Finite-length rate-compatible LDPC codes: a novel puncturing scheme - [transactions letters]

In this paper, we study rate-compatible puncturing of finite-length low-density parity-check (LDPC) codes. We present a novel rate-compatible puncturing scheme that is easy to implement. Our scheme uses the idea that the degradation in performance is reduced by selecting a puncturing pattern wherein the punctured bits are far apart from each other in the Tanner graph of the code. Although the puncturing scheme presented is tailored to regular codes, it is also directly applicable to irregular parent ensembles. By simulations, the proposed rate-compatible puncturing scheme is shown to be superior to the existing puncturing methods for both regular and irregular LDPC codes over the binary erasure channel (BEC) and the additive white Gaussian noise (AWGN) Channel.     

Results on the Improved Decoding Algorithm for Low-Density Parity-Check Codes Over the Binary Erasure Channel

In this correspondence, we first investigate some analytical aspects of the recently proposed improved decoding algorithm for low-density parity-check (LDPC) codes over the binary erasure channel (BEC). We derive a necessary and sufficient condition for the improved decoding algorithm to successfully complete decoding when the decoder is initialized to guess a predetermined number of guesses after the standard message-passing terminates at a stopping set. Furthermore, we present improved bounds on the number of bits to be guessed for successful completion of the decoding process when a stopping set is encountered. Under suitable conditions, we derive a lower bound on the number of iterations to be performed for complete decoding of the stopping set. We then present a superior, novel improved decoding algorithm for LDPC codes over the binary erasure channel (BEC). The proposed algorithm combines the observation that a considerable fraction of unsatisfied check nodes in the neighborhood of a stopping set are of degree two, and the concept of guessing bits to perform simple and intuitive graph-theoretic manipulations on the Tanner graph. The proposed decoding algorithm has a complexity similar to previous improved decoding algorithms. Finally, we present simulation results of short-length codes over BEC that demonstrate the superiority of our algorithm over previous improved decoding algorithms for a wide range of bit error rates     

Rateless Codes With Unequal Error Protection Property

In this correspondence, a generalization of rateless codes is proposed. The proposed codes provide unequal error protection (UEP). The asymptotic properties of these codes under the iterative decoding are investigated. Moreover, upper and lower bounds on maximum-likelihood (ML) decoding error probabilities of finite-length LT and Raptor codes for both equal and unequal error protection schemes are derived. Further, our work is verified with simulations. Simulation results indicate that the proposed codes provide desirable UEP. We also note that the UEP property does not impose a considerable drawback on the overall performance of the codes. Moreover, we discuss that the proposed codes can provide unequal recovery time (URT). This means that given a target bit error rate, different parts of information bits can be decoded after receiving different amounts of encoded bits. This implies that the information bits can be recovered in a progressive manner. This URT property may be used for sequential data recovery in video/audio streaming