We introduce a new family of unequal error protection (UEP) codes, based on low-density parity-check (LDPC) component codes and Plotkin-type constructions. The codes are decoded iteratively in multiple stages, and the order of decoding determines the level of error protection. The level of UEP among the code bits is also influenced by the choice of the LDPC component codes and by some new reliability features incorporated into the decoding process. The proposed scheme offers a very good tradeoff between code performance on one side and encoding/decoding and storage complexity on the other side. The novel approach to UEP also allows for finding simple approximations for the achievable degrees of UEP, which can be used to govern practical code design implementations

http://ecee.colorado.edu/~milenkov/TCOMM_04-0653_revised3.pdf

On unequal error protection LDPC codes based on plotkin-type constructions

On Unequal Error Protection LDPC codes based on plotkin-type constructions

In this paper we propose a graph-theoretic method based on linear congruence for constructing low-density parity check (LDPC) codes. In this method, we design a connection graph with three kinds of special paths to ensure that the Tanner graph of the parity check matrix mapped from the connection graph is without short cycles. The new construction method results in a class of (3, ρ)-regular quasi-cyclic LDPC codes with a girth of 12. Based on the structure of the parity check matrix, the lower bound on the minimum distance of the codes is found. The simulation studies of several proposed LDPC codes demonstrate powerful bit-error-rate performance with iterative decoding in additive white Gaussian noise channels.

Design of Quasi-Cyclic Low-Density Parity Check Codes with Large Girth

Wireless communication using multiple-input multiple-output (MIMO) systems improves throughput and enhances reliability for a given total transmit power In this paper, potential performance gains are investigated via a direct Galois field [GF(q)] low-density parity-check (LDPC) space-time coding and modulation scheme The field order q is chosen such that the number of bits per GF(q) LDPC symbol matches the number of bits per space-time symbol The result is an elegant coding and decoding scheme that leverages the powerful LDPC iterative decoding technique Results for 2, 3, and 4 transmitter systems with relatively short block lengths of around 2000 bits are provided, demonstrating frame-error- rate performances as close as 05 dB to the probability of outage upper bound

Direct Space-Time GF(q) LDPC Modulation

Multiple-input multiple-output (MIMO) wireless communication systems enhance reliability and improve throughput for a given total transmit power. In actual systems, the channel and noise parameters must be estimated to capture the MIMO gains. In this paper, we couple a direct, q-ary Galois field [GF(q)], low-density parity-check (LDPC) space-time coding and modulation scheme with a receiver that iterates between decoding the transmitted symbols, estimating the convolutive MIMO channel with pilots and symbol decisions, and removing inter-symbol interference. The result is a powerful system that outperforms linear space-time equalization and performs within one decibel of a system with perfect channel knowledge and no inter-symbol interference.

Iterative inter-symbol interference canceling receiver for direct space-time GF(q) LDPC modulation

It is well known that random-like low-density parity-check (LDPC) codes over the extension fields GF(2/sup m/) of GF(2), for m>1, tend to outperform their binary counterparts of comparable length and rate. At the same time, structured LDPC codes offer the advantage of reduced implementation and storage complexity, so that it is of interest to investigate mathematical design methods for codes on graphs over fields of large order. We propose a new class of combinatorially developed codes obtained by properly combining Reed-Solomon (RS) type parity-check matrices and sparse parity-check matrices based on permutation matrices. The proposed codes have large girth and minimum distance. In order to further reduce the decoding complexity of the proposed scheme, we introduce a new decoding algorithm based on matrix representations of the underlying field, which trades performance for complexity. The particular field representation described in this abstract is based on a power basis generated by a companion matrix of a primitive polynomial of the field GF(2/sup m/). It is observed that the choice of the primitive polynomial influences the cycle distribution of the code graph.

Structured LDPC codes over GF(2/sup m/) and companion matrix based decoding

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Structured LDPC codes over GF(2/sup m/) and companion matrix based decoding