Abstract- This paper deals with a new class of convolutional codes called Turbo-codes, whose performances in terms of Bit Error Rate (BER) are close to the SHANNON limit. The Turbo-Code encoder is built using a parallel concatenation of two Recursive Systematic Convolutional codes

cannot be negative. Since this inequality stands at the basis of the data processing theorem (DPT), and the DPT in turn is at the heart of most, if not all, proofs of converse theorems in Shannon theory, it is observed that conceptually, the roots of fundamental limits of Information Theory can actually

cannot be negative. Since this inequality stands at the basis of the data processing theorem (DPT), and the DPT in turn is at the heart of most, if not all, proofs of converse theorems in Shannon theory, it is observed that conceptually, the roots of fundamental limits of Information Theory can actually

We develop improved algorithms to construct good low-density parity-check codes that approach the Shannon limit very closely. For rate 1/2, the best code found has a threshold within 0.0045 dB of the Shannon limit of the binary-input additive white Gaussian noise channel. Simulation results with a

Abstract—In this paper, we present a novel method to construct nonbinary irregular LDPC codes whose parity check matrix has only column weights of 2 and t, where t ≥ 3. The constructed codes can be encoded in linear time and in a parallel fashion. Also, they can achieve near-Shannon-limit

be achieved; indeed the performance is almost as close to the Shannon limit as that of Turbo codes.

]. The information capacity of a linear channel with additive white Gaussian noise (AWGN) is often called the Shannon limit, stressing the fact that it is the maximum error-free data rate achievable in such channel [1] and in any channels sub optimal to AWGN. The optical fiber channel character-ized by additive

(LDPCs), another ECC, also provide near Shannon limit error correction ability. However, LDPCs use a decoding scheme which is much more amenable to hardware implementation. This paper will rst present an overview of these coding schemes, then discuss the issues involved in building an LDPC decoder using

. The decoding of both codes can be tackled with a practical sum-product algorithm. We prove that these codes are "very good," in that sequences of codes exist which, when optimally decoded, achieve information rates up to the Shannon limit. This result holds not only for the binary-symmetric channel

with finite intersymbol interference, we prove that reliable communication can be achieved if and only if 0 log 2 opt, for some constant opt that depends on the channel. To determine this constant, we consider the finite-state machine which represents the output sequences of the channel filter when driven by binary inputs.We then define opt as the maximum output power achieved by a simple cycle in this graph, and show that no other cycle or asymptotically long sequence can achieve an output power greater than this.We provide examples where the binary input constraint leads to a suboptimality, and other cases where binary signaling is just as effective as real signaling at very low signal-to-noise ratios. Index Terms—Information rates, intersymbol interference (ISI), magnetic recording, modulation coding. I.