Abstract
The maximum likelihood detection theory improves the error rate of a sub-optimal but cheaper, coded symbol recovery loop using oversampling proposed as an alternate solution for the decoding problem without the log-likelihood ratio computation. The former implementation delivers the output data in one-symbol delay, and the required transistor count makes this approach attractive for ultra-low-energy wireless applications. The proposed hardware upgrade includes an analog to digital converter and fixed-point accumulation logic to compute the soft values, replacing a trigger used as a hard detector. This work investigates the soft decoding in the presence of binary and non-binary source symbols. Simulation results show that the soft approach improves the signal-to-noise ratio by 3 dB and 2.5 dB when the encoding rates are 1/3 and 2/3.
Similar content being viewed by others
Data Availability
Please contact the author for data request or visit his Homepage.
Code Availability
Custom code, available on GitHub soon.
Abbreviations
- ACS:
-
Add-compare-select
- ADC:
-
Analog to digital converter
- ALC:
-
Automatic level control
- AWGN:
-
Additive white Gaussian noise
- DFA:
-
Deterministic finite automaton
- DSP:
-
Digital signal processor
- ISI:
-
Inter-symbolic interference
- LLR:
-
Log-likelihood ratio
- LNA:
-
Low-noise amplifier
- LPF:
-
Low-pass filter
- ML:
-
Maximum-likelihood
- MP-VCO:
-
Multi-phase voltage-controlled oscillator
- MSE:
-
Mean square error
- PAM:
-
Pulse amplitude modulation
- PDF:
-
Probability density function
- PMF:
-
Probability mass function
- PSK:
-
Phase-shift keying
- RAM:
-
Random access memory
- RF:
-
Radio-frequency
- SNR:
-
Signal-to-noise ratio
- TCM:
-
Trellis-code modulation
- VCA:
-
Voltage-controlled amplifier
References
Peng, H., Liu, R., Hou, Y., & Zhao, L. (2016). A Gb/s parallel block-based Viterbi decoder for convolutional codes on GPU. In 2016 8th International Conference on Wireless Communications Signal Processing (WCSP) (pp. 1–6). China: Yangzhou.
Hagenauer, J., & Hoeher, P. (1989). A Viterbi algorithm with soft-decision outputs and its applications. In 1989 IEEE Global Telecommunications Conference and Exhibition’Communications Technology for the 1990s and Beyond’ (pp. 1680-1686), TX, USA: Dallas.
Hagenauer, J., & Papke, L. (1994). Decoding turbo-codes with the soft output Viterbi algorithm (SOVA). In Proceedings of IEEE International Symposium on Information Theory (p. 164). Norway: Trondheim, Norway.
Ramteke, S., Kakde, S., Suryawanshi, Y., & Meshram, M. (2015). Performance analysis of Turbo decoder using soft output Viterbi algorithm. In 2015 International Conference on Communications and Signal Processing (ICCSP) (pp. 1332–1336). India: Melmaruvathur.
Visalli, G. (2019). Analysis and performance of coded symbol recovery loop using oversampling. EURASIP Journal on Advances in Signal Processing, 2019, 1–16.
Visalli, G., Pappalardo, F., Avellone, G., Rimi, F., & Galluzzo, A. (2008). Method and system for coding decoding signals and computer program product therefor. Google Patents. US Patent 7,424,068
Hagenauer, J., & Winklhofer, M. (1998). The analog decoder. In Proceedings of the IEEE International Symposium on Information Theory (p. 145). USA: Cambridge, MA.
Loeliger, H., Lustenberger, F., Helfenstein, M., & Tarkoy, F. (1998). Probability propagation and decoding in analog VLSI. In Proceedings of the IEEE International Symposium on Information Theory (p. 146). USA: Cambridge, MA.
Tretter, S. A. (1995). Double-sideband suppressed-carrier amplitude modulation and coherent detection (pp. 73–78). Boston, MA: Springer.
Ungerboeck, G. (1987). Trellis-coded modulation with redundant signal sets part I: Introduction. IEEE Communications Magazine, 25(2), 5–11.
Ungerboeck, G. (1987). Trellis-coded modulation with redundant signal sets part II: State of the art. IEEE Communications Magazine, 25(2), 12–21.
Wei, R., Ritcey, J. A., & Lu, B. (2015). TCM with differential encoding: Set partitioning, trellis designs, and distance analysis. IEEE Transactions on Communications, 63(8), 2776–2787.
Napolitano, A. (2016). Cyclostationarity: New trends and applications. Signal Processing, 120, 385–408.
Izzo, L., & Napolitano, A. (2003). Sampling of generalized almost-cyclostationary signals. IEEE Transactions on Signal Processing, 51(6), 1546–1556.
Cohen, D., Rebeiz, E., Eldar, Y.C., Cabric, D. (2013). Cyclic spectrum reconstruction and cyclostationary detection from sub-Nyquist samples. In 2013 IEEE 14th Workshop on Signal Processing Advances in Wireless Communications (SPAWC) (pp. 425–429).
Landau, L. T. N., Dörpinghaus, M., & Fettweis, G. P. (2018). 1-bit quantization and oversampling at the receiver: Sequence-based communication. EURASIP Journal on Wireless Communications and Networking, 2018, 1–24.
Krone, S., & Fettweis, G. (2012). Capacity of communications channels with 1-bit quantization and oversampling at the receiver. In 2012 35th IEEE Sarnoff Symposium (pp. 1–7).
Fettweis, G., Dörpinghaus, M., Bender, S., Landau, L., Neuhaus, P., & Schlüter, M. (2019). Zero crossing modulation for communication with temporally oversampled 1-bit quantization. In 2019 53rd Asilomar Conference on Signals, Systems, and Computers (pp. 207–214).
Proakis, J. G. (2007). Digital communications (5th ed.). New York: McGraw Hill.
Oppenheim, A. V., Willsky, A. S., & Nawab, S. H. (1996). Signals and systems (2nd ed.). USA: Prentice-Hall Inc.
Liao, Y.-T., & Richard Shi, C.-J. (2008). A 6–11Ghz multi-phase VCO design with active inductors. In 2008 IEEE International Symposium on Circuits and Systems (pp. 988–991).
Papoulis, A. (2007). Probability, random variables and stochastic processes (5th ed.). New York: McGraw-Hill Companies.
Mesgarzadeh., B., & Alvandpour, A. (2006). A wide-tuning range 1.8 Ghz quadrature VCO utilizing coupled ring oscillators. In 2006 IEEE International Symposium on Circuits and Systems (pp. 4–pp).
Katyal, V., Geiger, R.L., & Chen, D.J. (2008). Adjustable hysteresis CMOS Schmitt triggers. In 2008 IEEE International Symposium on Circuits and Systems (pp. 1938–1941).
Trivedi, R. (2006). Low power and high speed Sample-and-Hold Circuit. 2006 49th IEEE International Midwest Symposium on Circuits and Systems, 1, 453–456.
Kakarountas, A. P., Theodoridis, G., Papadomanolakis, K. S., & Goutis, C. (2003). A novel high-speed counter with counting rate independent of the counter’s length. In 10th IEEE International Conference on Electronics, Circuits and Systems, 2003. ICECS 2003. Proceedings of the 2003 (Vol. 3, pp. 1164–1167).
Mutz, D., & George, K. (2016). Costas loop and FFT based BPSK demodulation for pulsed radar receivers. 2016 IEEE Aerospace Conference (pp. 1–12). Big Sky: MT, USA.
Gallager, R. G. (2008). Principles of digital communication. Cambridge, UK: Cambridge University Press.
Benedetto, S., Biglieri, E., & Castellani, V. (1988). Digital transmission theory. USA: Prentice-Hall Inc.
Farsad, N., Rao, M., & Goldsmith, A. (2018). Deep learning for joint source-channel coding of text. In 2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) (pp. 2326–2330).
Jiang, Y., Kim, H., Asnani, H., Kannan, S., Oh, S., & Viswanath, P. (2020). Joint channel coding and modulation via deep learning. In 2020 IEEE 21st International Workshop on Signal Processing Advances in Wireless Communications (SPAWC) (pp. 1–5).
Acknowledgements
Not available.
Funding
Not applicable.
Author information
Authors and Affiliations
Contributions
The author read and approved the final manuscript.
Corresponding author
Ethics declarations
Conflict of interest
The author declares that he has no competing interests.
Consent for publication
Not applicable.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Visalli, G. Upgrading an analog recovery loop for optimized decoding jointly to an increased data rate. Telecommun Syst 78, 239–252 (2021). https://doi.org/10.1007/s11235-021-00807-9
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11235-021-00807-9