Superposition Coding Aided Bi-directional Relay Transmission Employing Iteratively Decoded Self-Concatenated Convolutional Codes

In this paper, we consider coding schemes designed for two nodes communicating with each other with the aid of a relay node, which receives information from the two nodes in the first time slot. At the relay node we combine a powerful Superposition Coding (SPC) scheme with Iteratively Decoded Self-Concatenated Convolutional Codes (SECCC-ID), which exchange mutual information between each other. It is assumed that decoding errors may be encountered at the relay node. The relay node then broadcasts this information in the second time slot after re-encoding it, again, using a SECCC encoder. At the destination, an amalgamated SPC-SECCC block then detects and decodes the signal either with or without the aid of a priori information. Our simulation results demonstrate that the proposed scheme is capable of reliably operating at a low BER for transmission over both AWGN and uncorrelated Rayleigh fading channels. We compare the proposed scheme’s performance to a direct transmission link between the two sources having the same throughput. Additionally, the SPC-SECCC system achieves a low BER even for realistic error-infested relaying

Low-Floor Tanner Codes via Hamming-Node or RSCC-Node Doping

We study the design of structured Tanner codes with low error-rate floors on the AWGN channel. The design technique involves the “doping” of standard LDPC (proto-)graphs, by which we mean Hamming or recursive systematic convolutional (RSC) code constraints are used together with single-parity-check (SPC) constraints to construct a code’s protograph. We show that the doping of a “good” graph with Hamming or RSC codes is a pragmatic approach that frequently results in a code with a good threshold and very low error-rate floor. We focus on low-rate Tanner codes, in part because the design of low-rate, low-floor LDPC codes is particularly difficult. Lastly, we perform a simple complexity analysis of our Tanner codes and examine the performance of lower-complexity, suboptimal Hamming-node decoders

Distributed Turbo-Like Codes for Multi-User Cooperative Relay Networks

In this paper, a distributed turbo-like coding scheme for wireless networks with relays is proposed. We consider a scenario where multiple sources communicate with a single destination with the help of a relay. The proposed scheme can be regarded as of the decode-and-forward type. The relay decodes the information from the sources and it properly combines and re-encodes them to generate some extra redundancy, which is transmitted to the destination. The amount of redundancy generated by the relay can simply be adjusted according to requirements in terms of performance, throughput and/or power. At the destination, decoding of the information of all sources is performed jointly exploiting the redundancy provided by the relay in an iterative fashion. The overall communication network can be viewed as a serially concatenated code. The proposed distributed scheme achieves significant performance gains with respect to the non-cooperation system, even for a very large number of users. Furthermore, it presents a high flexibility in terms of code rate, block length and number of users.Comment: Submitted to ICC 201

Mathematical Programming Decoding of Binary Linear Codes: Theory and Algorithms

Mathematical programming is a branch of applied mathematics and has recently been used to derive new decoding approaches, challenging established but often heuristic algorithms based on iterative message passing. Concepts from mathematical programming used in the context of decoding include linear, integer, and nonlinear programming, network flows, notions of duality as well as matroid and polyhedral theory. This survey article reviews and categorizes decoding methods based on mathematical programming approaches for binary linear codes over binary-input memoryless symmetric channels.Comment: 17 pages, submitted to the IEEE Transactions on Information Theory. Published July 201

Successive Cancellation Decoding of Single Parity-Check Product Codes

We introduce successive cancellation (SC) decoding of product codes (PCs) with single parity-check (SPC) component codes. Recursive formulas are derived, which resemble the SC decoding algorithm of polar codes. We analyze the error probability of SPC-PCs over the binary erasure channel under SC decoding. A bridge with the analysis of PCs introduced by Elias in 1954 is also established. Furthermore, bounds on the block error probability under SC decoding are provided, and compared to the bounds under the original decoding algorithm proposed by Elias. It is shown that SC decoding of SPC-PCs achieves a lower block error probability than Elias' decoding

Coding for Parallel Channels: Gallager Bounds for Binary Linear Codes with Applications to Repeat-Accumulate Codes and Variations

This paper is focused on the performance analysis of binary linear block codes (or ensembles) whose transmission takes place over independent and memoryless parallel channels. New upper bounds on the maximum-likelihood (ML) decoding error probability are derived. These bounds are applied to various ensembles of turbo-like codes, focusing especially on repeat-accumulate codes and their recent variations which possess low encoding and decoding complexity and exhibit remarkable performance under iterative decoding. The framework of the second version of the Duman and Salehi (DS2) bounds is generalized to the case of parallel channels, along with the derivation of their optimized tilting measures. The connection between the generalized DS2 and the 1961 Gallager bounds, addressed by Divsalar and by Sason and Shamai for a single channel, is explored in the case of an arbitrary number of independent parallel channels. The generalization of the DS2 bound for parallel channels enables to re-derive specific bounds which were originally derived by Liu et al. as special cases of the Gallager bound. In the asymptotic case where we let the block length tend to infinity, the new bounds are used to obtain improved inner bounds on the attainable channel regions under ML decoding. The tightness of the new bounds for independent parallel channels is exemplified for structured ensembles of turbo-like codes. The improved bounds with their optimized tilting measures show, irrespectively of the block length of the codes, an improvement over the union bound and other previously reported bounds for independent parallel channels; this improvement is especially pronounced for moderate to large block lengths.Comment: Submitted to IEEE Trans. on Information Theory, June 2006 (57 pages, 9 figures