Polar Coding for the Large Hadron Collider: Challenges in Code Concatenation

In this work, we present a concatenated repetition-polar coding scheme that is aimed at applications requiring highly unbalanced unequal bit-error protection, such as the Beam Interlock System of the Large Hadron Collider at CERN. Even though this concatenation scheme is simple, it reveals significant challenges that may be encountered when designing a concatenated scheme that uses a polar code as an inner code, such as error correlation and unusual decision log-likelihood ratio distributions. We explain and analyze these challenges and we propose two ways to overcome them.Comment: Presented at the 51st Asilomar Conference on Signals, Systems, and Computers, November 201

Concatenated Polar Codes and Joint Source-Channel Decoding

In this dissertation, we mainly address two issues: 1. improving the finite-length performance of capacity-achieving polar codes; 2. use polar codes to efficiently exploit the source redundancy to improve the reliability of the data storage system. In the first part of the dissertation, we propose interleaved concatenation schemes of polar codes with outer binary BCH and convolutional codes to improve the finite-length performance of polar codes. For asymptotically long blocklength, we show that our schemes achieve exponential error decay rate which is much larger than the sub-exponential decay rate of standalone polar codes. In practice we show by simulation that our schemes outperform stand-alone polar codes decoded with successive cancellation or belief propagation decoding. The performance of concatenated polar and convolutional codes can be comparable to stand-alone polar codes with list decoding in the high signal to noise ratio regime. In addition to this, we show that the proposed concatenation schemes require lower memory and decoding complexity in comparison to belief propagation and list decoding of polar codes. With the proposed schemes, polar codes are able to strike a good balance between performance, memory and decoding complexity. The second part of the dissertation is devoted to improving the decoding performance of polar codes where there is leftover redundancy after source compression. We focus on language-based sources, and propose a joint-source channel decoding scheme for polar codes. We show that if the language decoder is modeled as erasure correcting outer block codes, the rate of inner polar codes can be improved while still guaranteeing a vanishing probability of error. The improved rate depends on the frozen bit distribution of polar codes and we provide a formal proof for the convergence of that distribution. Both lower bound and maximum improved rate analysis are provided. To compare with the non-iterative joint list decoding scheme for polar codes, we study a joint iterative decoding scheme with graph codes. In particular, irregular repeat accumulate codes are exploited because of low encoding/decoding complexity and capacity achieving property for the binary erasure channel. We propose how to design optimal irregular repeat accumulate codes with different models of language decoder. We show that our scheme achieves improved decoding thresholds. A comparison of joint polar decoding and joint irregular repeat accumulate decoding is given

On the Concatenations of Polar Codes and Non-binary LDPC Codes

An interleaved concatenation scheme of polar codes with non-binary low-density parity check (NBLDPC) codes is proposed in this paper to improve the error-correcting performance of polar codes with finite code length. The information blocks of inner polar codes are split into several information sub-blocks, and several segment successive cancellation list (SSCL) decoders are carried out in parallel for all inner polar codes. Moreover, for a better error-correcting performance, an improved SCL decoder with a selective extension is proposed for the concatenated polar codes, which will be referred to selective extended segment SCL (SES-SCL) decoder. The SESSCL decoder uses soft information of some unreliable information sub-blocks for the decoding of subsequent sub-blocks so as to mitigate the error propagation of premature hard decision of S-SCL decoder. Simulation results show that NBLDPC-polar codes can outperform Reed Solomon (RS)-polar codes. NBLDPCpolar codes with the proposed SES-SCL algorithm can also be comparable to pure polar codes with cyclic redundancy check aided successive cancellation list (CA-SCL) decoding with list size L = 4 in the high SNR, but require lower decoding storage. Therefore, NBLDPC-polar codes may strike a better balance between memory space and performance compared to the state-of-art schemes in the finite length regime

Polar Code Constructions Based on LLR Evolution

Polar code constructions based on mutual information or Bhattacharyya parameters of bit-channels are intended for hard-output successive cancellation (SC) decoders, and thus might not be well designed for use with other decoders, such as soft-output belief propagation (BP) decoders or successive cancellation list (SCL) decoders. In this letter, we use the evolution of messages, i.e., log-likelihood ratios, of unfrozen bits during iterative BP decoding of polar codes to identify weak bit-channels, and then modify the conventional polar code construction by swapping these bit-channels with strong frozen bit-channels. The modified codes show improved performance not only under BP decoding, but also under SCL decoding. The code modification is shown to reduce the number of low-weight codewords, with and without CRC concatenation

The Effect of Error Propagation on the Performance of Polar Codes Utilizing Successive Cancellation Decoding Algorithm

 In this paper, we discuss and analyze the effect of error propagation on the performance polar codes decoded using the successive cancellation algorithm. We show that error propagation due to erroneous bit decision is a catastrophic issue for the successive cancellation decoding of polar codes. Even a wrong decision on a single bit may cause an abundance of successor bits to be wrongly decoded. Furthermore, we observe that the performance of polar codes is significantly improved if even single bit errors are detected and corrected before the decoding of successor bits