused on the design of binary self-concatenated coding schemes with the help of EXtrinsic Information Transfer (EXIT) charts and Union bound analysis. The design methodology of future iteratively decoded self-concatenated aided cooperative communication schemes is presented. In doing so, we will identify the most important milestones in the area of channel coding, concatenated coding schemes and cooperative communication systems till date and suggest future research directions

A New Class of Multiple-rate Codes Based on Block Markov Superposition Transmission

Hadamard transform~(HT) as over the binary field provides a natural way to implement multiple-rate codes~(referred to as {\em HT-coset codes}), where the code length $N=2^p$ is fixed but the code dimension $K$ can be varied from $1$ to $N-1$ by adjusting the set of frozen bits. The HT-coset codes, including Reed-Muller~(RM) codes and polar codes as typical examples, can share a pair of encoder and decoder with implementation complexity of order $O(N \log N)$. However, to guarantee that all codes with designated rates perform well, HT-coset coding usually requires a sufficiently large code length, which in turn causes difficulties in the determination of which bits are better for being frozen. In this paper, we propose to transmit short HT-coset codes in the so-called block Markov superposition transmission~(BMST) manner. At the transmitter, signals are spatially coupled via superposition, resulting in long codes. At the receiver, these coupled signals are recovered by a sliding-window iterative soft successive cancellation decoding algorithm. Most importantly, the performance around or below the bit-error-rate~(BER) of $10^{-5}$ can be predicted by a simple genie-aided lower bound. Both these bounds and simulation results show that the BMST of short HT-coset codes performs well~(within one dB away from the corresponding Shannon limits) in a wide range of code rates