List decoding

About: List decoding is a(n) research topic. Over the lifetime, 7251 publication(s) have been published within this topic receiving 151182 citation(s).

Low-Density Parity-Check Codes

Abstract: A low-density parity-check code is a code specified by a parity-check matrix with the following properties: each column contains a small fixed number j \geq 3 of l's and each row contains a small fixed number k > j of l's. The typical minimum distance of these codes increases linearly with block length for a fixed rate and fixed j . When used with maximum likelihood decoding on a sufficiently quiet binary-input symmetric channel, the typical probability of decoding error decreases exponentially with block length for a fixed rate and fixed j . A simple but nonoptimum decoding scheme operating directly from the channel a posteriori probabilities is described. Both the equipment complexity and the data-handling capacity in bits per second of this decoder increase approximately linearly with block length. For j > 3 and a sufficiently low rate, the probability of error using this decoder on a binary symmetric channel is shown to decrease at least exponentially with a root of the block length. Some experimental results show that the actual probability of decoding error is much smaller than this theoretical bound.

Error bounds for convolutional codes and an asymptotically optimum decoding algorithm

Abstract: The probability of error in decoding an optimal convolutional code transmitted over a memoryless channel is bounded from above and below as a function of the constraint length of the code. For all but pathological channels the bounds are asymptotically (exponentially) tight for rates above R_{0} , the computational cutoff rate of sequential decoding. As a function of constraint length the performance of optimal convolutional codes is shown to be superior to that of block codes of the same length, the relative improvement increasing with rate. The upper bound is obtained for a specific probabilistic nonsequential decoding algorithm which is shown to be asymptotically optimum for rates above R_{0} and whose performance bears certain similarities to that of sequential decoding algorithms.

Optimal decoding of linear codes for minimizing symbol error rate (Corresp.)

Abstract: The general problem of estimating the a posteriori probabilities of the states and transitions of a Markov source observed through a discrete memoryless channel is considered. The decoding of linear block and convolutional codes to minimize symbol error probability is shown to be a special case of this problem. An optimal decoding algorithm is derived.

Error-Correction Coding for Digital Communications

Abstract: 1. Fundamental Concepts of Coding.- 2. Group Codes.- 3. Simple Nonalgebraic Decoding Techniques for Group Codes.- 4. Soft Decision Decoding of Block Codes.- 5. Algebraic Techniques for Multiple Error Correction.- 6. Convolutional Code Structure and Viterbi Decoding.- 7. Other Convolutional Decoding Techniques.- 8. System Applications.- Appendix A. Code Generators for BCH Codes.- Appendix B. Code Generators for Convolutional Codes.- B.1. Viterbi Decoding.- B.2. Table Look-up Decoding.- B.3. Threshold Decoding.- B.4. Sequential Decoding.- References.