The main objective of our research is to design practical low-density parity-check (LDPC) codes which provide a wide range of code rates in a rate-compatible fashion. To this end, we first propose a rate-compatible puncturing algorithm for LDPC codes at short block lengths (up to several thousand symbols). The proposed algorithm is based on the claim that a punctured LDPC code with a smaller level of recoverability has better performance. The proposed algorithm is verified by comparing performance of intentionally punctured LDPC codes (using the proposed algorithm) with randomly punctured LDPC codes. The intentionally punctured LDPC codes show better bit error rate (BER) performances at practically short block lengths. Even though the proposed puncturing algorithm shows excellent performance, several problems are still remained for our research objective. First, how to design an LDPC code of which structure is well suited for the puncturing algorithm. Second, how to provide a wide range of rates since there is a puncturing limitation with the proposed puncturing algorithm. To attack these problems, we propose a new class of LDPC codes, called efficiently-encodable rate-compatible (E2RC) codes, in which the proposed puncturing algorithm concept is imbedded. The E2RC codes have several strong points. First, the codes can be efficiently encoded. We present low-complexity encoder implementation with shift-register circuits. In addition, we show that a simple erasure decoder can also be used for the linear-time encoding of these codes. Thus, we can share a message-passing decoder for both encoding and decoding in transceiver systems that require an encoder/decoder pair. Second, we show that the non-systematic parts of the parity-check matrix are cycle-free, which ensures good code characteristics. Finally, the E2RC codes having a systematic rate-compatible puncturing structure show better puncturing performance than any other LDPC codes in all ranges of code rates. The throughput performance of incremental redundancy (IR) hybrid automatic repeat request (HARQ) systems highly depends on the performance of high-rate codes. Since the E2RC codes show excellent puncturing performance in all ranges of code rates, especially at high puncturing rate, we verify that E2RC codes outperform in throughput than other LDPC codes in IR-HARQ systems.

The objective of this thesis is to improve the performance of real-time communication overa wireless channel, by means of specifically tailored channel coding. The deadlinedependent coding (DDC) communication protocol presented here lets the timeliness and thereliability of the delivered information constitute quality of service (QoS) parametersrequested by the application. The values of these QoS parameters are transformed intoactions taken by the link layer protocol in terms of adaptive coding strategies.Incremental redundancy hybrid automatic repeat request (IR-HARQ) schemes usingrate compatible punctured codes are appealing since no repetition of previously transmittedbits is made. Typically, IR-HARQ schemes treat the packet lengths as fixed and maximizethe throughput by optimizing the puncturing pattern, i.e. the order in which the coded bitsare transmitted. In contrast, we define an IR strategy as the maximum number of allowedtransmissions and the number of code bits to include in each transmission. An approach isthen suggested to find the optimal IR strategy that maximizes the average code rate, i.e., theoptimal partitioning of n-kparity bits over at most M transmissions, assuming a givenpuncturing pattern. Concatenated coding used in IR-HARQ schemes provides a new arrayof possibilities for adaptability in terms of decoding complexity and communication timeversus reliability. Hence, critical reliability and timing constraints can be readily evaluatedas a function of available system resources. This in turn enables quantifiable QoS and thusnegotiable QoS. Multiple concatenated single parity check codes are chosen as examplecodes due to their very low decoding complexity. Specific puncturing patterns for thesecomponent codes are obtained using union bounds based on uniform interleavers. Thepuncturing pattern that has the best performance in terms of frame error rate (FER) at a lowsignal-to-noise ratio (SNR) is chosen. Further, using extrinsic information transfer (EXIT)analysis, rate compatible puncturing ratios for the constituent component code are found.The puncturing ratios are chosen to minimize the SNR required for convergence.The applications targeted in this thesis are not necessarily replacement of cables inexisting wired systems. Instead the motivation lies in the new services that wireless real-time communication enables. Hence, communication within and between cooperatingembedded systems is typically the focus. The resulting IR-HARQ-DDC protocol presentedhere is an efficient and fault tolerant link layer protocol foundation using adaptiveconcatenated coding intended specifically for wireless real-time communications. / Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie, 2198, Technical report. D, 29,