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We present a novel iterative decoding algorithm for Reed-Muller (RM) codes, which takes advantage of a graph representation of the code. Vertices of the considered graph correspond to codewords, with two vertices being connected by an edge if and only if the Hamming distance between the corresponding codewords equals the minimum distance of the code. The algorithm uses a greedy local search to find a node optimizing a metric, e.g. the correlation between the received vector and the corresponding codeword. In addition, the cyclic redundancy check can be used to terminate the search as soon as a valid codeword is found, leading to an improvement in the average computational complexity of the algorithm. Simulation results for both binary symmetric channel and additive white Gaussian noise channel show that the presented decoder approaches the performance of maximum likelihood decoding for RM codes of length less than 1024 and for the second-order RM codes of length less than 4096. Moreover, it is demonstrated that the considered decoding approach outperforms state-of-the-art decoding algorithms of RM codes with similar computational complexity for a wide range of block lengths and rates. [ABSTRACT FROM AUTHOR]

A method to design efficient puncture-constrained interleavers for turbo codes (TCs) is introduced. Resulting TCs profit from a joint optimization of puncturing pattern and interleaver to achieve an improved error rate performance. First, the puncturing pattern is selected based on the constituent code Hamming distance spectrum and on the TC extrinsic information exchange under uniform interleaving. Then, the interleaver function is defined via a layered design process taking account of several design criteria, such as minimum span, correlation girth, and puncturing constraints. We show that applying interleaving with a periodic cross connection pattern that can be assimilated to a protograph improves error-correction performance when compared to the state-of-the-art TCs. An application example is elaborated and compared with the long-term evolution standard: a significant gain in performance can be observed. An additional benefit of the proposed technique resides in the important reduction of the search space for the different interleaver parameters. [ABSTRACT FROM PUBLISHER]

The weighted bit-reliability-based (wBRB) algorithm for nonbinary LDPC codes suffers certain loss of symbol-reliability. Thus, this paper enhances its soft-decision version by passing multiple symbol-reliability instead of bit-reliability. Furthermore, it demonstrates that plurality robustly indicates symbol-reliability of extrinsic information-sums. Thus, this paper enhances the hard-decision version by introducing symbol-reliability from plurality. Analysis results show that these two enhanced decoding algorithms significantly outperform the wBRB algorithm with reasonable overhead. [ABSTRACT FROM PUBLISHER]

This paper presents bit-reliability based majority-logic decoding (MLgD) algorithms for non-binary LDPC codes. The proposed algorithms pass only one Galois field element and its reliability along each edge of the Tanner graph of a non-binary LDPC code. Since their reliability updates are in terms of bits rather than symbols, they are more efficient than traditional MLgD based decoding algorithms. By weighting the soft reliability of the extrinsic information-sums based on their hard reliability, the proposed algorithms can achieve good error performance for non-binary LDPC codes with various column weights. Moreover, their computational complexity and memory consumption are remarkably reduced compared with existing MLgD based decoding algorithms. As a result, they provide effective tradeoffs between error performance and complexity for decoding of non-binary LDPC codes. [ABSTRACT FROM AUTHOR]

This paper proposes branch-and-prune algorithms for searching prefix-free joint source-channel codebooks with maximal free distance for given codeword lengths. For that purpose, it introduces improved techniques to bound the free distance of variable-length codes. [ABSTRACT FROM PUBLISHER]

Previous interleavers designed for Serially Concatenated Codes (SCCs) have achieved a limited Minimum Hamming Distance (MHD) between the legitimate permutations of the encoded bit sequence. Hence, we propose a novel Evolutionary Algorithm (EA) capable of designing improved interleavers for SCCs, without artificially limiting the achievable MHD. As a result, increased MHDs and therefore reduced error floors are achieved, even if only a modest EA complexity can be afforded. [ABSTRACT FROM PUBLISHER]

This paper considers the optimization of a class of joint source-channel codes described by finite-state encoders (FSEs) generating variable-length codes. It focuses on FSEs associated to joint source-channel integer arithmetic codes, which are uniquely decodable codes by design. An efficient method for computing the free distance of such codes using Dijkstra's algorithm is proposed. To facilitate the search for codes with good distance properties, FSEs are organized within a tree structure, which allows the use of efficient branch-and-prune techniques avoiding a search of the whole tree. [ABSTRACT FROM PUBLISHER]