Improved Successive Cancellation Flip Decoding of Polar Codes Based on Error Distribution

Polar codes are a class of linear block codes that provably achieves channel capacity, and have been selected as a coding scheme for $5^{\rm th}$ generation wireless communication standards. Successive-cancellation (SC) decoding of polar codes has mediocre error-correction performance on short to moderate codeword lengths: the SC-Flip decoding algorithm is one of the solutions that have been proposed to overcome this issue. On the other hand, SC-Flip has a higher implementation complexity compared to SC due to the required log-likelihood ratio (LLR) selection and sorting process. Moreover, it requires a high number of iterations to reach good error-correction performance. In this work, we propose two techniques to improve the SC-Flip decoding algorithm for low-rate codes, based on the observation of channel-induced error distributions. The first one is a fixed index selection (FIS) scheme to avoid the substantial implementation cost of LLR selection and sorting with no cost on error-correction performance. The second is an enhanced index selection (EIS) criterion to improve the error-correction performance of SC-Flip decoding. A reduction of $24.6\%$ in the implementation cost of logic elements is estimated with the FIS approach, while simulation results show that EIS leads to an improvement on error-correction performance improvement up to $0.42$ dB at a target FER of $10^{-4}$.Comment: This version of the manuscript corrects an error in the previous ArXiv version, as well as the published version in IEEE Xplore under the same title, which has the DOI:10.1109/WCNCW.2018.8368991. The corrections include all the simulations of SC-Flip-based and SC-Oracle decoders, along with associated comments in-tex

Error Correction for Index Coding With Coded Side Information

Index coding is a source coding problem in which a broadcaster seeks to meet the different demands of several users, each of whom is assumed to have some prior information on the data held by the sender. If the sender knows its clients' requests and their side-information sets, then the number of packet transmissions required to satisfy all users' demands can be greatly reduced if the data is encoded before sending. The collection of side-information indices as well as the indices of the requested data is described as an instance of the index coding with side-information (ICSI) problem. The encoding function is called the index code of the instance, and the number of transmissions employed by the code is referred to as its length. The main ICSI problem is to determine the optimal length of an index code for and instance. As this number is hard to compute, bounds approximating it are sought, as are algorithms to compute efficient index codes. Two interesting generalizations of the problem that have appeared in the literature are the subject of this work. The first of these is the case of index coding with coded side information, in which linear combinations of the source data are both requested by and held as users' side-information. The second is the introduction of error-correction in the problem, in which the broadcast channel is subject to noise. In this paper we characterize the optimal length of a scalar or vector linear index code with coded side information (ICCSI) over a finite field in terms of a generalized min-rank and give bounds on this number based on constructions of random codes for an arbitrary instance. We furthermore consider the length of an optimal error correcting code for an instance of the ICCSI problem and obtain bounds on this number, both for the Hamming metric and for rank-metric errors. We describe decoding algorithms for both categories of errors

Prefixless q-ary balanced codes with ECC

We present a Knuth-like method for balancing q-ary codewords, which is characterized by the absence of a prefix that carries the information of the balancing index. Look-up tables for coding and decoding the prefix are avoided. We also show that this method can be extended to include error correction of single channel errors

Joint Source-Channel Coding and Unequal Error Protection for Video Plus Depth

Abstract-We consider the joint source-channel coding (JSCC) problem of 3-D stereo video transmission in video plus depth format over noisy channels. Full resolution and downsampled depth maps are considered. The proposed JSCC scheme yields the optimum color and depth quantization parameters as well as the optimum forward error correction code rates used for unequal error protection (UEP) at the packet level. Different coding scenarios are compared and the UEP gain over equal error protection is quantified for flat Rayleigh fading channels. Index Terms-3-D video, joint source-channel coding, unequal error protection, video plus depth

Capacity Estimation for Error Correction Code-based Embedding in Adaptive Rate Wireless Communication Systems

In this paper, we explore the performance of error correction code-based embedding in adaptive rate wireless communication systems. We first develop a model to illustrate the relationship between the selected modulation and coding scheme index, the current channel state, and the embedding capacity. Extensive simulations facilitate the development of expressions to describe the estimated embedding capacity for the proposed scheme when implemented within the single carrier physical layer of the IEEE 802.11ad, directional multi-Gigabit standard. We further identify and characterize various types of distortion and describe additional constraints that may serve to reduce the available embedding margin and overall embedding capacity