Evaluation of Gallager Codes for Short Block Length and High Rate Applications

Gallager Codes for High Rate Applications

Gallager codes with large block length and low rate (e.g., N ' 10, 000–40, 000, R ' 0.25–0.5) have been shown to have recordbreaking performance for low signal-to-noise applications. Gallager codes with high rates (R ' 0.8–0.94) are also excellent, outperforming comparable BCH and Reed-Solomon codes, even at short blocklength (N ' 2, 000–4, 000) (MacKay and Davey, 2000). This paper looks in mor...

A Class of High-rate, Low-complexity, Well- structured LDPC Codes from Combinatorial Designs and their Applications on ISI Channels

We present a systematic construction of a class of highrate, well-structured low density parity check (LDPC) codes based on combinatorial designs. We show that the proposed -design results in a class of -regular LDPC codes, which are systematic, quasicyclic, free of length-4 and length-6 cycles, linear-time encodable and decodable, and which have high code rates of . Analysis from the maximum l...

Gallager codes for CDMA applications .I. Generalizations, constructions, and performance bounds

We focus on applications of low-rate Gallager (low-density parity-check) codes in code-division multiple-access schemes. The codes that we present here achieve good performance with relatively short frame-lengths in additive white Gaussian noise channels and, perhaps more importantly, in fading channels. These codes can be decoded with low complexity by using iterative decoding procedures. We p...

Evaluation of Gallager Codes for Short Blo k Lengthand High Rate Appli

Exponential bounds on error probability with Feedback

Feedback is useful in memoryless channels for decreasing complexity and increasing reliability; the capacity of the memoryless channels, however, can not be increased by feedback. For fixed length block codes even the decay rate of error probability with block length does not increase with feedback for most channel models. Consequently for making the physical layer more reliable for higher laye...