Dear Prof. Platonov,

Hope you are well and every thing is fine with you. 

Concerning your question. i think there is overlap between the analog and the digital system. In digital systems we speak about signals in form of binary numbers. I mean the signals represent binary numbers and so purposely in order to assess the quality of the transmission of such signals representing data is by bit error rate. It is logical to assess the transmission efficiency of binary numbers by the number of bits in errors for a given number of transmitted bits. The measurement of the bit error rate is straight forward here we just use a digital comparator between the input and output bits.and count the difference.

In case of analog signal transmission ideally we have to deliver the transited waveform of the signal  with zero distortion and noise. But there is no ideal communication system. So, one allows an acceptable level of distortion and noise according to the minimum allowed signal to noise plus distortion ratio.This distortion is practically defined in different form such as harmonic distortion and inter modulation distortion.measure normally by single tone base band signal or by two tones with with two different but near frequencies. Okay you can measure the divination between the received and the transmitted signal by mean square error as a sum of noise and distortion.

LET US RETURN BACK TO THE DIGITAL SYSTEM, basically the transmitted digital signal is encoded into waveform called symbols, these symbols will be distorted in the transmission process and delivered in this deviated form to the receiver . The receiver must decide on the logic values contained in the symbols. This is  a conversion process from wave forms into binary numbers. It is the bit decision processes which must evaluate the received signal to extract the correct bits. There is the hard decision which is less than optimum process. But there is the soft decision which is based on the euclidean distance which is a form of mean square error.

So, the mean square error is used ultimately to decide on the logic value of the symbols in the soft decision process as your hypothesis. 

Best wishes for you

Dear Prof. Platonov,

Hope you are well and every thing is fine with you. 

Concerning your question. i think there is overlap between the analog and the digital system. In digital systems we speak about signals in form of binary numbers. I mean the signals represent binary numbers and so purposely in order to assess the quality of the transmission of such signals representing data is by bit error rate. It is logical to assess the transmission efficiency of binary numbers by the number of bits in errors for a given number of transmitted bits. The measurement of the bit error rate is straight forward here we just use a digital comparator between the input and output bits.and count the difference.

In case of analog signal transmission ideally we have to deliver the transited waveform of the signal  with zero distortion and noise. But there is no ideal communication system. So, one allows an acceptable level of distortion and noise according to the minimum allowed signal to noise plus distortion ratio.This distortion is practically defined in different form such as harmonic distortion and inter modulation distortion.measure normally by single tone base band signal or by two tones with with two different but near frequencies. Okay you can measure the divination between the received and the transmitted signal by mean square error as a sum of noise and distortion.

LET US RETURN BACK TO THE DIGITAL SYSTEM, basically the transmitted digital signal is encoded into waveform called symbols, these symbols will be distorted in the transmission process and delivered in this deviated form to the receiver . The receiver must decide on the logic values contained in the symbols. This is  a conversion process from wave forms into binary numbers. It is the bit decision processes which must evaluate the received signal to extract the correct bits. There is the hard decision which is less than optimum process. But there is the soft decision which is based on the euclidean distance which is a form of mean square error.

So, the mean square error is used ultimately to decide on the logic value of the symbols in the soft decision process as your hypothesis. 

Best wishes for you

I like the discussion, thanks Anatoliy and Abdulhalim. I think that BER is not only generalized and rough characteristic of the quality of transmission. The quality of signal recovery or decoding is adding as well. So we have the transmiter, the channel, and the receiver, they participate in the transmission quality.

So I take BER is mostly measured/solved at the receiver. In wireless the noise is the biggest problem and noise is unpredictable which makes the characterization difficult. However, I don't think  we should not use MSE or more, because any new measure can give more details/information of such unknown behavior/characteristics.

Overall, I agree that the topic needs to be discuss more, but I will need to relate topic to specific scenarios and to read your paper you published.

Dear Colleagues, excuse me for temporary silence. Me and my team pass the "point of  Curie" in complex experiment. It takes the all time. Thank you for the comments.

I'll turn back to this page in nearest days. 

The topic we touched is interesting and important. It's enough to look at the small question: what is more important in wireless sensor nets - accuracy of measured values delivered to addresse, or BER?

Dear Colleagues,

I'll repeat excellent greeting of Prof. Zekry^:  

"Hope you are well and everything is fine with you!"  

Excuse me for a long silence. At the end of 2014, me and my team entered the consortium and we received grant for elaboration of the prototype of the perfect adaptive CS with a feedback channel (AFCS) transmitting signals without coding. We realized and tested prototype in two versions: as the mixed signal system (on serial digital elements, only original element is analog adaptive modulator), and as the digital system realized only on serial elements used in modern DCS.

Both versions were tested, and results of experiments confirmed their functioning according to the aims of grant and both ones transmit the signals with the limit accuracy, bitrate and energy-spectral efficiency.

Overcoming the "Curie point" at the end of 2015 transferred our research to the new level with a number of new Curie points to be passed, and we passed them. The work gave a lot of new information that permits me to answer much deeper to the own and other questions which appeared in the course of previous discussion.

The protoyype was realized in two wersions: 

I will try to answer on all questions, and will be sincerely pleased for every comment and question including doubts.

____________________________

Question we discuss also concerns my earlier question:   “Can somebody tell why MSE is not used as the basic measure of analog signals transmission quality (e.g. in wireless sensors)?"

Error correction codes used in digital CS (DCS) ensure practically ideal transmission, if a number of errors in the code block does not exceed error correction threshold. This number depends of SNR at the channel output which decreases for greater distances between the transmitters and receivers. At a definite distance, number of errors exceeds the threshold that causes sharp growth of errors which violates the transmission.

Thus, while the error threshold is not exceeded, DCS transmits signals ideally, and MSE of recovered signals has zero values. If the number of errors is greater the threshold, MSE “explodes” and takes the values close to the variance of input signals. For these reasons, in digital communications, MSE can be useful only for evaluation of the range of reliable transmission that can be done more simply.

Currently, performance of DCS as a communication channel is assessed by the bit error rate (BER) and error correction capability of the code, energy efficiency (ratio of the “energy per bit” to the spectral power density of the channel noise), and by the spectral efficiency of transmission (bit/s/Hz). The low informative MSE is not used. 

One should note that another and usually not discussed reason of the lack of MSE in digital transmission of analog signals is the coding. Digital CS do not allow the formulation of any general “input-output” mathematical model of encoders, which would describe a dependence of output codes on the parameters of real coding units. This does not permit to formulate MSE of transmission and to find the parameters of coding units (also of the other units of the system) minimizing values of MSE, as it is being done in optimization of analog controlling or measurement systems by the methods of Bayesian estimation theory.

For this reason, although existence of optimal encoding and decoding methods is proved, there are no strict methods indicated for the construction or technical realization of these results, and basic theorems in the theory of information transmission have the character of existence theorems [1],[2].  

Currently, optimization of wireless DCS is carried out taking into account the listed above information criterions, scenario of teh suggested application, tasks solved by the system, as well employment, technological, cost and other characteristics. All these criteria are mutually connected, and search of optimal balance between them is carried out employing and improving known theoretical, technical and technological solutions. The final result depends, in large extent, on the experience and intuition of researchers and engineers, but evaluation of a degree of utilization of the energy, spectral and other recourses of the designed systems is, in the best case, rough approximate. For its complexity, design of wireless DCS deserved the title of "black magic" [3]. This is the cost of ideal transmission provided by the correcting codes.

These difficulties disappear in AFCS theory and design. Instead of the coders, end node (EN) transmitters of AFCS employ adaptive PAM modulators adjusted by the controls formed in base stations (BS) and delivered to EN over feedback channel.

This permits to formulate MSE of transmission as a function of all influencing its values parameters and characteristics of input signals, noises, as well “free” and adjusted parameters of the modulator and estimating-controlling algorithm stored in memory units of BS. Solution of (MSE based) optimization task determines the parameters and characteristics of the main units of optimal AFCS including algorithms, as well the approach to designing of the system transmitting the signals with minimal MSE.

Experiments had shown that so designed prototype of AFCS transmits input analog signals according to the theoretical expectations, with minimal MSE, bitrate equal to the capacity of the system, and energy - spectral efficiency of transmission attains the limits established by information theory [4],[5]. 

The last research shows that short code blocks (of 10-15 bits length) also can be transmitted by optimal AFCS in real time with the limit energy-spectral efficiency and the given confidence level (reliability).  

__________________________________ 

Investigations on AFCS had the “golden age" in 1960-1970s and were suddenly humpered after 1975. Until last decade, research had being carrioed out by a small group of researchers. Currently, intensity of research grows but they remain stricto academic. Until now, I could find neither information about any implementation of the results.

Simplicity of EN transmitters and optimal utilization of their energy and spectral recourses make AFCS potentially useful for applications class of top-efficient narrowband, low energy, and low cost systems. It seems, we have a great field for further theoretical and applied research. 

Remark: I think, the said above also answers the question from Dec. 2013:

“Can somebody tell why MSE is not used as the basic measure of analog signals transmission quality (e.g. in wireless sensors)?”

With regards

Anatoliy Platonov

P.S.  I express my gratitude to Prof. Zekry for non-standard questions and thoughts on the information theory and analog or digital systems, which initiated further serious discussion.the 

References

[1]   Dobrushin R.L., Prelov V.V.,  Information Theory, Encyclopedia  of         Mathematics, http://www.encyclopediaofmath.org/index.php?title=Information_theory&oldid=18981, 2011.      

[2]   Haykin S., Communication Systems, NY, J. Wiley, 2001.

[3]   Hunn N., Essentials of Short-Range Wireless. Cambridge, UK, 2010.  

[4]   Platonov A., Capacity and power-bandwidth efficiency of wireless  adaptive feedback communication systems, IEEE Communication Letters, vol. 16, no. 5, 2012, pp.573-576.

[5]   Platonov A., Zaitsev Ie., Jeleński B., Opalski L., Piekarski J., Chaciński H., “Prototype of Analog Feedback Communication System: First Results of Experimental Study”, 4th IEEE Conf. on Comm. and Networks. (BlackSeaCom),  Varna, Bulgaria, 2016, IEEE Xplore