2018/01/01 by Mahesh Babu Vaddi, Vaddi, Mahesh Babu, B. Sundar Rajan +1
Computer Science · Engineering · #Advanced Wireless Communication Technologies #Coding theory and cryptography #Cooperative Communication and Network Coding #FOS: Computer and information sciences #Information Theory (cs.IT)
paper · pdf · doi:10.48550/arxiv.1801.00406
openalex publication_date 2018/01/01 · openalex created_date 2022/09/17 · openalex updated_date 2026/07/28
A single unicast index coding problem (SUICP) with symmetric neighboring and\nconsecutive side-information (SNCS) has K messages and K receivers, the\nkth receiver Rk wanting the kth message xk and having the\nside-information \Kk= xk-U,\…,xk-2,xk-1 \∪ xk+1,\nxk+2,\…,xk+D . The single unicast index coding problem with\nsymmetric neighboring and consecutive side-information, SUICP(SNCS), is\nmotivated by topological interference management problems in wireless\ncommunication networks. Maleki, Cadambe and Jafar obtained the symmetric\ncapacity of this SUICP(SNCS) and proposed optimal length codes by using\nVandermonde matrices. In our earlier work, we gave optimal length\n(U+1)-dimensional vector linear index codes for SUICP(SNCS) satisfying some\nconditions on K,D and U citeVaR1. In this paper, for SUICP(SNCS) with\narbitrary K,D and U, we construct optimal length\n\(U+1)/(gcd(K,D-U,U+1))-dimensional vector linear index codes. We\nprove that the constructed vector linear index code is of minimal dimension if\ngcd(K-D+U,U+1) is equal to gcd(K,D-U,U+1). The proposed\nconstruction gives optimal length scalar linear index codes for the SUICP(SNCS)\nif (U+1) divides both K and D-U. The proposed construction is independent\nof field size and works over every field. We give a low-complexity decoding for\nthe SUICP(SNCS). By using the proposed decoding method, every receiver is able\nto decode its wanted message symbol by simply adding some index code symbols\n(broadcast symbols).\n