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Non-Equiprobable Signaling for Wireless Channels Subject to Mobility and Delay Spread

Sandesh Rao Mattu, Nishant Mehrotra, Robert Calderbank

TL;DR

The paper tackles BER degradation in OFDM wireless channels with mobility and delay spread by introducing non-equiprobable signaling through shaping on rings of standard QAM constellations and integrating this shaping with LDPC decoding. It develops shaping encoders/decoders and a method to compute LDPC log-likelihood ratios that account for the nonuniform energy distribution, enabling flexible fractional bit rates. Across 4-QAM and 16-QAM, simulations on a Vehicular-A channel show up to about 4 dB BER gains at BER = 10^-3, with a manageable PAPR trade-off, while maintaining effectiveness at higher rates. The work demonstrates that energy-biased signaling with ring shaping provides a practical mechanism to improve wireless performance using existing modulation families and LDPC coding, especially at lower-to-moderate spectral efficiencies.

Abstract

This letter describes how to improve performance of OFDM systems by combining non-equiprobable signaling with low density parity check (LDPC) coding. We partition a standard QAM constellation into annular subconstellations of equal size, and we implement non-equiprobable signaling through a shaping code which selects subconstellations with large average energy less frequently than subconstellations with small average energy. In equiprobable signaling, the LDPC code selects a signal point from the inner subconstellation. In non-equiprobable signaling this inner signal point has a representative in each subconstellation and the shaping code selects the representative for transmission. It is possible to use standard QAM constellations to achieve any desired fractional bit rate with this method of shaping the energy distribution of the transmitted signal. We describe how to combine coding and shaping by integrating shaping into the calculation of log-likelihood ratios (LLRs) necessary for decoding LDPC codes. We present simulation results for non-equiprobable transmission at $1.5$ bits/symbol on a representative Veh-A channel showing gains of $4$ dB at a bit error rate (BER) of $10^{-3}$. As the transmission rate increases, the gains from non-equiprobable signaling diminish, but we show through simulation that they are still significant for $16$-QAM.

Non-Equiprobable Signaling for Wireless Channels Subject to Mobility and Delay Spread

TL;DR

The paper tackles BER degradation in OFDM wireless channels with mobility and delay spread by introducing non-equiprobable signaling through shaping on rings of standard QAM constellations and integrating this shaping with LDPC decoding. It develops shaping encoders/decoders and a method to compute LDPC log-likelihood ratios that account for the nonuniform energy distribution, enabling flexible fractional bit rates. Across 4-QAM and 16-QAM, simulations on a Vehicular-A channel show up to about 4 dB BER gains at BER = 10^-3, with a manageable PAPR trade-off, while maintaining effectiveness at higher rates. The work demonstrates that energy-biased signaling with ring shaping provides a practical mechanism to improve wireless performance using existing modulation families and LDPC coding, especially at lower-to-moderate spectral efficiencies.

Abstract

This letter describes how to improve performance of OFDM systems by combining non-equiprobable signaling with low density parity check (LDPC) coding. We partition a standard QAM constellation into annular subconstellations of equal size, and we implement non-equiprobable signaling through a shaping code which selects subconstellations with large average energy less frequently than subconstellations with small average energy. In equiprobable signaling, the LDPC code selects a signal point from the inner subconstellation. In non-equiprobable signaling this inner signal point has a representative in each subconstellation and the shaping code selects the representative for transmission. It is possible to use standard QAM constellations to achieve any desired fractional bit rate with this method of shaping the energy distribution of the transmitted signal. We describe how to combine coding and shaping by integrating shaping into the calculation of log-likelihood ratios (LLRs) necessary for decoding LDPC codes. We present simulation results for non-equiprobable transmission at bits/symbol on a representative Veh-A channel showing gains of dB at a bit error rate (BER) of . As the transmission rate increases, the gains from non-equiprobable signaling diminish, but we show through simulation that they are still significant for -QAM.

Paper Structure

This paper contains 13 sections, 20 equations, 6 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model
  3. Channel estimation
  4. Shaping
  5. Shaping Encoder
  6. Shaping Decoder
  7. LDPC Decoding
  8. Rate, PAPR, and Complexity Considerations
  9. Numerical Results
  10. $4$-QAM, $15$-length shaping
  11. $4$-QAM, $23$-length shaping
  12. $16$-QAM, $23$-length shaping
  13. Conclusions

Figures (6)

  • Figure 1: Block diagram of the OFDM communication scheme with shaping.
  • Figure 2: Constellation points used for communication in the shaping scheme.
  • Figure 3: Block diagram showing a shaping encoder. Uncoded bits are provided as input. A shaping code $[1\ 0\ 0]^\top$ (length $3$) is used.
  • Figure 4: Coded bit-error performance comparison between OFDM modulation with and without shaping. $4$-QAM, $15$-length shaping with $1$ sparsity.
  • Figure 5: Coded bit-error performance comparison between OFDM modulation with and without shaping. $4$-QAM, $23$-length shaping with $3$ sparsity.
  • ...and 1 more figures