Distributed Polar Coded Single Carrier-FDMA Based on Multilevel Construction Over Multipath Channels

RS Codes and Optimized Distributed RS-Coded Relay Cooperative Communications: Code Constructions and Performance Analysis

“…Example 1. Let α is a primitive element in GF 2 4 ÀÁ constructed based on the primitive polynomial 1 þ x þ x 4 shown in Table 1. Consider the double-errorcorrecting RS codes with the symbols from GF 2 4 ÀÁ .…”

“…Let α is a primitive element in GF 2 4 ÀÁ constructed based on the primitive polynomial 1 þ x þ x 4 shown in Table 1. Consider the double-errorcorrecting RS codes with the symbols from GF 2 4 ÀÁ . The generator polynomial gx ðÞof this code has α, α 2 , α 3 , α 4 as all its roots.…”

“…The code is (15,11) RS code over the GF 2 4 ÀÁ that can correct two errors. And, the minimum distance of this RS code is 5.…”

“…Example 2. Consider the triple-error-correcting RS code of length n ¼ 15 over GF 2 4 ÀÁ , α be a primitive element of GF 2 4 ÀÁ such that…”

“…Therefore, coded cooperative diversity with the aid of the relay was proposed to provide uplink diversity via single antenna sharing. Factually, various distributed linear block codes have been employed in the coded cooperation such as the distributed turbo codes (DTC) [2], distributed low-density parity-check codes (D-LDPC) [3], and polar codes [4]. Nevertheless, for the non-binary codes with short information sizes in coded cooperation, the literature has not been thoroughly investigated.…”