Design of low-density parity-check codes in relay channels

Recent breakthroughs in forward error correction, in the form of low-density parity-check (LDPC) and turbo codes, have seen near Shannon limit performances especially for pointto- point channels. The construction of capacity-achieving codes in relay channels, for LDPC codes in particular, is currently the subject of intense interest in the research and development community. This thesis adds to this field, developing methods and supporting theory in designing capacity-achieving LDPC codes for decode-and-forward (DF) schemes in relay channels. In the first part of the thesis, new theoretical results toward optimizing the achievable rate of DF scheme in half-duplex relay channels under simplified and pragmatic conditions (equal power or equal time allocation) are developed. We derive the closed-form solutions for the optimum parameters (time or power) that maximize the achievable rates of the DF scheme in the half-duplex relay channel. We also derive the closed-form expression for the DF achievable rates under these simplified and pragmatic conditions. The second part of the thesis is dedicated to study the problem of designing several classes of capacity-achieving LDPC codes in relay channels. First, a new ensemble of LDPC codes, termed multi-edge-type bilayer-expurgated LDPC (MET-BE-LDPC) codes, is introduced to closely approach the theoretical limit of the DF scheme in the relay channel. We propose two design strategies for optimizing MET-BE-LDPC codes; the bilayer approach and the bilayer approach with intermediate rates. Second, we address the issue of constructing capacity-achieving distributed LDPC codes in the multiple-access and two-way relay channels, with broadcast transmissions and time-division multiple accesses. We propose a new methodology to asymptotically optimize the code’s degree distribution when different segments within the distributed codeword have been transmitted through separate channels and experienced distinct signal-to-noise ratio in the relay system. Third, we investigate the use of LDPC codes under the soft-decode-and forward (SDF) scheme in the half-duplex relay channel. We introduce the concept of a K-layer doping matrix that enables one to design the rate-compatible (RC) LDPC code with a lower triangular parity-check matrix, subsequently allowing the additional parity bits to be linearly and systematically encoded at the relay. We then present the soft-decoding and soft-re-encoding algorithms for the designed RC-LDPC code so that the relay can forward soft messages to the destination when the relay fails to decode the source’s messages. Special attention is given to the detection problem of the SDF scheme. We propose a novel method, which we refer to as soft fading, to compute the log-likelihood ratio of the received signal at the destination for the SDF scheme

Selective Video Coding based on Bezier Curves

In this paper the problem of reconstruction of video frames is addressed, when there are missing pixels in each video frame or is corrupted with noise and also the locations of corrupted pixels are not known. The modified data can be corrected using Forward Error Correcting Codes. Forward Error correcting codes detect and correct errors with the help of complex decoders. This work proposes a new approach called Selective encoding for reconstruction of Video Frames from Error. This algorithm combines the Bezier curves over Galois Field GF (p^m) and the Low Density Parity Check Codes for performing encoding and decoding. The proposed decoder is capable of detecting and correcting errors in each video frame, where only selected pixel values are encoded and decoded. This reduces the decoding time significantly. Further, when binary representation of the Galois Field is used, the speed of the decoder is enhanced as there is no carry generation and carry propagation when any modular arithmetic operation is carried out. Further time complexity is improvised by using parallel processing. The coding of the algorithm is carried out using MATLAB

Design of low-density parity-check codes in relay channels

Recent breakthroughs in forward error correction, in the form of low-density parity-check (LDPC) and turbo codes, have seen near Shannon limit performances especially for pointto-point channels. The construction of capacity-achieving codes in relay channels, for LDPC codes in particular, is currently the subject of intense interest in the researchand development community. This thesis adds to this field, developing methods and supporting theory in designing capacity-achieving LDPC codes for decode-and-forward (DF) schemes in relay channels.In the first part of the thesis, new theoretical results toward optimizing the achievable rate of DF scheme in half-duplex relay channels under simplified and pragmatic conditions (equal power or equal time allocation) are developed. We derive the closed-form solutions for the optimum parameters (time or power) that maximize the achievable rates of theDF scheme in the half-duplex relay channel. We also derive the closed-form expressionfor the DF achievable rates under these simplified and pragmatic conditions.The second part of the thesis is dedicated to study the problem of designing several classesof capacity-achieving LDPC codes in relay channels. First, a new ensemble of LDPC codes,termed multi-edge-type bilayer-expurgated LDPC (MET-BE-LDPC) codes, is introducedto closely approach the theoretical limit of the DF scheme in the relay channel. We proposetwo design strategies for optimizing MET-BE-LDPC codes; the bilayer approach andthe bilayer approach with intermediate rates. Second, we address the issue of constructingcapacity-achieving distributed LDPC codes in the multiple-access and two-way relay channels,with broadcast transmissions and time-division multiple accesses. We propose a new methodology to asymptotically optimize the code’s degree distribution when different segmentswithin the distributed codeword have been transmitted through separate channelsand experienced distinct signal-to-noise ratio in the relay system. Third, we investigatethe use of LDPC codes under the soft-decode-and forward (SDF) scheme in the half-duplexrelay channel. We introduce the concept of a K-layer doping matrix that enables one todesign the rate-compatible (RC) LDPC code with a lower triangular parity-check matrix,subsequently allowing the additional parity bits to be linearly and systematically encodedat the relay. We then present the soft-decoding and soft-re-encoding algorithms for thedesigned RC-LDPC code so that the relay can forward soft messages to the destinationwhen the relay fails to decode the source’s messages. Special attention is given to thedetection problem of the SDF scheme. We propose a novel method, which we refer to assoft fading, to compute the log-likelihood ratio of the received signal at the destinationfor the SDF scheme