Channel Capacity - Heuristic proof

Quick recap of the channel capacity heuristic proof. Reference here: https://www.eecs.berkeley.edu/~dtse/Chapters_PDF/Fundamentals_Wireless_Communication_chapter5.pdf Assume we are transmitting a codeword in N dimensions. The dimension could represent time or any other signal characteristic. Assume it is corrupted with a noise vector (also N dimensions). Now each of the codewords can be represented as a point in N dimensional space. Assume also that we have a power constraint P (total power transmitted must not exceed P)- so all the received codewords must lie in an N-dimensional sphere of radius sqrt(N(P+sigma^2)). For error free decoding, all the received vectors (transmitted point + noise vector) should lie inside non-overlapping spheres inside this large sphere of radius sqrt(N(P+sigma^2)). The radius of this non-overlapping noise spheres has to be sigma^2 (noise variance) for a large N. Thus, max number of codewords that can be transmitted in this scenario can be geometrically deduced as sqrt(N(P+sigma^2))^N/sqrt(sigma^2)^N or equivalently the max number of bits that can be conveyed is log2(max_num_codewords). This yields the famous shannon expression for channel capacity. I.e no more information can be transmitted with the given power constraint on an AWGN channel with arbitrarily small error rate.

Today, while going through all the documents that have collected dust over the years, I started organizing them in to separate folders-by category. Bank related, income tax related, Visas, passport, stock certificates, real-estate investments, rental agreements, insurance etc.. the usual stuff. In the process, I came across my marks sheet from my under-grad. I stared it for a while. Most people hold themselves to some simple expectations. The expectation is that, one has to do what one is good at... regardless of the area of the job. "Well" here means whether one can do or has done new and innovative work in that area. For me, it is a bit late in life. However, to repeat a cliche, one should keep exploring. I am trying to recollect what I really-really enjoyed doing. What was I really-really good at? Should we all ask ourselves this question? May be the answer could even change from time to time. If you ask yourself that question often enough and you get an answer- I feel you are probably living a more fulfilling life. Let me know what u think.

What a wonderful day!

We choreographed a dance for dad's birthday. It was almost childish. In our conservative family environs, dancing itself was a big deal - so getting it right was not that important. The bigger part of "self growth" was for the first time in my life, I coordinated with people on the organization of an event. It felt so wonderful. We worked without taking ourselves too seriously but just wanted to make it fun for a bunch of people around us. The outcome was beautiful- none of us were perfect- but it was fun, nevertheless. I think the "key" learning that day was to not worry about getting things right- but just doing something different. My daughter was one of the best dancers.

Remembering a weekend at Pines

I shouted, pass the ball, here, here. In came the pass, I was right below the basket and all I had to do was jump. And swoosh.
Chamath complained laughingly.. He was fast but not tall enough to guard me and I had done well enough to create a toe-crushing fear (literally), if they get too close. I was this tall clumsy guy always hanging out near the basket. I could irritate even the usually quiet guy in the group with some rough play.
We won yet another game and headed back to the apartment. We showered and it was time for some dinner. Chaat house? California Pizza? the usual list was tossed around and one of them got selected. Randomly.
After dinner, we used to bid farewell to those friends who would head out to SFO for nocturnal activities and the rest of us would go back to the apartment, watched TV and joked and laughed at Suresh’s subtle humor, played cards or in-room cricket. One pitch catch was out. Supi troubled us with his flippers. Suresh was the aggressive one. He didn’t care if my TV broke as long as he was not out. Rama would always get out to a surprise full-toss. Dumb Charades or Pictionary used to be clean fun till late into the night. Rama used to be the most fun with his pictures and his incessant pointing to the same unidentifiable picture that he drew in first 10 seconds of the minute. Was it bird or was it a bottle? We would find out that it was an elephant. We would fall asleep eventually, to wake up late on Sunday morning.
After 11 am, all of us headed out for coffee. A short Mocha for me, a short latte for Rama and regular black coffee for the dude wearing sun-glasses. Suresh was always the dude among us. The black coffee eventually gave the dude, acute acidity. We hung out at Starbucks for an hour or so, reading the news paper left behind by others (occasionally buying one), looking at white girls and salivating at brand new cars parked around there.
We would get groceries and cook, eat, and sleep without even realizing another delightful weekend had come to an end.
Eventually Supi got tired of the routine and got married and would not join us for coffee. Luckily for us, though, the spouse turned out to be as much fun as Supi was, after the initial dislike for some of us! )
Long weekends had to be travel weekends, even if it was the same place that we had visited several times.
I came back to my current world when my little one, shouted with glee. Pointing at the sky, she said “Appa, Birdie”. I said “Yes, Birdie”.

My new BB mate

List of Day Cares for infants in Marthahalli/outer ring road area, Bangalore

Tom and Jerry - Varthur road - 4500 per month
This place is located in a quiet neighbourhood in BEML layout. Takes infants over 6 months. Has a decent ratio of kids/Teacher and Kids/helpers. It is set up in an independent house. There is a grill in the front portion of the house which keeps the kids safe. When we went to see the place, it was cleanly kept. There were stairs inside the house which were leading upto the top floor which is not occupied by the day-care. There is one room for sleeping. There are lot of beds sprawled on the floor. There were a few cribs for the young ones.

Kidzee - outer ring road (between Marthahalli and KR puram)
This is a chain. However, they do not accept kids below 1.5 years
http://kidzee.com/
AppleKids
This is a new franchise opened up in Marthahalli area. We didnt visit the place but from the website it does seem like a nice place.
http://applekids.in/

Kara International - Sarjapur Road - 7000 per month (overall)
This is truly world-class day-care. They even have pick up and drop off at additioal costs.
http://www.kara.in
Nand Gokul - Rajashree Layout - Marthahalli - 5000 per month
This is brand new and is set up in a quiet neighbourhood in the ground floor of an independent house. It is safe but I found it too small a place for the kids. It is still very very new. They had only 2 children at the time we visited. They were ready to accept children above 6 months.
http://nandgokul.com/
Podar Happy Kids - Sarjapur road (right next to Total Mall) - 5000-6000 per month http://podarhappykids.com
They accept children over one year. They have a very large place. Separate outdoor play area. Segragation of toddlers from infants, CCTVs and other things. Found it to be a bit on the expensive side. However, we liked it the most in the neighbourhood.

Vidyarambh - Sarjapur Road - 4500 per month
Infants are cared-for in a small apartment. The place is clean and the only teacher present at the time we visited looked well-trained. There were other 20-somethings ladies assisting her and we felt they were pretty OK. There is an attached play-home for older children (over 2 years) near by. The place has a tie-up with Wipro. It did seem pretty OK. This would have been next in the list for us. http://www.vidyarambh.com/

Soul of a new machine

What really runs this world is the passion of a few men. As in most professions, it is the creative urge which drives every good engineer. Wallach architects many machines which do not end up going to the market. He is on the verge of becoming a cynic when he gets prodded on to create a 32-bit version of an existing machine. Tracy Kidder describes the story of the hard work and the passion that goes into building this new machine.

Interesting Read.