A Modified-SCD for Optimize Performance Rate at Polar Code

Introduction

Several types of capacity approaching codes has been developed and used for the real-time application such as in data storage and wireless network communication in order to achieve better data-rates. Earlier, the Shannon’s proof for the noisy channel code theorem was used as random coding approach (Shannon, 1948), but the random approach causes complexity during encoding and decoding. Therefore, to achieve the high capacity of code sequence with less encoding and decoding complications has been a major goal for the researchers. The first verified capacity-achieving codes were developed by Arikan and called as “polar codes” (Arikan, 2009), it has achieved required channel capacity with the explicit construction and attracted many courtesies for that.

The most important property of polar codes is their low designing complexity of decoding ( (), where is order and is block length), the implementation of polar codes with high block length is up to (Leroux, Raymond, Sarkis, & Gross, 2013). The initial classic SCD for the polar codes is very important element in order to provide capacity theorem, in addition SCD consist of some important properties like as deterministic and fixed complexity recursive architecture for better performance. In original form of polar codes, the decoder has the inferior performance at the finite ‘block-lengths’ as compared to the LDPC codes (Tal & Vardy, 2011). The channel polarization is the major breakthrough in the coding process, where the polar codes with different construction is asymptotically obtained by the symmetric binary input with the several memory-less channels and block codes. However, the application for error correction has recently shows the chances of polar codes applicability, also the phenomena of polarization in several signal processing and communications difficulty like as multiple access channels (Mahdavifar, El-Khamy, Lee, & Kang, 2016), wiretap channels (Mahdavifar & Vardy, 2011), BICM channels (Mahdavifar, El-Khamy, Lee, & Kang, 2015), broadcast channels (Goela, Abbe, & Gastpar, 2015) and data compression (Abbe, 2011). Moreover, there has been different enhanced prototype of polar codes for different type of applications such as concatenated polar codes (Mahdavifar, El-Khamy, Lee, & Kang, 2014), generalized polar codes (Korada, S¸as¸og˘lu, & Urbanke, 2014), universal polar codes (Hassani & Urbanke, 2014) and compound polar codes (Mahdavifar, El-Khamy, Lee, & Kang, 2013).