Explore the vast range of titles available.

Polar coding gives rise to the first explicit family of codes that provably achieve capacity with efficient encoding and decoding for a wide range of channels. However, its performance at short blocklengths under standard successive cancellation decoding is far from optimal. A well-known way to improve the performance of polar codes at short blocklengths is CRC precoding followed by successive-cancellation list decoding. This approach, along with various refinements thereof, has largely remained the state of the art in polar coding since it was introduced in 2011. Recently, Arıkan presented a new polar coding scheme, which he called polarization-adjusted convolutional (PAC) codes. At short blocklengths, such codes offer a dramatic improvement in performance as compared to CRC-aided list decoding of conventional polar codes. PAC codes are based primarily upon the following main ideas: replacing CRC codes with convolutional precoding (under appropriate rate profiling) and replacing list decoding by sequential decoding. One of our primary goals in this paper is to answer the following question: is sequential decoding essential for the superior performance of PAC codes? We show that similar performance can be achieved using list decoding when the list size L is moderately large (say, L⩾128). List decoding has distinct advantages over sequential decoding in certain scenarios, such as low-SNR regimes or situations where the worst-case complexity/latency is the primary constraint. Another objective is to provide some insights into the remarkable performance of PAC codes. We first observe that both sequential decoding and list decoding of PAC codes closely match ML decoding thereof. We then estimate the number of low weight codewords in PAC codes, and use these estimates to approximate the union bound on their performance. These results indicate that PAC codes are superior to both polar codes and Reed–Muller codes. We also consider random time-varying convolutional precoding for PAC codes, and observe that this scheme achieves the same superior performance with constraint length as low as ν=2.

In this paper, we prove a quantum union bound that is relevant when performing a sequence of binary-outcome quantum measurements on a quantum state. The quantum union bound proved here involves a tunable parameter that can be optimized, and this tunable parameter plays a similar role to a parameter involved in the Hayashi–Nagaoka inequality (Hayashi & Nagaoka 2003 IEEE Trans. Inf. Theory 49 , 1753–1768. ( doi:10.1109/TIT.2003.813556 )), used often in quantum information theory when analysing the error probability of a square-root measurement. An advantage of the proof delivered here is that it is elementary, relying only on basic properties of projectors, Pythagoras' theorem, and the Cauchy–Schwarz inequality. As a non-trivial application of our quantum union bound, we prove that a sequential decoding strategy for classical communication over a quantum channel achieves a lower bound on the channel's second-order coding rate. This demonstrates the advantage of our quantum union bound in the non-asymptotic regime, in which a communication channel is called a finite number of times. We expect that the bound will find a range of applications in quantum communication theory, quantum algorithms and quantum complexity theory.

Because a quantum measurement generally disturbs the state of a quantum system, one might think that it should not be possible for a sender and receiver to communicate reliably when the receiver performs a large number of sequential measurements to determine the message of the sender. We show here that this intuition is not true, by demonstrating that a sequential decoding strategy works well even in the most general 'one-shot' regime, where we are given a single instance of a channel and wish to determine the maximal number of bits that can be communicated up to a small failure probability. This result follows by generalizing a non-commutative union bound to apply for a sequence of general measurements. We also demonstrate two ways in which a receiver can recover a state close to the original state after it has been decoded by a sequence of measurements that each succeed with high probability. The second of these methods will be useful in realizing an efficient decoder for fully quantum polar codes, should a method ever be found to realize an efficient decoder for classical-quantum polar codes.

The complexity of belief propagation algorithms for decoding LDPC codes can be significantly reduced by storing the precomputed sum of messages in variable nodes. This optimization is particularly useful for layered schedule decoders, where it also simplifies the hardware implementation. To reduce the requirement for the amount of information to be processed during decoding, the information bottleneck method is used, which reduces the bit width of all updated messages. However, under this approach, re-calculation of the sum when excluding one of messages becomes complicated. The paper is devoted to development of an algorithm for construction of a discrete binary function corresponding to such subtraction. When using this algorithm, the number of stored and used lookup tables for variable nodes is reduced.

The following paper adapts the classical Zigangirov-Jelinek algorithm to the decoding of nonbinary block codes under severe mixed jamming. To ensure reliable communications in this scenario we combine reception techniques based on distribution free statistical tests with sequential decoding on syndrome trellises. It will be shown that the proposed approach can ensure relatively high transmission rate with reasonable complexity.

Sequential decoding can achieve a very low computational complexity and short decoding delay when the signal-to-noise ratio (SNR) is relatively high. In this article, a low-complexity high-throughput decoding architecture based on a sequential decoding algorithm is proposed for convolutional codes. Parallel Fano decoders are scheduled to the codewords in parallel input buffers according to buffer occupancy, so that the processing capabilities of the Fano decoders can be fully utilized, resulting in high decoding throughput. A discrete time Markov chain (DTMC) model is proposed to analyze the decoding architecture. The relationship between the input data rate, the clock speed of the decoder and the input buffer size can be easily established via the DTMC model. Different scheduling schemes and decoding modes are proposed and compared. The novel high-throughput decoding architecture is shown to incur 3-10% of the computational complexity of Viterbi decoding at a relatively high SNR.

This chapter contains sections titled: Convolutional Codes Representation and Encoding Viterbi Decoding Algorithm List Decoding Upper Bound on Bit Error Probability for Viterbi Decoding Sequential Decoding Parallel‐Concatenated Convolutional Codes and Soft Input Soft Output Decoding SISO Decoding Algorithms References

This chapter describes a class of algorithm, known as sequential decoding algorithms, whose intricacy is essentially independent of the memory of the encoder. The chapter begins by introducing a quality measure that could guide a decoder in its search for the most promising path to explore. This leads naturally to the stack algorithm, which is the simplest one to describe and analyze. After discussing the stack algorithm, it provides a more intricate Fano algorithm. Then the chapter discusses Creeper, which combines the best properties of the other two algorithms. For all three algorithms, it analyzes their computational performances and obtain upper bounds on the decoding error probabilities.

Many libraries and librarians have embraced graphic novels. A number of books, articles, and presentations focus on the history of the medium and offer advice on building and maintaining collections. Few, however, give attention to the integration of graphic novels into a library's instructional efforts. This paper explores the characteristics of graphic novels that make them a valuable resource for research and information literacy instruction, identifies skills and competencies that can be taught through the study of graphic novels, and provides specific examples of how to incorporate graphic novels into instruction. Adapted from the source document.