Ph.D, MS, B-Tech

Dr. Karthi Balasubramanian received his Bachelor of Technology degree from Netaji Subhas Institute of Technology (formerly known as Delhi Institute of Technology) in Electronics and Communication engineering and MS degree in VLSI Design from Simon Fraser University, Canada. Later, he obtained his doctorate degree from Amrita Vishwa Vidyapeetham for his work on 'A new complexity measure for time series analysis and classification'. He is now working as an Assistant Professor in the department of Electronics and Communication Engineering,  Amrita School of Engineering, Coimbatore. 


His areas of interest include

  • Application of nonlinear dynamics and complexity analysis for analysis and characterization of EEG, ECG and EMG signals.
  • VLSI architectures for decoding of Modern Error-Correcting Codes.

Research Focus

  • Heart Rate Variability analysis in patients with epilepsy(In collaboration with Pati Labs, University of Alabama epilepsy center).
    We explore the use of non-linear dynamics and complexity analysis to study the changes in the heart rate variability (HRV) caused due to epileptic seizures. The relationship between EEG and ECG is being explored for identification of biomarkers for early detection of sudden unexpected death in epilepsy (SUDEP).
  • VLSI architecture for Reliability based soft decision decoding of turbo codes for satellite communication (Funded by Indian Space Research Organization- RESPOND Project)


Publication Type: Journal Article

Year of Publication Title


N. Nagaraj and Dr. Karthi Balasubramanian, “Three perspectives on complexity: entropy, compression, subsymmetry”, The European Physical Journal Special Topics, vol. 226, pp. 3251–3272, 2017.[Abstract]

There is no single universally accepted definition of `Complexity'. There are several perspectives on complexity and what constitutes complex behaviour or complex systems, as opposed to regular, predictable behaviour and simple systems. In this paper, we explore the following perspectives on complexity: effort-to-describe (Shannon entropy H, Lempel-Ziv complexity LZ), effort-to-compress (ETC complexity) and degree-of-order (Subsymmetry or SubSym). While Shannon entropy and LZ are very popular and widely used, ETC is relatively a new complexity measure. In this paper, we also propose a novel normalized complexity measure SubSym based on the existing idea of counting the number of subsymmetries or palindromes within a sequence. We compare the performance of these complexity measures on the following tasks: (A) characterizing complexity of short binary sequences of lengths 4 to 16, (B) distinguishing periodic and chaotic time series from 1D logistic map and 2D Hénon map, (C) analyzing the complexity of stochastic time series generated from 2-state Markov chains, and (D) distinguishing between tonic and irregular spiking patterns generated from the `Adaptive exponential integrate-and-fire' neuron model. Our study reveals that each perspective has its own advantages and uniqueness while also having an overlap with each other.

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Dr. Karthi Balasubramanian, Harikumar, K., Nagaraj, N., and Pati, S., “Vagus nerve stimulation modulates complexity of heart rate variability differently during sleep and wakefulness”, Annals of Indian Academy of Neurology, vol. 20, no. 4, pp. 403-407, 2017.[Abstract]

Progressive loss of heart rate variability (HRV) and complexity are associated with increased risk of mortality in patients with cardiovascular disease and are a candidate marker for patients at risk of sudden cardiac death. HRV is influenced by the cardiac autonomic nervous system (ANS), although it is unclear which arm of the ANS (sympathetic or parasympathetic) needs to be perturbed to increase the complexity of HRV. In this case-control study, we have analyzed the relation between modulation of vagus nerve stimulation (VNS) and changes in complexity of HRV as a function of states of vigilance. We hypothesize that VNS - being a preferential activator of the parasympathetic system - will decrease the heart rate (HR) and increase the complexity of HRV maximum during sleep. The electrocardiogram (EKG) obtained from a 37-year-old, right-handed male with known intractable partial epilepsy and left therapeutic VNS was analyzed during wakefulness and sleep with VNS ON and OFF states. Age-matched control EKG was obtained from five participants (three with intractable epilepsy and two without epilepsy) that had no VNS implant. The study demonstrated the following: (1) VNS increased the complexity of HRV during sleep and decreased it during wakefulness. (2) An increase in parasympathetic tone is associated with increased complexity of HRV even in the presence of decreased HR. These results need to be replicated in a larger cohort before developing patterned stimulation using VNS to stabilize cardiac dysautonomia and prevent fatal arrhythmias.

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N. Nithin and Dr. Karthi Balasubramanian, “Dynamical Complexity Of Short and Noisy Time Series”, The European Physical Journal Special Topics, vol. 226, pp. 2191-2204, 2017.[Abstract]

Shannon Entropy has been extensively used for characterizing complexity of time series arising from chaotic dynamical systems and stochastic processes such as Markov chains. However, for short and noisy time series, Shannon entropy performs poorly. Complexity measures which are based on lossless compression algorithms are a good substitute in such scenarios. We evaluate the performance of two such Compression-Complexity Measures namely Lempel-Ziv complexity (LZ) and Effort-To-Compress (ETC) on short time series from chaotic dynamical systems in the presence of noise. Both LZ and ETC outperform Shannon entropy (H) in accurately characterizing the dynamical complexity of such systems. For very short binary sequences (which arise in neuroscience applications), ETC has higher number of distinct complexity values than LZ and H, thus enabling a finer resolution. For two-state ergodic Markov chains, we empirically show that ETC converges to a steady state value faster than LZ. Compression-Complexity Measures are promising for applications which involve short and noisy time series.

More »»
PDF iconDynamical-Complexity-of-Short-and-Noisy-Time-Series.pdf


Dr. Karthi Balasubramanian and Nagaraj, N., “Aging and cardiovascular complexity: effect of the length of RR tachograms”, PeerJ, vol. 4, p. e2755, 2016.[Abstract]

As we age, our hearts undergo changes that result in a reduction in complexity of physiological interactions between different control mechanisms. This results in a potential risk of cardiovascular diseases which are the number one cause of death globally. Since cardiac signals are nonstationary and nonlinear in nature, complexity measures are better suited to handle such data. In this study, three complexity measures are used, namely Lempel–Ziv complexity (LZ), Sample Entropy (SampEn) and Effort-To-Compress (ETC). We determined the minimum length of RR tachogram required for characterizing complexity of healthy young and healthy old hearts. All the three measures indicated significantly lower complexity values for older subjects than younger ones. However, the minimum length of heart-beat interval data needed differs for the three measures, with LZ and ETC needing as low as 10 samples, whereas SampEn requires at least 80 samples. Our study indicates that complexity measures such as LZ and ETC are good candidates for the analysis of cardiovascular dynamics since they are able to work with very short RR tachograms. More »»


Dr. Karthi Balasubramanian, NAIR, S. I. L. P. A. S., and Nagaraj, N., “Classification of periodic, chaotic and random sequences using approximate entropy and Lempel–Ziv complexity measures”, Pramana, vol. 84, pp. 365–372, 2015.[Abstract]

`Complexity' has several definitions in diverse fields. These measures are indicators of some aspects of the nature of the signal. Such measures are used to analyse and classify signals and as a signal diagnostics tool to distinguish between periodic, quasiperiodic, chaotic and random signals. Lempel–Ziv (LZ) complexity and approximate entropy (ApEn) are such popular complexity measures that are widely used for characterizing biological signals also. In this paper, we compare the utility of ApEn, LZ complexities and Shannon's entropy in characterizing data from a nonlinear chaotic map (logistic map). In this work, we show that LZ and ApEn complexity measures can characterize the data complexities correctly for data sequences as short as 20 in length while Shannon's entropy fails for length less than 50. In the case of noisy sequences with 10{%} uniform noise, Shannon's entropy works only for lengths greater than 200 while LZ and ApEn are successful with sequences of lengths greater than 30 and 20, respectively. More »»


Dr. Karthi Balasubramanian, Prabhu, G. R., and Nagaraj, N., “Comment on'Interpretation of the Lempel-Ziv Complexity Measure in the context of Biomedical Signal Analysis'”, arXiv preprint arXiv:1308.0130, 2013.[Abstract]

In this Communication, we express our reservations on some aspects of the interpretation of the Lempel-Ziv Complexity measure (LZ) by Mateo et al. in "Interpretation of the Lempel-Ziv complexity measure in the context of biomedical signal analysis," IEEE Trans. Biomed. Eng., vol. 53, no. 11, pp. 2282-2288, Nov. 2006. In particular, we comment on the dependence of the LZ complexity measure on number of harmonics, frequency content and amplitude modulation. We disagree with the following statements made by Mateo et al. 1. "LZ is not sensitive to the number of harmonics in periodic signals." 2. "LZ increases as the frequency of a sinusoid increases." 3. "Amplitude modulation of a signal doesnot result in an increase in LZ." We show the dependence of LZ complexity measure on harmonics and amplitude modulation by using a modified version of the synthetic signal that has been used in the original paper. Also, the second statement is a generic statement which is not entirely true. This is true only in the low frequency regime and definitely not true in moderate and high frequency regimes. More »»


N. Nagaraj, Dr. Karthi Balasubramanian, and Dey, S., “A new complexity measure for time series analysis and classification”, The European Physical Journal Special Topics, vol. 222, pp. 847–860, 2013.[Abstract]

Complexity measures are used in a number of applications including extraction of information from data such as ecological time series, detection of non-random structure in biomedical signals, testing of random number generators, language recognition and authorship attribution etc. Different complexity measures proposed in the literature like Shannon entropy, Relative entropy, Lempel-Ziv, Kolmogrov and Algorithmic complexity are mostly ineffective in analyzing short sequences that are further corrupted with noise. To address this problem, we propose a new complexity measure ETC and define it as the ``Effort To Compress'' the input sequence by a lossless compression algorithm. Here, we employ the lossless compression algorithm known as Non-Sequential Recursive Pair Substitution (NSRPS) and define ETC as the number of iterations needed for NSRPS to transform the input sequence to a constant sequence. We demonstrate the utility of ETC in two applications. ETC is shown to have better correlation with Lyapunov exponent than Shannon entropy even with relatively short and noisy time series. The measure also has a greater rate of success in automatic identification and classification of short noisy sequences, compared to entropy and a popular measure based on Lempel-Ziv compression (implemented by Gzip). More »»

Publication Type: Book Chapter

Year of Publication Title


N. Nagaraj and Dr. Karthi Balasubramanian, “Measuring Complexity of Chaotic Systems With Cybernetics Applications”, in Handbook of Research on Applied Cybernetics and Systems Science, 2017, pp. 301-334.[Abstract]

Measuring complexity of systems is very important in Cybernetics. An aging human heart has a lower complexity than that of a younger one indicating a higher risk of cardiovascular diseases, pseudo-random sequences used in secure information storage and transmission systems are designed to have high complexity (to resist malicious attacks), brain networks in schizophrenia patients have lower complexity than corresponding networks in a healthy human brain. Such systems are typically modeled as deterministic nonlinear (chaotic) system which is further corrupted with stochastic noise (Gaussian or uniform distribution). After briefly reviewing various complexity measures, this chapter explores characterizing the complexity of deterministic nonlinear chaotic systems (tent, logistic and Hénon maps, Lorenz and Rössler flows) using specific measures such as Lempel-Ziv complexity, Approximate Entropy and Effort-To-Compress. Practical applications to neuron firing model, intra-cranial pressure monitoring, and cardiac aging detection are indicated.

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Publication Type: Conference Paper

Year of Publication Title


Dr. Karthi Balasubramanian, Vineeth, K. V., Neeraj, A., and Nikhil, K. M., “MOS characteristics and a modified linear MOS resistor”, in International Conference for Technical Postgraduates (TECHPOS), 2009, 2009.[Abstract]

This paper presents an overview of MOS device characteristics and its use as voltage controlled resistors. A modified gate driving mechanism is proposed to enhance the MOS resistor properties. Generally, MOS resistors behave linearly only for a small value of Drain-to-Source voltage (VDS). With the new scheme, the non-linearity that arises out of its dependence on VDS is removed and the linearity property of the resistor is kept intact even for larger values of VDS. More »»


P. Gautham, Parthasarathy, R., and Dr. Karthi Balasubramanian, “Low-power pipelined MIPS processor design”, in Proceedings of the 2009 12th International Symposium on Integrated Circuits, ISIC '09, 2009.[Abstract]

This paper presents the design and implementation of a low power five-stage parallel pipelined structure of a MIPS-32 compatible CPU. The various blocks include the data-path, control logic, data and program memories. Hazard detection and data forwarding units have been included for efficient implementation of the pipeline. A modified architecture is proposed that leads to significant power reduction by reducing unwanted transitions. Verilog design followed by synthesis on to Xilinx spartan-3E FPGA was done. On-chip distributed memory of Spartan-3E was used for the data and the program memory implementations. More »»


Dr. Karthi Balasubramanian, Arunkumar, R., Jayachandran, J., Jayapal, V., Chundatt, B. A., and Freeman, J. D., “Object recognition and obstacle avoidance robot”, in 2009 Chinese Control and Decision Conference, 2009.[Abstract]

Design highlights of a ldquoThree-wheeled Autonomous Navigational Robotrdquo are presented in this paper. An efficient modular architecture is proposed for ease of adding various modules to the robot. Obstacle detection, pattern recognition and obstacle avoidance are the key aspects of the design. The robot has intelligence built into it that enables it to recognize and pick up balls of a particular colour and ignore other objects in its path. A single board computer mounted on the robot acts as the central controller. It communicates with ultrasonic sensors and motors through multiple microcontrollers and controls the entire motion of the unit. As part of the robot design, a modified H-bridge circuit for driving DC motors efficiently is proposed in this paper. More »»