List decoding

About: List decoding is a research topic. Over the lifetime, 7251 publications have been published within this topic receiving 151182 citations.

Dynamic-SCFlip Decoding of Polar Codes

Abstract: This paper proposes a generalization of the recently introduced successive cancellation flip (SCFlip) decoding of polar codes, characterized by a number of extra decoding attempts, where one or several positions are flipped from the standard SC decoding. To make such an approach effective, we first introduce the concept of higher order bit flips and propose a new metric to determine the bit flips that are more likely to correct the trajectory of the SC decoding. We then propose a generalized SCFlip decoding algorithm, referred to as dynamic-SCFlip (D-SCFlip), which dynamically builds a list of candidate bit flips, while guaranteeing that the next attempt has the highest probability of success among the remaining ones. Simulation results show that D-SCFlip is an effective alternative to SC-list decoding of polar codes, by providing very good error correcting performance, with an average computation complexity close to the one of the SC decoder.

Improved bit flipping decoding of low-density parity check codes

Abstract: In this correspondence, a new method for improving hard-decision bit-flipping decoding of low-density parity-check (LDPC) codes is presented. Bits with a number of unsatisfied check sums larger than a predetermined threshold are flipped with a probability p /spl les/ 1 which is independent of the code considered. The probability p is incremented during decoding according to some rule. With a proper choice of the initial p, the proposed improved bit-flipping (BF) algorithm achieves gain not only in performance, but also in average decoding time for signal-to-noise ratio (SNR) values of interest with respect to p = 1.

Decoding "turbo"-codes with the soft output Viterbi algorithm (SOVA)

Abstract: Iterative decoding of two dimensional systematic convolutional codes has been termed "turbo"-(de)coding. It is shown that the simple soft output viterbi algorithm (SOVA) meets all the requirements for iterative decoding if an a priori term is added. With simple 4 and 16 state codes surprisingly good performance is achieved for the Gaussian and Rayleigh channel with a very small degradation relative to the complicated MAP algorithm. >

Fast List Decoders for Polar Codes

Abstract: Polar codes asymptotically achieve the symmetric capacity of memoryless channels, yet their error-correcting performance under successive-cancellation (SC) decoding for short and moderate length codes is worse than that of other modern codes such as low-density parity-check (LDPC) codes. Of the many methods to improve the error-correction performance of polar codes, list decoding yields the best results, especially when the polar code is concatenated with a cyclic redundancy check (CRC). List decoding involves exploring several decoding paths with SC decoding, and therefore tends to be slower than SC decoding itself, by an order of magnitude in practical implementations. In this paper, we present a new algorithm based on unrolling the decoding tree of the code that improves the speed of list decoding by an order of magnitude when implemented in software. Furthermore, we show that for software-defined radio applications, our proposed algorithm is faster than the fastest software implementations of LDPC decoders in the literature while offering comparable error-correction performance at similar or shorter code lengths.

Introduction to coding theory

Abstract: Part I: AN ELEMENTARY INTRODUCTION TO CODING THE CONCEPT OF CODING Bitstrings and Binary Operations The Hamming Distance Binary Codes Error-Correcting Codes in General The Binary Symmetric Channel The Sphere-Packing Bound BINARY LINEAR CODES The Concept of Binary Linear Codes Block Coding The Effect of Coding Duality Binary Hamming and Simplex Codes Principle of Duality GENERAL LINEAR CODES Prime Fields Finite Fields Linear Codes Over Finite Fields Duality and Orthogonal Arrays Weight Distribution The Game of Set Syndrome Decoding REED-SOLOMON CODES RECURSIVE CONSTRUCTION I UNIVERSAL HASHING DESIGNS AND THE BINARY GOLAY CODE SHANNON ENTROPY ASYMPTOTIC RESULTS 3-DIMENSIONAL CODES, PROJECTIVE PLANES SUMMARY AND OUTLOOK Part II: THE THEORY OF CODES AND THEIR APPLICATIONS SUBFIELD CODES AND TRACE CODES The Trace Trace Codes and Subfield Codes Galois Closed Codes Automorphism Groups CYCLIC CODES Some Primitive Cyclic Codes of Length 15 Theory of Cyclic Codes Decoding BCH-Codes Constacyclic Codes Remarks RECURSIVE CONSTRUCTIONS, COVERING RADIUS Construction X Covering Radius OA IN STATISTICS AND COMPUTER SCIENCE OA and Independent Random Variables Linear Shift Register Sequences Cryptography Two-Point Based Sampling Resilient Functions Derandomization of Algorithms Authentication and Universal Hashing THE GEOMETRIC DESCRIPTION OF CODES Linear Codes as Sets of Points Quadratic Forms, Bilinear Forms and Caps Caps: Constructions and Bounds ADDITIVE CODES Basic Constructions and Applications Additive Cyclic Codes Quantum Codes THE LAST CHAPTER The Linear-Programming Bound Algebraic-Geometric Codes List Decoding Expander Codes tms-Nets Sphere Packings Designs Nonlinear Codes REFERENCES