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 ...

Proof. (of Theorem 2.1) The encoding function E : {0, 1} → {0, 1}, is chosen randomly, that is, for every messagem ∈ {01, }, the corresponding codeword, E(m) is chosen uniformly at random from {0, 1}. 1 The decoding function will be the maximum likelihood decoding, that is, choose the closest codeword to the received word. More formally, the decoding function D : {0, 1} → {0, 1} is defined as f...

This paper provides some universal information-theoretic bounds related to capacity-approaching ensembles of low-density parity-check (LDPC) codes. These bounds refer to the behavior of the degree distributions of such ensembles, and also to the graphical complexity and the fundamental system of cycles associated with the Tanner graphs of LDPC ensembles. The transmission of these ensembles is a...

This paper describes two freely available convolutional decoders written in the C language. One implements the Fano algorithm for sequentially decoding three rate l/2 K=32 codes while the other implcmcnts the Viterbi algorithm for maximum likelihood decoding of the rate l/2 K=7 NASA Standard code. Both support 8-W soft-decision decoding with arbitrary metric tables and perform according to theory.

The maximum-likelihood decoding of linear block codes by the Wagner rule decoding is discussed. In this approach, the Wagner rule decoding which has been primarily applied to single parity check codes is employed on acyclic Tanner graphs. Accordingly, a coset decoding equipped with the Wagner rule decoding is applied to the decoding of a code C having a Tanner graph with cycles. A subcode C1 of...

31 Abstract—This paper investigates on the low density parity-check (LDPC) decoding algorithms and the detection methods of the multiple-input multiple-output (MIMO) systems. For LDPC codes, min-sum and layered decoding algorithms are discussed, and for MIMO detection, the maximum likelihood (ML) decision based on the sphere decoding algorithm is mainly analyzed. Also, the performance of the co...

In this paper, the iterative Vertical-Bell-lab Layered Space-Time (V-BLAST) decoding algorithm of an Adaptive Modulation and Coding (AMC) system is proposed, and the corresponding MIMO scheme is analyzed. The proposed decoding algorithm adopts iteratively extrinsic information from a Maximum A Posteriori (MAP) decoder as an a priori probability in the two decoding procedures of the V-BLAST sche...

In this paper, we derive the maximum likelihood (ML) performance for low-density parity check (LDPC) codes, considering BPSK and QPSK transmission over a Gaussian channel. We compare the theoretical ML performance with the performance of the iterative decoding algorithm. It turns out that the performance of the iterative decoding algorithm is close to the ML performance when the girth of the co...

In this paper, we propose an iterative soft decision decoding scheme for Reed Solomon codes with near maximum likelihood performance. The advantage of this decoding algorithm over previously proposed algorithms is its fast convergence in terms of the number of iterations required. This is achieved by combining two powerful soft decision decoding techniques which were previously regarded in the ...