Source-linked AI summary
Diffusion Based Nanonetworking: A New Modulation Technique and Performance Analysis
Hamidreza Arjmandi, Amin Gohari, Masoume Nasiri Kenari, Farshid Bateni
TL;DR
The paper addresses interference and error propagation in molecular communication schemes for nanonetworks. It proposes MOCSK with a Poisson-based system model and derives error probabilities and a general lower bound; numerical results show lower error probability than CSK and MOSK.
Problem
Existing CSK and MOSK schemes are affected by delayed-molecule interference, while CSK also suffers error propagation through adaptive thresholds.
Method
The paper proposes MOCSK, alternating molecule types across slots while encoding symbols through diffusion rates, and evaluates it with a Poisson molecular communication model.
Results
The proposed scheme has a lower probability of error than CSK and MOSK in the numerical results.
Takeaways & Limitations
MOCSK avoids error propagation because current-symbol decoding is independent of previously transmitted and decoded symbols.
Abstract
from arXiv · showhide
In this letter, we propose a new molecular modulation scheme for nanonetworks. To evaluate the scheme we introduce a more realistic system model for molecule dissemination and propagation processes based on the Poisson distribution. We derive the probability of error of our proposed scheme as well as the previously introduced schemes, including concentration and molecular shift keying modulations by taking into account the error propagation effect of previously decoded symbols. Since in our scheme the decoding of the current symbol does not depend on the previously transmitted and decoded symbols, we do not encounter error propagation; and so as our numerical results indicate, the proposed scheme outperforms the previously introduced schemes. We then introduce a general molecular communication system and use information theoretic tools to derive fundamental limits on its probability of error.
I. INTRODUCTION
The paper examines diffusion-based molecular communication for short- and medium-range nanonetworks, where molecule concentration carries information. It proposes a new modulation method, a Poisson-based model, error analysis, and an information-theoretic error limit.
- I. INTRODUCTION: Diffusion-based molecular communication encodes information through molecule concentration in short- and medium-range nanonetworks.The transmitter varies molecule type and intensity, while propagation and receptor binding enable decoding.
- I. INTRODUCTION: Existing CSK and MOSK schemes suffer interference from molecules arriving after previous transmissions.CSK can also experience error leakage when a previous symbol is decoded incorrectly, while MOSK requires more complex molecular mechanisms.
- I. INTRODUCTION: The proposed modulation uses distinct molecule types in consecutive slots to suppress interference and outperforms existing schemes in the reported numerical results.The evaluation models propagation with a Poisson distribution and accounts for dependence on previously decoded symbols.
- I. INTRODUCTION: The paper derives error probabilities for the proposed and previous schemes and a fundamental minimum-error limit for an arbitrary molecular communication scheme.The paper also introduces a more general molecular communication system for information-theoretic analysis.
A. Previously introduced modulation schemes
CSK encodes symbols through molecule diffusion rates and adapts receiver thresholds to prior decoded symbols, whereas MOSK encodes them through molecule types and threshold detection.
- A. Previously introduced modulation schemes: CSK represents symbols using different molecule diffusion rates, with the receiver comparing received concentration against decision thresholds.For b bits, CSK uses 2^b diffusion rates.
- A. Previously introduced modulation schemes: CSK adapts current decision thresholds to the last decoded symbol because molecules from the previous slot may arrive late.A prior decoding error therefore leaks into the current symbol decision.
- A. Previously introduced modulation schemes: MOSK uses 2^b molecule types for b bits and decodes a symbol when exactly one type exceeds threshold τ.An error occurs if no type or multiple types exceed τ.
B. Proposed modulation scheme
MOCSK combines CSK-like diffusion-rate signaling with alternating molecule types across consecutive slots, reducing prior-symbol interference without encoding data in molecule type.
- B. Proposed modulation scheme: MOCSK alternates molecule types A1 and A2 between odd and even slots while encoding each symbol with diffusion rates.Each slot uses 2^b propagation rates to represent b bits.
- B. Proposed modulation scheme: Because consecutive slots use different molecule types, previous-symbol interference has almost disappeared.This separation distinguishes the proposed scheme from schemes affected by delayed molecules from earlier transmissions.
- B. Proposed modulation scheme: MOCSK makes the current decision threshold independent of the last decoded symbol.This removes the error-propagation mechanism described for CSK.
- B. Proposed modulation scheme: The number of molecule types remains two as b increases because data is encoded in concentration rather than molecule type.Thus the molecule-type count, and associated complexity, does not increase with b.
C. A Poisson model for molecular communication
The paper models molecular transmission with current-slot molecules, one-slot residue, and environmental Poisson noise, using Poisson diffusion and propagation processes to characterize received molecules.
- C. A Poisson model for molecular communication: The general model divides received molecules into current-slot molecules, residue from the last slot, and environmental noise.Residue from two or more earlier slots is ignored, and symbols occupy equal durations t_s.
- C. A Poisson model for molecular communication: Each molecule either misses the receiver or hits it in the current or next slot with probabilities P1 and P2, respectively.The model requires P1 + P2 ≤ 1 and assumes intra-molecule collisions have little effect on movement.
- C. A Poisson model for molecular communication: Molecules exiting each transmitter storage in a time slot follow Poisson(X), where X is the message-dependent diffusion rate.The Poisson assumption follows from many stored molecules and a small probability that each passes through the outlet.
- C. A Poisson model for molecular communication: Using Poisson thinning and addition of independent Poisson variables, the model derives the current-slot received molecule count from diffusion rates, hitting probabilities, and noise.The received count includes contributions associated with consecutive transmissions and environmental Poisson noise.
D. Decoding probabilities for CSK, MOSK and MOCSK
The section formulates symbol-by-symbol decoding probabilities for CSK, MOSK, and the proposed MOCSK under interference from neighboring transmissions. The comparisons use equal transmission powers and account for the molecule observations available to each decoder.
- CSK: CSK decodes by comparing received molecules of one type with a threshold determined by the last decoded symbol.The threshold can differ according to the previously decoded value, regardless of whether that value was correct.
- MOSK: MOSK decoding uses molecule type and compares one or two received molecule counts with a threshold, depending on whether consecutive symbols match.When consecutive symbols differ, the receiver considers observations for both the current and previous molecule types.
- MOCSK: MOCSK decoding compares the received count for the known current molecule type with thresholds to decode the current symbol.The receiver knows the molecule type associated with the current symbol in the proposed scheme.
- Comparison setting: The comparisons are restricted to simple symbol-by-symbol decoders evaluated with the same transmission powers.This keeps the comparison within a practically appealing decoder class.
- Higher modulation levels: The same conditional-probability calculation approach extends from binary schemes to quaternary and higher modulation levels.The passage states that higher-level cases can be calculated similarly.
A. Probability of error
The section derives average error probabilities while distinguishing schemes whose current decoding depends on previous decoded symbols from schemes whose decoding is independent of them. For BCSK, error propagation enters through recursive conditional-probability equations.
- BCSK: BCSK average error probability depends on both the previous transmitted symbol and the previous decoded symbol.The previous decoded symbol selects the current decision threshold, so an earlier decoding error affects the current decision.
- BCSK: BCSK conditional error probabilities are computed recursively because the previous decoded symbol may be correct or incorrect.The resulting relation is a system of linear equations, with analogous calculations for higher CSK levels.
- MOSK: MOSK current-symbol decoding is independent of the previous decoded symbol, so its average error probability is formed from conditional errors weighted by symbol probabilities.The relevant weighting uses the current and previous transmitted-symbol probabilities.
- MOCSK: MOCSK current-symbol decoding is independent of both the transmitted and previously decoded symbols used in the preceding slot.Its error probability therefore does not require the same dependence on prior decoding states.
B. Lower bound on probability of error of molecular communication system
The paper analyzes a general molecular communication system with Poisson molecule observations and a one-symbol decoder memory, then uses information-theoretic inequalities to lower-bound average decoding error. The bound is stated for an alphabet of size |B| and extends to M molecule types.
- System model: The general system uses two molecule types, with an encoder selecting diffusion rates from current and previous input symbols.Input symbols are independent and uniformly distributed over alphabet B.
- System model: The received molecule counts follow Poisson distributions after propagation, and the current symbol is decoded from the current observation and previous decoded symbol.The average error is represented as P(bB_i ≠ B_i).
- Information-theoretic bound: The mutual information between an input symbol and its decoded value is upper-bounded using the decoder’s one-symbol memory and the channel structure.The proof uses functional dependence, conditional-information reduction, input independence, and a Markov-chain relation.
- Information-theoretic bound: Fano’s inequality and entropy convexity convert the mutual-information bound into a lower bound on average probability of error.The alphabet size |B| appears in the entropy term used for this bound.
- Scope: The analysis extends straightforwardly to M molecule types, although those details are omitted because of space limitations.The stated extension is beyond the two-molecule-type presentation.
IV. NUMERICAL RESULTS
Numerical results compare error probability across CSK, MOSK, and proposed MOCSK schemes, and compare BMOCSK with an information-theoretic lower bound. The proposed scheme generally outperforms CSK, while the lower-bound gap grows rapidly with maximum transmission power.
- Simulation assumptions: The evaluations assume d = 16µm, t_s = 5.9 sec., P1 = 0.22, P2 = 0.04, and λ0 = 20 unless otherwise stated.These parameters define the baseline numerical setting.
- Error-probability comparisons: For binary and quaternary modulations, Fig. 1 compares probability of error against average transmission power per bit.The comparison includes CSK, MOSK, and proposed MOCSK schemes.
- Error-probability comparisons: MOCSK outperforms CSK at binary and higher levels, with the improvement becoming more significant as the hitting probability P2 increases.Increasing P2 increases interference from the previous symbol and degrades CSK performance.
- Error-probability comparisons: For binary modulation, BMOCSK substantially outperforms BMOSK, whereas quaternary MOSK performs better than QMOCSK using four molecule types.The quaternary MOSK comparison involves more complex transmitters and receivers.
- Lower-bound comparison: For BMOCSK with r_av/r_max = 0.5 and two molecule types, the gap from the matched lower bound increases rapidly with maximum transmission power.Additional lower-bound curves are shown for |B| = 4, 8, and 16 with M = 2.