Tag: Channel Polarization (Polar Codes)

Arıkan’s goal was to transmit messages accurately over a noisy channel at the fastest possible speed. … Arıkan’s new solution was to create near-perfect channels from ordinary channels by a process he called “Channel Polarization.” Noise would be transferred from one channel to a copy of the same channel to create a cleaner copy and a dirtier one. After a recursive series of such steps, two sets of channels emerge, one set being extremely noisy, the other being almost noise-free. The channels that are scrubbed of noise, in theory, can attain the Shannon limit. He dubbed his solution polar codes. It’s as if the noise was banished to the North Pole, allowing for pristine communications at the South Pole.
—WIRED, “Huawei, 5G, and the Man Who Conquered Noise”

In information theory, a Polar Code is a linear block error-correcting code. The code construction is based on a multiple recursive concatenation of a short kernel code which transforms the physical channel into virtual outer channels. When the number of recursions becomes large, the virtual channels tend to either have high reliability or low reliability (in other words, they polarize or become sparse), and the data bits are allocated to the most reliable channels. It is the first code with an explicit construction to provably achieve the channel capacity for symmetric binary-input, discrete, memoryless channels (B-DMC) with polynomial dependence on the gap to capacity. Notably, polar codes have modest encoding and decoding complexity O(n log n), which renders them attractive for many applications. Moreover, the encoding and decoding energy complexity of generalized polar codes can reach the fundamental lower bounds for energy consumption of two dimensional circuitry to within an O(nε polylog n) factor for any ε > 0.
—Wikipedia, “Polar code (coding theory)“