When you convert the floating-point value to a fixed-point value, you should change the value. It is rounding.
For example, there is a value "1.5".
fixed point (1.5) is 1 or 2, which one is the right value?
There are many rounding methods.
https://en.wikipedia.org/wiki/Rounding
1. normal round: Round_half_away_from_zero
2. bankers' round: Round half to even or http://www.xbeat.net/vbspeed/i_BankersRounding.htm (Gaussian rounding, round to even, bankers' rounding)
Polar Codes: https://simons.berkeley.edu/talks/polar-codes
From this site https://www.polarcodes.com/ you can watch the videos & download the documents.
https://www.ocf.berkeley.edu/~sasoglu/0100000041.pdf
15-859: Information Theory and its applications in theory of computation, Spring 2013, lecture 10, 11, 12
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A Practical Introduction to Polar Codes (A very simple tutorial for beginners)
- K (message) bits and N (code) bits (where K is a message and N is a code)
- BI-DMS: binary input discrete memoryless symmetric
- Attractive features:
- Fixed, low, and deterministic encoding and decoding
- Explicit construction
- Easy to implement
- BSC: binary symmetric channel
- BEC: binary erasure channel
- AWGN: additive white Gaussian channel
- Bhattacharyya parameter
Every primitive polynomial will have an odd number of terms, which means that every mask for a primitive polynomial will have an even number of 1 bit. Every primitive polynomial also defines a second primitive polynomial, its dual. The dual can be found by subtracting the exponent from the degree of the polynomial for each term. For example, given the 6th-degree polynomial, x6 + x + 1, its dual is x6-6 + x6-1 + x6-0, which is equal to x6 + x5 + 1. In Table 1, polynomials 1 and 2, 3 and 4, 5 and 6 are the duals of each other.
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