This paper gives a new approach to decoding Hermite codes using the key equation, avoiding the use of majority voting. Our approach corrects up to (dmin − 1)/2 errors, and works up to some extent also beyond. We present an efficient implementation of our algorithm based on a Sugiyamatype iterative procedure for computing solutions of a key equation.

Turbo codes and low density parity check codes are two classes of most powerful error correcting codes. What makes these codes so powerful is the use of the so-called iterative decoding or turbo decoding. Roughly speaking, an iterative decoding process is an iterative learning process for a complex system where the objective is to provide a good suboptimal estimate of a desired signal. Iterativ...

This paper investigates the performance of a LowDensity Parity Check codes (LDPC)-coded system transmitted over A WGN channels using octal partial response Continuous Phase Modulation (CPM). The system provides an attractive option for spectral efficient communications systems. The CPM modulator can be decomposed into a ring continuous-phase encoder (CPE) followed by a memoryless modulator (MM)...

In this paper, we will describe the close connection between the now celebrated iterative turbo decoding algorithm of Berrou et al. and an algorithm that has been well known in the artificial intelligence community for a decade, but which is relatively unknown to information theorists: Pearl’s belief propagation algorithm. We shall see that if Pearl’s algorithm is applied to the “belief network...

In this paper, we define a stopping set of turbo codes with the iterative decoding in the binary erasure channel. Based on the stopping set analysis, we study the block and bit erasure probabilities of turbo codes and the performance degradation of the iterative decoding against the maximum-likelihood decoding. The error floor performance of turbo codes with the iterative decoding is dominated ...

The goal of the present paper is the derivation of a framework for the finite-length analysis of message-passing iterative decoding of low-density parity-check codes. To this end we introduce the concept of graph-cover decoding. Whereas in maximum-likelihood decoding all codewords in a code are competing to be the best explanation of the received vector, under graph-cover decoding all codewords...

The 5th generation (5G) mobile communication system requires high throughput for high quality user experience. In this paper, a novel Hybrid Automatic Repeat Request (HARQ) scheme based on packet coding is proposed. The idea is that a parity block is transmitted when code block error rate (CBER) of all turbo code blocks of transmission packet is less than or equal to the threshold of P0 and gre...