Polar Codes over Fading Channels with Power and Delay Constraints

The inherent nature of polar codes being channel specific makes it difficult to use them in a setting where the communication channel changes with time. In particular, to be able to use polar codes in a wireless scenario, varying attenuation due to fading needs to be mitigated. To the best of our knowledge, there has been no comprehensive work in this direction thus far. In this work, a practical scheme involving channel inversion with the knowledge of the channel state at the transmitter, is proposed. An additional practical constraint on the permissible average and peak power is imposed, which in turn makes the channel equivalent to an additive white Gaussian noise (AWGN) channel cascaded with an erasure channel. It is shown that the constructed polar code could be made to achieve the symmetric capacity of this channel. Further, a means to compute the optimal design rate of the polar code for a given power constraint is also discussed.Comment: 6 pages, 6 figure

Low-Complexity Puncturing and Shortening of Polar Codes

In this work, we address the low-complexity construction of shortened and punctured polar codes from a unified view. While several independent puncturing and shortening designs were attempted in the literature, our goal is a unique, low-complexity construction encompassing both techniques in order to achieve any code length and rate. We observe that our solution significantly reduces the construction complexity as compared to state-of-the-art solutions while providing a block error rate performance comparable to constructions that are highly optimized for specific lengths and rates. This makes the constructed polar codes highly suitable for practical application in future communication systems requiring a large set of polar codes with different lengths and rates.Comment: to appear in WCNC 2017 - "Polar Coding in Wireless Communications: Theory and Implementation" Worksho

Study of the operational SNR while constructing polar codes

Channel coding is commonly based on protecting information to be communicated across an unreliable medium, by adding patterns of redundancy into the transmission path. Also referred to as forward error control coding (FECC), the technique is widely used to enable correcting or at least detecting bit errors in digital communication systems. In this paper we study an original FECC known as polar coding which has proven to meet the typical use cases of the next generation mobile standard. This work is motivated by the suitability of polar codes for the new coming wireless era. Hence, we investigate the performance of polar codes in terms of bit error rate (BER) for several codeword lengths and code rates. We first perform a discrete search to find the best operating signal-to-noise ratio (SNR) at two different code rates, while varying the blocklength. We find in our extensive simulations that the BER becomes more sensitive to operating SNR (OSNR) as long as we increase the blocklength and code rate. Finally, we note that increasing blocklength achieves an SNR gain, while increasing code rate changes the OSNR domain. This trade-off sorted out must be taken into consideration while designing polar codes for high-throughput application

Throughput-based Design for Polar Coded-Modulation

Typically, forward error correction (FEC) codes are designed based on the minimization of the error rate for a given code rate. However, for applications that incorporate hybrid automatic repeat request (HARQ) protocol and adaptive modulation and coding, the throughput is a more important performance metric than the error rate. Polar codes, a new class of FEC codes with simple rate matching, can be optimized efficiently for maximization of the throughput. In this paper, we aim to design HARQ schemes using multilevel polar coded-modulation (MLPCM). Thus, we first develop a method to determine a set-partitioning based bit-to-symbol mapping for high order QAM constellations. We simplify the LLR estimation of set-partitioned QAM constellations for a multistage decoder, and we introduce a set of algorithms to design throughput-maximizing MLPCM for the successive cancellation decoding (SCD). These codes are specifically useful for non-combining (NC) and Chase-combining (CC) HARQ protocols. Furthermore, since optimized codes for SCD are not optimal for SC list decoders (SCLD), we propose a rate matching algorithm to find the best rate for SCLD while using the polar codes optimized for SCD. The resulting codes provide throughput close to the capacity with low decoding complexity when used with NC or CC HARQ