Design of joint source-channel coding systems based on double P-LDPC codes

Abstract

In a traditional joint source-channel coding system based on double protograph-based LDPC (DP-LDPC) codes, two P-LDPC codes are employed as the source code and the channel code, respectively. They are connected by a source-check-channel-variable (SCCV) linking matrix, which consists of an identity matrix and a zero matrix. This linking matrix connects check nodes (CNs) in the source P-LDPC code and variable nodes (VNs) in the channel P-LDPC code. A joint source-channel decoder that facilitates message exchange between the source decoder and the channel decoder is used to decode the source. Based on this traditional structure, this thesis proposes several novel joint source-channel coding systems, aiming at improving error performance further. Firstly, a novel class of DP-LDPC codes is proposed for the joint source-channel coding, where the identity matrix in the SCCV linking matrix of traditional DP-LDPC codes is replaced with a lower or upper triangular matrix with “1”s on its diagonal. By doing this, the flexibility of code design is increased and the linear source compression is preserved. Theoretical and simu­lation results have shown the superior performance of the proposed DP-LDPC codes compared to the traditional ones. Secondly, we propose a novel joint source-channel coding scheme based on spatially cou­pled DP-LDPC (SC-DP-LDPC) codes. It has been proved that a concatenated spatially coupled protograph-based LDPC (SC-P-LDPC) code can have better error performance than a tradi­tional DP-LDPC block code. Motivated by this point, SC-DP-LDPC codes are proposed, where the source spatially coupled P-LDPC (SC-P-LDPC) code and the channel SC-P-LDPC code are linked by spatially coupled SCCV (SC-SCCV) connections. By doing this, source SC-P-LDPC and channel SC-P-LDPC are not in a simple concatenated relationship. Like decoding the con­catenated SC-P-LDPC code, we use a sliding window joint belief propagation (BP) decoding algorithm to decode the SC-DP-LDPC code. Theoretical and simulation results show that the proposed codes are superior to the concatenated SC-LDPC codes and state-of-the-art DP-LDPC block codes. Thirdly, we propose two new types of joint source-channel coding systems for both low-entropy and high-entropy sources. Studies done by others have shown that for the traditional DP-LDPC codes, the source threshold can be improved by adding connections between VNs in source P-LDPC code and CNs in channel P-LDPC code, which is represented by a source-variable-channel-check (SVCC) linking (base) matrix. According to this finding and our first proposal, we propose a novel joint source-channel block code (JSC-BC) based on double P­-LDPC block codes. Two P-LDPC block codes are connected not only by a source-variable­-channel-check (SVCC) linking (base) matrix but also by a source-check-channel-variable (SCCV) linking (base) matrix, which consists of a zero matrix and a lower or upper triangular (base) ma­trix with “1”s on its diagonal. Also, we modify the traditional joint protograph-based extrinsic information transfer (JP-EXIT) algorithm to calculate the source threshold of a JSC-BC. The JP-EXIT algorithm uses the whole joint protomatrix to calculate the source threshold of a code. The new technique is called the untransmitted protograph-based EXIT (UP-EXIT) algorithm. Compared to the JP-EXIT algorithm, the proposed UP-EXIT algorithm is more efficient be­cause a smaller protograph consisting of only the untransmitted VNs (i.e., the source VNs and the punctured channel VNs) and their connected check nodes need to be considered. We first search for the candidate codes with the proposed code structure and high source thresholds by using the UP-EXIT algorithm. Then we select those also with low channel thresholds among the candidate codes by using the JP-EXIT algorithm. Moreover, we construct new JSC-BCs whose decoding complexities are controlled by limiting their maximum row weights. Theoret­ical and simulation results show that the codes newly constructed outperform state-of-the-art DP-LDPC block codes. Next, we spatially couple the joint source-channel block code and ob­tain a spatially coupled joint source-channel code (SC-JSCC) for further error performance im­provement. Theoretical analyses and simulation results show that even with a smaller window size and lower decoding complexity, the SC-JSCC with the spatially coupled structure for each sub-block (source protomatrix, channel protomatrix, SCCV linking matrix, and SVCC linking matrix) can have better error performance than existing spatially-coupled DP-LDPC codes.