Everyone sighed and said we are all done here, but then a funny thing happened. There was an interesting rediscovery around 1999 of low-density parity check (LDPC) codes, which everyone forgot really worked well, too. These codes were initially invented by Gallagher in 1963, meaning that by 1999 this technology was largely available patent free. A nice differentiator when compared to Turbo codes that were licensed by France Telecom until patent expiry in 2013.
Today: Turbo codes vs. LDPC codes
This brings us to where we are today: an ongoing heavyweight tussle between Turbo codes and LDPC codes, each claiming victory over the other in various use cases and applications. These codes are both so wonderful in their performance that it is quite reasonable to ask the question: Are we done in the channel coding space?
I don't believe so, and the reason is simple. It is all about the use cases. Remember, each technology generation is driven by new use cases and new technical requirements. 2G was about voice and very low data rates. 3G and 4G were increasingly more about the mobile internet and video. Turbo Codes and LDPC have served perfectly up to this point and will very likely do for a good while longer, but the requirements coming down the pipe for 5G are a lot more than just voice and video.These requirements are all over the use case map. Turbo and LDPC codes are unproven or are already known to fall short in many of these new applications, opening the door once again to another surprise.
Enter Polar codes
Lucky enough, consistent with the previous timeline of channel coding surprises and breakthrough achievements in history, some exciting research has once again emerged. Invented by Arikan in 2009, Polar codes are the first class of codes that areexplicitly proven (not only demonstrated/simulated in some cases) to achieve channel-capacity within an implementablecomplexity. In other words, compared to LDPC and Turbo codes, which are demonstrated to perform close to channel capacity in some scenarios particularly within the interest of today's systems and their requirements, Polar codes guarantee highest performance for any region of interest, in any applications.
Without considering any fundamental issues in coding and overall system design, the story would end here. However, that is once again not the case (fortunately or unfortunately, depending on your angle of interest in this space). The stellar throughput and bit-error-rate performance of today's most practical Polar codes come with the expense of slightly higher latency at the receiving end due to the inherent nature of the code construction. Moreover, the complexity of generating Polar codes at the transmitter end and also decoding at the receiving end still looks beyond the implementation capacity for a nearer-term timeline of interest, though they still provide the best performance under the same complexity requirements.
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