The properties of linear codes over GF (q) that provide unequal error protection (UEP) of information digits are discussed. A design is proposed for optimal binary systematic linear UEP codes. Broad classes of iterative and concatenated UEP codes are constructed. Majority decoding algorithms for linear iterative UEP codes are described.

Linear unequal error protection codes

Algorithms to decode iterated codes when at least one of the "component codes" is majority decodable are given. The decoding algorithms allow the use of the decoders of the component codes and still make it possible to correct all error patterns guaranteed to be correctable by the minimum distance of the iterated code.

On decoding iterated codes

We present a new soft-decision majority decoding algorithm for Reed-Muller codes RM(r,m). First, the reliabilities of 2/sup m/ transmitted symbols are recalculated into the reliabilities of 2/sup m-r/ parity checks that represent each information bit. In turn, information bits are obtained by the weighted majority that gives more weight to more reliable parity checks. It is proven that for long low-rate codes RM(r,m), our soft-decision algorithm outperforms its conventional hard-decision counterpart by 10 log/sub 10/(/spl pi//2)/spl ap/2 dB at any given output error probability. For fixed code rate R and m/spl rarr//spl infin/, our algorithm increases almost 2/sup r/2/ times the correcting capability of soft-decision bounded distance decoding.

Soft-decision majority decoding of Reed-Muller codes

A new class of codes, called product generator codes, which are similar to Elias's iterated codes, are investigated. An important subclass of these codes is the generalized Reed-Muller codes. If the original codes that are iterated to produce a product code are L_1 and L_2 -step orthogonalizable, then the product code is ( L_1 + L_2 - 1 )-step orthogonalizable. Further if a \nu th-order product generator code is produced from these original L -step orthogonal izable codes, the new code is at most (\nu +1) step orthogonalizable.

Further results on product codes

A general solution is obtained for the probability density function of the low-pass output of a crosscorrelator with bandpass inputs. The input signals are sinusoidal with arbitrary amplitudes and phases, and the noise inputs are Gaussian and uncorrelated. An approximation to simplify the necessary calculations is developed and examined.

The probability density function for the output of an analog crosscorrelator with bandpass inputs (Corresp.)

This correspondence shows the formal equivalence between Massey's decoding scheme called threshold decoding involving L -step orthogonalizable codes and Reed's decoding scheme originally conceived for the Muller codes. Upon examining these two decoding algorithms it is shown that each can be described in terms of a decoding logic circuit. The formal equivalence of the algorithms is proved by showing the formal equivalence of their respective decoding circuits.

W. Gore

Papers

The equivalence of L-step orthogonalization and a Reed decoding procedure (Corresp.)