The family of Low Density Parity Check (LDPC) codes is a strong candidate to be used as Forward Error Correction (FEC) in future communication systems due to its strong error correction capability. Most LDPC decoders use the Message Passing algorithm for decoding, which is an iterative algorithm that passes messages between its variable nodes and check nodes. It is not until recently that computation power has become strong enough to make Message Passing on LDPC codes feasible. Although locally simple, the LDPC codes are usually large, which increases the required computation power. Earlier work on LDPC codes has been concentrated on the binary Galois Field, GF(2), but it has been shown that codes from higher order fields have better error correction capability. However, the most efficient LDPC decoder, the Belief Propagation Decoder, has a squared complexity increase when moving to higher order Galois Fields. Transmission over a channel with M-PSK signalling is a common technique to increase spectral efficiency. The information is transmitted as the phase angle of the signal. The focus in this Master’s Thesis is on simplifying the Message Passing decoding when having inputs from M-PSK signals transmitted over an AWGN channel. Symbols from higher order Galois Fields were mapped to M-PSK signals, since M-PSK is very bandwidth efficient and the information can be found in the angle of the signal. Several simplifications of the Belief Propagation has been developed and tested. The most promising is the Table Vector Decoder, which is a Message Passing Decoder that uses a table lookup technique for check node operations and vector summation as variable node operations. The table lookup is used to approximate the check node operation in a Belief Propagation decoder. Vector summation is used as an equivalent operation to the variable node operation. Monte Carlo simulations have shown that the Table Vector Decoder can achieve a performance close to the Belief Propagation. The capability of the Table Vector Decoder depends on the number of reconstruction points and the placement of them. The main advantage of the Table Vector Decoder is that its complexity is unaffected by the Galois Field used. Instead, there will be a memory space requirement which depends on the desired number of reconstruction points.

<p>This licentiate thesis work investigates two medium access control (MAC) methods, when used in traffic safety applications over vehicular <em>ad hoc</em> networks (VANETs). The MAC methods are carrier sense multiple access (CSMA), as specified by the leading standard for VANETs IEEE 802.11p, and self-organizing time-division multiple access (STDMA) as used by the leading standard for transponders on ships. All vehicles in traffic safety applications periodically broadcast cooperative awareness messages (CAMs). The CAM based data traffic implies requirements on a predictable, fair and scalable medium access mechanism. The investigated performance measures are <em>channel access delay</em>, <em>number of consecutive packet drops</em> and the <em>distance between concurrently transmitting nodes</em>. Performance is evaluated by computer simulations of a highway scenario in which all vehicles broadcast CAMs with different update rates and packet lengths. The obtained results show that nodes in a CSMA system can experience <em>unbounded channel access delays</em> and further that there is a significant difference between the best case and worst case channel access delay that a node could experience. In addition, with CSMA there is a very high probability that several <em>concurrently transmitting nodes are located close to each other</em>. This occurs when nodes start their listening periods at the same time or when nodes choose the same backoff value, which results in nodes starting to transmit at the same time instant. The CSMA algorithm is therefore both <em>unpredictable</em> and <em>unfair</em> besides the fact that it <em>scales badly</em> for broadcasted CAMs. STDMA, on the other hand, will always grant channel access for all packets before a predetermined time, regardless of the number of competing nodes. Therefore, the STDMA algorithm is <em>predictable</em> and <em>fair</em>. STDMA, using parameter settings that have been adapted to the vehicular environment, is shown to outperform CSMA when considering the performance measure <em>distance between concurrently transmitting nodes</em>. In CSMA the distance between concurrent transmissions is random, whereas STDMA uses the side information from the CAMs to properly schedule concurrent transmissions in space. The price paid for the superior performance of STDMA is the required network synchronization through a global navigation satellite system, e.g., GPS. That aside since STDMA was shown to be scalable, predictable and fair; it is an excellent candidate for use in VANETs when complex communication requirements from traffic safety applications should be met.</p>