Systematic polar coding

Cataloged from PDF version of article.Polar codes were originally introduced as a class of non-systematic linear block codes. This paper gives encoding and decoding methods for systematic polar coding that preserve the low-complexity nature of non-systematic polar coding while guaranteeing the same frame error rate. Simulation results are given to show that systematic polar coding offers significant advantages in terms of bit error rate performance

Hybrid Polar Encoding with Applications in Non-Coherent Channels

In coding theory, an error-correcting code can be encoded either systematically or non-systematically. In a systematic encode, the input data is embedded in the encoded output. Conversely, in a non-systematic code, the output does not contain the input symbols. In this paper, we propose a hybrid encoding scheme for polar codes, in which some data bits are systematically encoded while the rest are non-systematically encoded. Based on the proposed scheme, we design a joint channel estimation and data decoding scheme. We use the systematic bits in the hybrid encoding scheme as pilots for channel estimation. To mitigate the code rate loss caused by the pilots and to provide additional error detecting capability, we propose a dynamic pilot design by building connections between the systematic bits and non-systematic bits. Simulation results show that the performance of the proposed scheme approaches that of the traditional non-systematic polar coding scheme with perfect channel state information (CSI) with the increase of SNR.Comment: 12 pages, 5 figure

Eye position modulates retinotopic responses in early visual areas: a bias for the straight-ahead direction

Even though the eyes constantly change position, the location of a stimulus can be accurately represented by a population of neurons with retinotopic receptive fields modulated by eye position gain fields. Recent electrophysiological studies, however, indicate that eye position gain fields may serve an additional function since they have a non-uniform spatial distribution that increases the neural response to stimuli in the straight-ahead direction. We used functional magnetic resonance imaging and a wide-field stimulus display to determine whether gaze modulations in early human visual cortex enhance the blood-oxygenation-level dependent (BOLD) response to stimuli that are straight-ahead. Subjects viewed rotating polar angle wedge stimuli centered straight-ahead or vertically displaced by ±20° eccentricity. Gaze position did not affect the topography of polar phase-angle maps, confirming that coding was retinotopic, but did affect the amplitude of the BOLD response, consistent with a gain field. In agreement with recent electrophysiological studies, BOLD responses in V1 and V2 to a wedge stimulus at a fixed retinal locus decreased when the wedge location in head-centered coordinates was farther from the straight-ahead direction. We conclude that stimulus-evoked BOLD signals are modulated by a systematic, non-uniform distribution of eye-position gain fields

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

Polar codes have attracted much recent attention as the first codes with low computational complexity that provably achieve optimal rate-regions for a large class of information-theoretic problems. One significant drawback, however, is that for current constructions the probability of error decays sub-exponentially in the block-length (more detailed designs improve the probability of error at the cost of significantly increased computational complexity \cite{KorUS09}). In this work we show how the the classical idea of code concatenation -- using "short" polar codes as inner codes and a "high-rate" Reed-Solomon code as the outer code -- results in substantially improved performance. In particular, code concatenation with a careful choice of parameters boosts the rate of decay of the probability of error to almost exponential in the block-length with essentially no loss in computational complexity. We demonstrate such performance improvements for three sets of information-theoretic problems -- a classical point-to-point channel coding problem, a class of multiple-input multiple output channel coding problems, and some network source coding problems