Low-Density Graph Codes for Coded Cooperation on Slow Fading Relay Channels

Abstract

We study Low-Density Parity-Check (LDPC) codes with iterative decoding on block-fading (BF) Relay Channels. We consider two users that employ coded cooperation, a variant of decode-andforward with a smaller outage probability than the latter. An outage probability analysis for discrete constellations shows that full diversity can be achieved only when the coding rate does not exceed a maximum value that depends on the level of cooperation. We derive a new code structure by extending the previously published full-diversity root-LDPC code, designed for the BF point-to-point channel, to exhibit a rate-compatibility property which is necessary for coded cooperation. We estimate the asymptotic performance through a new density evolution analysis and the word error rate performance is determined for finite length codes. We show that our code construction exhibits near-outage limit performance for all block lengths and for a range of coding rates up to 0.5, which is the highest possible coding rate for two cooperating users.

Design of diversity-achieving LDPC codes for H-ARQ with cross-packet channel coding

“…Besides for point-to-point communication, the concept of rootchecks was also applied for relay channels [6], [7]. We show that our proposed LDPC code performs close to the information theoretical limit and outperforms the previous approaches in [3], [4] whose structures do not guarantee full-diversity.…”

Universal LDPC codes for cooperative communications

“…The instantaneous SNR of each channel is denoted as (i, j = a; , j '"Yi, j , where /i, j is the average SNR of the channel. Without loss of generality, we assume: / 2, 3 = / 1, 3 ; / 1,2 = / 2,1 = / 1, 3 + 5dB, so that a comparison with [5] can be made. In the following, the set (,1,2, / 2,1, / 1, 3 , / 2, 3 ) will be denoted as f.…”

“…The full codeword has coding rate Re = K/N. The full codeword, designed in [5], C[N, Kh with block length N and dimension K, is defined by an (N -K) x N parity-check matrix H, which includes H 1: Note that four classes of bits are distinguished: Vo and V3 only participate in C1, while V1 and V2 participate in both C1 and C2. The parity-check matrix H2 defines code C2[NFD, Kh with block length NFD, dimension K and coding rate Re2 = 0.5.…”

“…The parity-check matrix H2 defines code C2[NFD, Kh with block length NFD, dimension K and coding rate Re2 = 0.5. For more information on C2, we refer to [2], [5]. Note that full-diversity remains an important property for Rice channels, even for increasing k-factor [10].…”

“…The solution is to use capacity achieving codes [3], for example LDPC codes. LDPC codes designed for block fading (BF) [1] relay channels are Rate Compatible RootCheck (RCRC)-LDPC codes [4], [5], exhibit ing the two necessary properties for coded cooperation: rate compatibility and full-diversity. For Gaussian relay channels, bilayer LDPC codes [11] have been proposed to implement the binning techniques of decode-and-forward.…”