Case 2: Odd Parit) Rule Subcase 2a ( m and n are even) : Equation (1) is replaced by m ai,m+ = 1 + ai,j [modulo 21, i = 1, 2,. . , n.Subcase 2b (m and n are odd): The derivation follows that of subcase 2a except that the value of an+ l , m + equals one plus that value of subcase 2a.Subcase 2c (m and n are different in kind): Calculation of a,+ l,m+ yields two answers differing by one, depending on the bits used in the calculation. The calculation using an even number of terms must be increased by one so that decoding may be performed independently of encoding (row or column).This proof can be extended to an rdimensional parity check matrix, but such matrices are not used in practice.The above theorem leads to the following corollary.
COROLLARYParity bit a,, ,m+ detects an odd number of errors in the information portion of the block (including bit a,, ,m+ 1) independent of errors in the other parity bits. This is a direct result of (3) and (10).Abstract-Combined power outputs are obtained from highefficiency avalanche-diode oscillators connected in series as a multiple-stacked unit. Increased circuit impedances for stacked diodes are measured. The results demonstrate the locking capability of such diodes and the prospect o f attaining power levels in the kilowatt range.
A self-aligned-gate GaInAs metal-insulator-semiconductor FET (MISFET) fabrication process that minimizes gate overlap capacitance and offers the potential of achieving submicrometer gate lengths is described. GaInAs MISFETs (1-gm gate length) fabricated with this process have given 0.49-W/mm gate width and corresponding poweradded efficiencies of 48 and 39 percent at 4 and 8 GHz, respectively, at a drain voltage of 5.5. V. A small-signal gain of 3.2 dB was obtained at 15 GHz. The estimated carrier velocity was 1.7 x lo7 cm/s. More recent devices have carrier velocities of 2.5 x 10' cm/s and are expected to have improved microwave performance.
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