On the recognition of Speech

Speech is a highly complicated random signal, yet as simple as a deterministic periodic signal. We cannot imagine a day without having a speech conversation with anyone else. This signal conveys a lot of meaning and understanding - it is considered as one of the most significant modes of information transfer.

Speech is very much omnipresent, that we wish it can be used to build speech recognition systems and make the systems (or machines)  around us also understand speech. Speech recognition consists of a receptor (or input device/ similar to the ear) and a processor (where the speech recognition system is built/ similar to the brain). 

The speech signal processing here is a two fold problem - one which is its generation and the second its processing. Thus, the speech recognition problem is the study of the two sides of the same coin - synthesis/analysis. The synthesis step enables us to determine the features that are useful in the analysis. Common feature of speech are the formant frequencies, pitch, vowel/consonant etc.  

An isolated word recognition system is a very realistic problem to start with. Suppose we are using a vehicle that uses an Automatic Speech Recognition (ASR) system, then by the utterance of single words the driver will be able to perform tasks like turning on the head lights, increasing the volume of the stereo, or turning the windshield wipers when it is raining. The most common words in this scenario will be "Lights on", "Lights off", "Mute Stereo", "plus Volume" etc.


It has been reported that an ASR with ten words in the dictionary can work with an accuracy of 0.5%. This suggests that it is possible to treat the systems around us also as human - yes they can understand speech too.

How to Split Information ?

Splitting the information into non-overlapping chunks seems to be the problem ahead. Looking into the information as a vector space, we might ask if there exist a set of (non intersecting) subspaces that sums up to give the entire vector space (or the direct sum).

Showing that information is a vector space is not an easy task though. Depending on the class of information (for instance audio, text, image etc.) the vector space as well as the field over which it is defined changes. However a coding scheme can be associated with a vector space. 

Depending on the dimension of the code we are able to divide the space into sufficient number of subspaces that will depend upon the number of relay nodes as well. Information splitting hence becomes a code splitting or rate splitting problem.

Separation of Common and Unique Information

In the last post we were discussing about examples of common and unique information and were trying to explore its options in relay communication. Let us assume that the each relay node gets a part of the  codeword \(C\). The relay nodes if equipped to determine the common and the unique part of the information it received can use more power on the unique information part and a comparatively less power on the common information part.

For signals like images, the common and unique separation can be done using a multi-resolution filter. The low frequency(slowly varying) part forms the common information and the two orthogonal bandpass filters forms the unique information for the respective relay nodes. 

Suppose the source node performs a 2 slotted TDMA transmission, and half the relay nodes observes the first TDM symbol and the rest of the relay nodes observes the second TDM symbols what is the optimum coding that will result in achieving the decode-forward capacity? It is not very clear as to say in which domain does the separation exist. In the case of images though, we said it is the frequency domain.

Now once the separation domain becomes clear, the common information can be allotted some power level \(P_c\) and the unique part can be allotted some \(P_{u_1}\) and \(P_{u_2}\) respectively. If there exists two relay nodes then the power spent on the common part needs to be only \(\frac 12 P_c\). The other potential is that the common information can be transmitted when the channel gain is low, and an opportunistic communication can be performed for the unique information when the channel improves.

Common Informations Around Us

There is a good analogy for explaining common information. Consider the news of the Indian Cricket Team winning a test match. It does not really matter from which source you heard the news. This is because the PTI has handed over the news commonly to all the "newsmakers". Now consider news of the retirement of SRT. The decision (and of course the feelings associated) about his retirement is only known to him (and his close people) and different media reports in its unique way. The uniqueness in the reporting generates new information, and as a reader (viewer/listener) it is required to gather all these distinct pieces of information. 

SRT Retirement

 

Lords Test Win

The two news instances explains the term common information or shared information. 

Relating this to the relay communication scenario, we can observe that if the source is able to send unique information to each of the relay nodes, then the relay nodes can be used to its full efficiency. But this is a seemingly difficult task. Natural information comes as a combination of common information and certain unique information.

Information needs to be processed at the source to identify the common and unique information, and  then passed on to the relay. Each relay hence acts only as decode-forward nodes capable of only re-transmission of the information.

Device to Device Communication

In a few years to come, we will reach a point where the number of computing devices will cross the total human population. This phenomenal growth of the wireless technology brings new avenues to improve its efficiency and capacity. Days will not be far where you can turn these computing devices into sensor nodes and energy harvesters. The trend now is to make one device talk with the others.

Courtesy: www.citizenwarrior.com

The network engineers are already in the process of shifting to Ipv6  to inter-network this mammoth figure of mobile devices. A physical layer engineer is also very concerned since the modulation and coding schemes have to be modified from top to bottom. We can try to see some aspects of this upcoming scheme using a human analogy.

Alice wants to communicate some message to Bob.  Now Bob is standing in a building which is adjacent to where Alice stays. If Alice shouts at the top of her voice, Bob will be able to hear. But Alice does not prefer that mainly because the message is confidential. So Alice does the following: Alice tells her assistant Charlie the message (not the complete message)  and asks him to convey it to Bob. Alice will now call Bob from the balcony of her apartment and tell Bob the part of message not conveyed through Charlie.

Courtesy: ourcountryroad.blogspot.com

So has Alice lost her voice by shouting? If she if afraid of that, she would   call her second assistant Don and pass the remaining part of the message through him.

It is nice to see some technical aspects of this message communication where Alice and Bob are the source and destination respectively and Charlie and Don are the relay nodes. We begin with the simple model where Alice has a direct channel with Bob.

\( y_C = h_{AC} X_{AC}+Z_C \), 
\( y_D = h_{AD} X_{AD}+Z_D \),
\( y_B = h_{AB} X_{AB}+ h_{CB} X_{CB} + h_{DB} X_{DB} + Z_B \)

 The goal now is to determine a coding scheme such that the common information in \(X_{AB}\), \(X_{CB}\) and \(X_{DB}\) is zero.

Quiz 1

These are some multiple choice questions hand-picked to test your level of understanding in Engineering Mathematics. First take the quiz(preferably time bound) and let me know your response.

Happy news!!! Solutions to the quiz is now uploaded.
But there is a hurdle. The password of the solution file is the answer to the first 5 problems(All the alphabets are in uppercase) eg password: AADDB


Download Quiz 1                                                                                  Download Solution 1